Quizbank/calcPhyEMqAll/c05

calcPhyEMqAll/c05 ID153478379917

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Exams:  Template:Nowrap beginA0  A1  A2  Template:Nowrap end Template:Nowrap beginB0  B1  B2  Template:Nowrap end Template:Nowrap beginC0  C1  C2  Template:Nowrap end Template:Nowrap beginD0  D1  D2  Template:Nowrap end Template:Nowrap beginE0  E1  E2  Template:Nowrap end Template:Nowrap beginF0  F1  F2  Template:Nowrap end Template:Nowrap beginG0  G1  G2  Template:Nowrap end Template:Nowrap beginH0  H1  H2  Template:Nowrap end Template:Nowrap beginI0  I1  I2  Template:Nowrap end Template:Nowrap beginJ0  J1  J2  Template:Nowrap end Template:Nowrap beginK0  K1  K2  Template:Nowrap end Template:Nowrap beginL0  L1  L2  Template:Nowrap end Template:Nowrap beginM0  M1  M2  Template:Nowrap end Template:Nowrap beginN0  N1  N2  Template:Nowrap end Template:Nowrap beginO0  O1  O2  Template:Nowrap end Template:Nowrap beginP0  P1  P2  Template:Nowrap end Template:Nowrap beginQ0  Q1  Q2  Template:Nowrap end Template:Nowrap beginR0  R1  R2  Template:Nowrap end Template:Nowrap beginS0  S1  S2  Template:Nowrap end Template:Nowrap beginT0  T1  T2  Template:Nowrap end Template:Nowrap beginU0  U1  U2  Template:Nowrap end Template:Nowrap beginV0  V1  V2  Template:Nowrap end Template:Nowrap beginW0  W1  W2  Template:Nowrap end Template:Nowrap beginX0  X1  X2  Template:Nowrap end Template:Nowrap beginY0  Y1  Y2  Template:Nowrap end Template:Nowrap beginZ0  Z1  Z2  Template:Nowrap end

Answers:   Template:Nowrap beginA0  A1  A2  Template:Nowrap end Template:Nowrap beginB0  B1  B2  Template:Nowrap end Template:Nowrap beginC0  C1  C2  Template:Nowrap end Template:Nowrap beginD0  D1  D2  Template:Nowrap end Template:Nowrap beginE0  E1  E2  Template:Nowrap end Template:Nowrap beginF0  F1  F2  Template:Nowrap end Template:Nowrap beginG0  G1  G2  Template:Nowrap end Template:Nowrap beginH0  H1  H2  Template:Nowrap end Template:Nowrap beginI0  I1  I2  Template:Nowrap end Template:Nowrap beginJ0  J1  J2  Template:Nowrap end Template:Nowrap beginK0  K1  K2  Template:Nowrap end Template:Nowrap beginL0  L1  L2  Template:Nowrap end Template:Nowrap beginM0  M1  M2  Template:Nowrap end Template:Nowrap beginN0  N1  N2  Template:Nowrap end Template:Nowrap beginO0  O1  O2  Template:Nowrap end Template:Nowrap beginP0  P1  P2  Template:Nowrap end Template:Nowrap beginQ0  Q1  Q2  Template:Nowrap end Template:Nowrap beginR0  R1  R2  Template:Nowrap end Template:Nowrap beginS0  S1  S2  Template:Nowrap end Template:Nowrap beginT0  T1  T2  Template:Nowrap end Template:Nowrap beginU0  U1  U2  Template:Nowrap end Template:Nowrap beginV0  V1  V2  Template:Nowrap end Template:Nowrap beginW0  W1  W2  Template:Nowrap end Template:Nowrap beginX0  X1  X2  Template:Nowrap end Template:Nowrap beginY0  Y1  Y2  Template:Nowrap end Template:Nowrap beginZ0  Z1  Z2  Template:Nowrap end

78 Tests = 3 versions x 26 variations: Each of the 26 variations (A, B, ...) represents a different random selection of questions taken from the study guide.The 3 versions (0,1,..) all have the same questions but in different order and with different numerical inputs. Unless all students take version "0" it is best to reserve it for the instructor because the questions are grouped according to the order in which they appear on the study guide.

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c05 A0

1)

Three small charged objects are placed as shown, where $b=2a$, and $a=2\times 10^{-7}\text{m}$. What is the magnitude of the net force on $q_2$ if $q_1=1e$, $q_2=-7e$, and $q_3=2e$?

a) 3.391E-14 N

b) 3.731E-14 N

c) 4.104E-14 N

d) 4.514E-14 N

e) 4.965E-14 N

2)

Three small charged objects are placed as shown, where $b=2a$, and $a=2\times 10^{-7}\text{m}$.what angle does the force on $q_2$ make above the $-x$ axis if $q_1=2e$, $q_2=-9e$, and $q_3=4e$?

a) 5.243E+01 degrees

b) 5.767E+01 degrees

c) 6.343E+01 degrees

d) 6.978E+01 degrees

e) 7.676E+01 degrees

3)

 $E_z(x=0,z)=\underset{-a}{\overset{b}{\int }}f(x,z)dx$
is an integral that calculates the z-component of the electric field at point P situated above the x-axis where a charged rod of length (a+b) is located. The distance between point P and the x-axis is z=1.4 m. Evaluate $f(x,y)$ at x=1.1 m if a=0.69 m, b=2.2 m. The total charge on the rod is 6 nC.

a) 3.161E+00 V/m²

b) 3.477E+00 V/m²

c) 3.825E+00 V/m²

d) 4.208E+00 V/m²

e) 4.628E+00 V/m²

4)

A ring is uniformly charged with a net charge of 9 nC. The radius of the ring is R=1.9 m, with its center at the origin and oriented normal to the z axis as shown. what is the magnitude of the electric field at a distance z=1.4 m (on axis) away from the loop's center?

a) 7.119E+09 N/C²

b) 7.831E+09 N/C²

c) 8.614E+09 N/C²

d) 9.476E+09 N/C²

e) 1.042E+10 N/C²

5)  $E(z)=\underset{0}{\overset{R}{\int }}f(r^{\prime },z)d{r}^{\prime }$
is an integral that calculates the magnitude of the electric field at a distance $z$ fromthe center of a thin circular disk as measured along a line normal to the plane of the disk. The disk's radius is $R=7.2\text{ m}$ and the surface charge density is $\sigma =3{\text{ nC/m}}^3$. Evaluate $f(r^{\prime },z)$ at $r^{\prime }=3.6\text{ m}$.

a) 1.606E+00 V/m²

b) 1.767E+00 V/m²

c) 1.943E+00 V/m²

d) 2.138E+00 V/m²

e) 2.351E+00 V/m²

6) A large thin isolated square plate has an area of 6 m². It is uniformly charged with 6 nC of charge. What is the magnitude of the electric field 2 mm from the center of the plate's surface?

a) 5.647E+01 N/C

b) 6.212E+01 N/C

c) 6.833E+01 N/C

d) 7.516E+01 N/C

e) 8.268E+01 N/C

c05 A1

1) A large thin isolated square plate has an area of 8 m². It is uniformly charged with 6 nC of charge. What is the magnitude of the electric field 1 mm from the center of the plate's surface?

a) 3.500E+01 N/C

b) 3.850E+01 N/C

c) 4.235E+01 N/C

d) 4.659E+01 N/C

e) 5.125E+01 N/C

2)

Three small charged objects are placed as shown, where $b=2a$, and $a=4\times 10^{-7}\text{m}$. What is the magnitude of the net force on $q_2$ if $q_1=1e$, $q_2=-7e$, and $q_3=4e$?

a) 9.750E-15 N

b) 1.072E-14 N

c) 1.180E-14 N

d) 1.298E-14 N

e) 1.427E-14 N

3)  $E(z)=\underset{0}{\overset{R}{\int }}f(r^{\prime },z)d{r}^{\prime }$
is an integral that calculates the magnitude of the electric field at a distance $z$ fromthe center of a thin circular disk as measured along a line normal to the plane of the disk. The disk's radius is $R=3.0\text{ m}$ and the surface charge density is $\sigma =8{\text{ nC/m}}^3$. Evaluate $f(r^{\prime },z)$ at $r^{\prime }=2.0\text{ m}$.

a) 9.459E+00 V/m²

b) 1.040E+01 V/m²

c) 1.145E+01 V/m²

d) 1.259E+01 V/m²

e) 1.385E+01 V/m²

4)

A ring is uniformly charged with a net charge of 4 nC. The radius of the ring is R=1.6 m, with its center at the origin and oriented normal to the z axis as shown. what is the magnitude of the electric field at a distance z=1.0 m (on axis) away from the loop's center?

a) 5.352E+09 N/C²

b) 5.887E+09 N/C²

c) 6.476E+09 N/C²

d) 7.124E+09 N/C²

e) 7.836E+09 N/C²

5)

 $E_z(x=0,z)=\underset{-a}{\overset{b}{\int }}f(x,z)dx$
is an integral that calculates the z-component of the electric field at point P situated above the x-axis where a charged rod of length (a+b) is located. The distance between point P and the x-axis is z=1.5 m. Evaluate $f(x,y)$ at x=1.0 m if a=1.1 m, b=1.4 m. The total charge on the rod is 5 nC.

a) 4.602E+00 V/m²

b) 5.062E+00 V/m²

c) 5.568E+00 V/m²

d) 6.125E+00 V/m²

e) 6.738E+00 V/m²

6)

Three small charged objects are placed as shown, where $b=2a$, and $a=6\times 10^{-7}\text{m}$.what angle does the force on $q_2$ make above the $-x$ axis if $q_1=2e$, $q_2=-9e$, and $q_3=4e$?

a) 4.766E+01 degrees

b) 5.243E+01 degrees

c) 5.767E+01 degrees

d) 6.343E+01 degrees

e) 6.978E+01 degrees

c05 A2

1)  $E(z)=\underset{0}{\overset{R}{\int }}f(r^{\prime },z)d{r}^{\prime }$
is an integral that calculates the magnitude of the electric field at a distance $z$ fromthe center of a thin circular disk as measured along a line normal to the plane of the disk. The disk's radius is $R=8.1\text{ m}$ and the surface charge density is $\sigma =3{\text{ nC/m}}^3$. Evaluate $f(r^{\prime },z)$ at $r^{\prime }=4.2\text{ m}$.

a) 5.134E-01 V/m²

b) 5.648E-01 V/m²

c) 6.212E-01 V/m²

d) 6.834E-01 V/m²

e) 7.517E-01 V/m²

2)

Three small charged objects are placed as shown, where $b=2a$, and $a=2\times 10^{-7}\text{m}$.what angle does the force on $q_2$ make above the $-x$ axis if $q_1=2e$, $q_2=-7e$, and $q_3=5e$?

a) 4.357E+01 degrees

b) 4.793E+01 degrees

c) 5.272E+01 degrees

d) 5.799E+01 degrees

e) 6.379E+01 degrees

3) A large thin isolated square plate has an area of 5 m². It is uniformly charged with 8 nC of charge. What is the magnitude of the electric field 3 mm from the center of the plate's surface?

a) 6.171E+01 N/C

b) 6.788E+01 N/C

c) 7.467E+01 N/C

d) 8.214E+01 N/C

e) 9.035E+01 N/C

4)

 $E_z(x=0,z)=\underset{-a}{\overset{b}{\int }}f(x,z)dx$
is an integral that calculates the z-component of the electric field at point P situated above the x-axis where a charged rod of length (a+b) is located. The distance between point P and the x-axis is z=1.2 m. Evaluate $f(x,y)$ at x=0.73 m if a=0.52 m, b=1.6 m. The total charge on the rod is 7 nC.

a) 9.655E+00 V/m²

b) 1.062E+01 V/m²

c) 1.168E+01 V/m²

d) 1.285E+01 V/m²

e) 1.414E+01 V/m²

5)

A ring is uniformly charged with a net charge of 6 nC. The radius of the ring is R=1.9 m, with its center at the origin and oriented normal to the z axis as shown. what is the magnitude of the electric field at a distance z=0.4 m (on axis) away from the loop's center?

a) 2.013E+09 N/C²

b) 2.214E+09 N/C²

c) 2.435E+09 N/C²

d) 2.679E+09 N/C²

e) 2.947E+09 N/C²

6)

Three small charged objects are placed as shown, where $b=2a$, and $a=6\times 10^{-7}\text{m}$. What is the magnitude of the net force on $q_2$ if $q_1=2e$, $q_2=-8e$, and $q_3=4e$?

a) 8.613E-15 N

b) 9.474E-15 N

c) 1.042E-14 N

d) 1.146E-14 N

e) 1.261E-14 N

c05 B0

1)

Three small charged objects are placed as shown, where $b=2a$, and $a=4\times 10^{-7}\text{m}$. What is the magnitude of the net force on $q_2$ if $q_1=1e$, $q_2=-7e$, and $q_3=4e$?

a) 9.750E-15 N

b) 1.072E-14 N

c) 1.180E-14 N

d) 1.298E-14 N

e) 1.427E-14 N

2)

Three small charged objects are placed as shown, where $b=2a$, and $a=4\times 10^{-7}\text{m}$.what angle does the force on $q_2$ make above the $-x$ axis if $q_1=3e$, $q_2=-9e$, and $q_3=6e$?

a) 5.767E+01 degrees

b) 6.343E+01 degrees

c) 6.978E+01 degrees

d) 7.676E+01 degrees

e) 8.443E+01 degrees

3)

 $E_z(x=0,z)=\underset{-a}{\overset{b}{\int }}f(x,z)dx$
is an integral that calculates the z-component of the electric field at point P situated above the x-axis where a charged rod of length (a+b) is located. The distance between point P and the x-axis is z=1.5 m. Evaluate $f(x,y)$ at x=0.79 m if a=0.75 m, b=2.1 m. The total charge on the rod is 6 nC.

a) 5.825E+00 V/m²

b) 6.407E+00 V/m²

c) 7.048E+00 V/m²

d) 7.753E+00 V/m²

e) 8.528E+00 V/m²

4)

A ring is uniformly charged with a net charge of 2 nC. The radius of the ring is R=1.8 m, with its center at the origin and oriented normal to the z axis as shown. what is the magnitude of the electric field at a distance z=1.3 m (on axis) away from the loop's center?

a) 1.764E+09 N/C²

b) 1.941E+09 N/C²

c) 2.135E+09 N/C²

d) 2.348E+09 N/C²

e) 2.583E+09 N/C²

5)  $E(z)=\underset{0}{\overset{R}{\int }}f(r^{\prime },z)d{r}^{\prime }$
is an integral that calculates the magnitude of the electric field at a distance $z$ fromthe center of a thin circular disk as measured along a line normal to the plane of the disk. The disk's radius is $R=8.3\text{ m}$ and the surface charge density is $\sigma =5{\text{ nC/m}}^3$. Evaluate $f(r^{\prime },z)$ at $r^{\prime }=5.3\text{ m}$.

a) 1.022E+00 V/m²

b) 1.125E+00 V/m²

c) 1.237E+00 V/m²

d) 1.361E+00 V/m²

e) 1.497E+00 V/m²

6) A large thin isolated square plate has an area of 9 m². It is uniformly charged with 8 nC of charge. What is the magnitude of the electric field 3 mm from the center of the plate's surface?

a) 3.428E+01 N/C

b) 3.771E+01 N/C

c) 4.148E+01 N/C

d) 4.563E+01 N/C

e) 5.020E+01 N/C

c05 B1

1)  $E(z)=\underset{0}{\overset{R}{\int }}f(r^{\prime },z)d{r}^{\prime }$
is an integral that calculates the magnitude of the electric field at a distance $z$ fromthe center of a thin circular disk as measured along a line normal to the plane of the disk. The disk's radius is $R=6.8\text{ m}$ and the surface charge density is $\sigma =6{\text{ nC/m}}^3$. Evaluate $f(r^{\prime },z)$ at $r^{\prime }=3.6\text{ m}$.

a) 1.258E+00 V/m²

b) 1.384E+00 V/m²

c) 1.522E+00 V/m²

d) 1.674E+00 V/m²

e) 1.842E+00 V/m²

2)

A ring is uniformly charged with a net charge of 2 nC. The radius of the ring is R=1.6 m, with its center at the origin and oriented normal to the z axis as shown. what is the magnitude of the electric field at a distance z=0.99 m (on axis) away from the loop's center?

a) 2.429E+09 N/C²

b) 2.672E+09 N/C²

c) 2.939E+09 N/C²

d) 3.233E+09 N/C²

e) 3.556E+09 N/C²

3)

 $E_z(x=0,z)=\underset{-a}{\overset{b}{\int }}f(x,z)dx$
is an integral that calculates the z-component of the electric field at point P situated above the x-axis where a charged rod of length (a+b) is located. The distance between point P and the x-axis is z=1.3 m. Evaluate $f(x,y)$ at x=0.96 m if a=0.63 m, b=1.4 m. The total charge on the rod is 3 nC.

a) 3.719E+00 V/m²

b) 4.091E+00 V/m²

c) 4.500E+00 V/m²

d) 4.950E+00 V/m²

e) 5.445E+00 V/m²

4)

Three small charged objects are placed as shown, where $b=2a$, and $a=2\times 10^{-7}\text{m}$.what angle does the force on $q_2$ make above the $-x$ axis if $q_1=2e$, $q_2=-7e$, and $q_3=5e$?

a) 4.357E+01 degrees

b) 4.793E+01 degrees

c) 5.272E+01 degrees

d) 5.799E+01 degrees

e) 6.379E+01 degrees

5)

Three small charged objects are placed as shown, where $b=2a$, and $a=6\times 10^{-7}\text{m}$. What is the magnitude of the net force on $q_2$ if $q_1=1e$, $q_2=-8e$, and $q_3=2e$?

a) 5.732E-15 N

b) 6.305E-15 N

c) 6.936E-15 N

d) 7.629E-15 N

e) 8.392E-15 N

6) A large thin isolated square plate has an area of 6 m². It is uniformly charged with 5 nC of charge. What is the magnitude of the electric field 1 mm from the center of the plate's surface?

a) 3.214E+01 N/C

b) 3.536E+01 N/C

c) 3.889E+01 N/C

d) 4.278E+01 N/C

e) 4.706E+01 N/C

c05 B2

1)

 $E_z(x=0,z)=\underset{-a}{\overset{b}{\int }}f(x,z)dx$
is an integral that calculates the z-component of the electric field at point P situated above the x-axis where a charged rod of length (a+b) is located. The distance between point P and the x-axis is z=1.3 m. Evaluate $f(x,y)$ at x=0.83 m if a=0.82 m, b=1.3 m. The total charge on the rod is 7 nC.

a) 8.690E+00 V/m²

b) 9.559E+00 V/m²

c) 1.051E+01 V/m²

d) 1.157E+01 V/m²

e) 1.272E+01 V/m²

2)  $E(z)=\underset{0}{\overset{R}{\int }}f(r^{\prime },z)d{r}^{\prime }$
is an integral that calculates the magnitude of the electric field at a distance $z$ fromthe center of a thin circular disk as measured along a line normal to the plane of the disk. The disk's radius is $R=4.3\text{ m}$ and the surface charge density is $\sigma =2{\text{ nC/m}}^3$. Evaluate $f(r^{\prime },z)$ at $r^{\prime }=2.4\text{ m}$.

a) 5.647E+00 V/m²

b) 6.212E+00 V/m²

c) 6.833E+00 V/m²

d) 7.517E+00 V/m²

e) 8.268E+00 V/m²

3)

Three small charged objects are placed as shown, where $b=2a$, and $a=6\times 10^{-7}\text{m}$.what angle does the force on $q_2$ make above the $-x$ axis if $q_1=2e$, $q_2=-9e$, and $q_3=5e$?

a) 5.272E+01 degrees

b) 5.799E+01 degrees

c) 6.379E+01 degrees

d) 7.017E+01 degrees

e) 7.719E+01 degrees

4)

A ring is uniformly charged with a net charge of 9 nC. The radius of the ring is R=1.9 m, with its center at the origin and oriented normal to the z axis as shown. what is the magnitude of the electric field at a distance z=1.4 m (on axis) away from the loop's center?

a) 7.119E+09 N/C²

b) 7.831E+09 N/C²

c) 8.614E+09 N/C²

d) 9.476E+09 N/C²

e) 1.042E+10 N/C²

5)

Three small charged objects are placed as shown, where $b=2a$, and $a=2\times 10^{-7}\text{m}$. What is the magnitude of the net force on $q_2$ if $q_1=1e$, $q_2=-8e$, and $q_3=2e$?

a) 3.876E-14 N

b) 4.263E-14 N

c) 4.690E-14 N

d) 5.159E-14 N

e) 5.675E-14 N

6) A large thin isolated square plate has an area of 5 m². It is uniformly charged with 8 nC of charge. What is the magnitude of the electric field 3 mm from the center of the plate's surface?

a) 6.171E+01 N/C

b) 6.788E+01 N/C

c) 7.467E+01 N/C

d) 8.214E+01 N/C

e) 9.035E+01 N/C

c05 C0

1)

Three small charged objects are placed as shown, where $b=2a$, and $a=2\times 10^{-7}\text{m}$. What is the magnitude of the net force on $q_2$ if $q_1=1e$, $q_2=-9e$, and $q_3=4e$?

a) 5.014E-14 N

b) 5.515E-14 N

c) 6.067E-14 N

d) 6.674E-14 N

e) 7.341E-14 N

2)

Three small charged objects are placed as shown, where $b=2a$, and $a=2\times 10^{-7}\text{m}$.what angle does the force on $q_2$ make above the $-x$ axis if $q_1=3e$, $q_2=-9e$, and $q_3=5e$?

a) 6.125E+01 degrees

b) 6.738E+01 degrees

c) 7.412E+01 degrees

d) 8.153E+01 degrees

e) 8.968E+01 degrees

3)

 $E_z(x=0,z)=\underset{-a}{\overset{b}{\int }}f(x,z)dx$
is an integral that calculates the z-component of the electric field at point P situated above the x-axis where a charged rod of length (a+b) is located. The distance between point P and the x-axis is z=1.8 m. Evaluate $f(x,y)$ at x=0.65 m if a=0.85 m, b=1.8 m. The total charge on the rod is 5 nC.

a) 3.959E+00 V/m²

b) 4.355E+00 V/m²

c) 4.790E+00 V/m²

d) 5.269E+00 V/m²

e) 5.796E+00 V/m²

4)

A ring is uniformly charged with a net charge of 7 nC. The radius of the ring is R=1.7 m, with its center at the origin and oriented normal to the z axis as shown. what is the magnitude of the electric field at a distance z=1.1 m (on axis) away from the loop's center?

a) 8.336E+09 N/C²

b) 9.170E+09 N/C²

c) 1.009E+10 N/C²

d) 1.110E+10 N/C²

e) 1.220E+10 N/C²

5)  $E(z)=\underset{0}{\overset{R}{\int }}f(r^{\prime },z)d{r}^{\prime }$
is an integral that calculates the magnitude of the electric field at a distance $z$ fromthe center of a thin circular disk as measured along a line normal to the plane of the disk. The disk's radius is $R=3.0\text{ m}$ and the surface charge density is $\sigma =8{\text{ nC/m}}^3$. Evaluate $f(r^{\prime },z)$ at $r^{\prime }=2.0\text{ m}$.

a) 9.459E+00 V/m²

b) 1.040E+01 V/m²

c) 1.145E+01 V/m²

d) 1.259E+01 V/m²

e) 1.385E+01 V/m²

6) A large thin isolated square plate has an area of 6 m². It is uniformly charged with 5 nC of charge. What is the magnitude of the electric field 1 mm from the center of the plate's surface?

a) 3.214E+01 N/C

b) 3.536E+01 N/C

c) 3.889E+01 N/C

d) 4.278E+01 N/C

e) 4.706E+01 N/C

c05 C1

1)  $E(z)=\underset{0}{\overset{R}{\int }}f(r^{\prime },z)d{r}^{\prime }$
is an integral that calculates the magnitude of the electric field at a distance $z$ fromthe center of a thin circular disk as measured along a line normal to the plane of the disk. The disk's radius is $R=4.3\text{ m}$ and the surface charge density is $\sigma =2{\text{ nC/m}}^3$. Evaluate $f(r^{\prime },z)$ at $r^{\prime }=2.4\text{ m}$.

a) 5.647E+00 V/m²

b) 6.212E+00 V/m²

c) 6.833E+00 V/m²

d) 7.517E+00 V/m²

e) 8.268E+00 V/m²

2) A large thin isolated square plate has an area of 3 m². It is uniformly charged with 5 nC of charge. What is the magnitude of the electric field 3 mm from the center of the plate's surface?

a) 9.412E+01 N/C

b) 1.035E+02 N/C

c) 1.139E+02 N/C

d) 1.253E+02 N/C

e) 1.378E+02 N/C

3)

Three small charged objects are placed as shown, where $b=2a$, and $a=2\times 10^{-7}\text{m}$. What is the magnitude of the net force on $q_2$ if $q_1=3e$, $q_2=-9e$, and $q_3=6e$?

a) 1.308E-13 N

b) 1.439E-13 N

c) 1.583E-13 N

d) 1.741E-13 N

e) 1.915E-13 N

4)

Three small charged objects are placed as shown, where $b=2a$, and $a=6\times 10^{-7}\text{m}$.what angle does the force on $q_2$ make above the $-x$ axis if $q_1=3e$, $q_2=-7e$, and $q_3=4e$?

a) 5.914E+01 degrees

b) 6.506E+01 degrees

c) 7.157E+01 degrees

d) 7.872E+01 degrees

e) 8.659E+01 degrees

5)

 $E_z(x=0,z)=\underset{-a}{\overset{b}{\int }}f(x,z)dx$
is an integral that calculates the z-component of the electric field at point P situated above the x-axis where a charged rod of length (a+b) is located. The distance between point P and the x-axis is z=1.2 m. Evaluate $f(x,y)$ at x=0.73 m if a=0.52 m, b=1.6 m. The total charge on the rod is 7 nC.

a) 9.655E+00 V/m²

b) 1.062E+01 V/m²

c) 1.168E+01 V/m²

d) 1.285E+01 V/m²

e) 1.414E+01 V/m²

6)

A ring is uniformly charged with a net charge of 4 nC. The radius of the ring is R=1.6 m, with its center at the origin and oriented normal to the z axis as shown. what is the magnitude of the electric field at a distance z=1.0 m (on axis) away from the loop's center?

a) 5.352E+09 N/C²

b) 5.887E+09 N/C²

c) 6.476E+09 N/C²

d) 7.124E+09 N/C²

e) 7.836E+09 N/C²

c05 C2

1)

Three small charged objects are placed as shown, where $b=2a$, and $a=6\times 10^{-7}\text{m}$. What is the magnitude of the net force on $q_2$ if $q_1=1e$, $q_2=-7e$, and $q_3=2e$?

a) 3.426E-15 N

b) 3.768E-15 N

c) 4.145E-15 N

d) 4.560E-15 N

e) 5.015E-15 N

2)

 $E_z(x=0,z)=\underset{-a}{\overset{b}{\int }}f(x,z)dx$
is an integral that calculates the z-component of the electric field at point P situated above the x-axis where a charged rod of length (a+b) is located. The distance between point P and the x-axis is z=1.5 m. Evaluate $f(x,y)$ at x=0.79 m if a=0.75 m, b=2.1 m. The total charge on the rod is 6 nC.

a) 5.825E+00 V/m²

b) 6.407E+00 V/m²

c) 7.048E+00 V/m²

d) 7.753E+00 V/m²

e) 8.528E+00 V/m²

3)

A ring is uniformly charged with a net charge of 3 nC. The radius of the ring is R=1.7 m, with its center at the origin and oriented normal to the z axis as shown. what is the magnitude of the electric field at a distance z=0.34 m (on axis) away from the loop's center?

a) 1.202E+09 N/C²

b) 1.322E+09 N/C²

c) 1.454E+09 N/C²

d) 1.599E+09 N/C²

e) 1.759E+09 N/C²

4)

Three small charged objects are placed as shown, where $b=2a$, and $a=4\times 10^{-7}\text{m}$.what angle does the force on $q_2$ make above the $-x$ axis if $q_1=3e$, $q_2=-7e$, and $q_3=5e$?

a) 5.569E+01 degrees

b) 6.125E+01 degrees

c) 6.738E+01 degrees

d) 7.412E+01 degrees

e) 8.153E+01 degrees

5) A large thin isolated square plate has an area of 5 m². It is uniformly charged with 7 nC of charge. What is the magnitude of the electric field 1 mm from the center of the plate's surface?

a) 6.534E+01 N/C

b) 7.187E+01 N/C

c) 7.906E+01 N/C

d) 8.696E+01 N/C

e) 9.566E+01 N/C

6)  $E(z)=\underset{0}{\overset{R}{\int }}f(r^{\prime },z)d{r}^{\prime }$
is an integral that calculates the magnitude of the electric field at a distance $z$ fromthe center of a thin circular disk as measured along a line normal to the plane of the disk. The disk's radius is $R=6.8\text{ m}$ and the surface charge density is $\sigma =6{\text{ nC/m}}^3$. Evaluate $f(r^{\prime },z)$ at $r^{\prime }=3.6\text{ m}$.

a) 1.258E+00 V/m²

b) 1.384E+00 V/m²

c) 1.522E+00 V/m²

d) 1.674E+00 V/m²

e) 1.842E+00 V/m²

c05 D0

1)

Three small charged objects are placed as shown, where $b=2a$, and $a=6\times 10^{-7}\text{m}$. What is the magnitude of the net force on $q_2$ if $q_1=1e$, $q_2=-7e$, and $q_3=2e$?

a) 3.426E-15 N

b) 3.768E-15 N

c) 4.145E-15 N

d) 4.560E-15 N

e) 5.015E-15 N

2)

Three small charged objects are placed as shown, where $b=2a$, and $a=2\times 10^{-7}\text{m}$.what angle does the force on $q_2$ make above the $-x$ axis if $q_1=3e$, $q_2=-9e$, and $q_3=5e$?

a) 6.125E+01 degrees

b) 6.738E+01 degrees

c) 7.412E+01 degrees

d) 8.153E+01 degrees

e) 8.968E+01 degrees

3)

 $E_z(x=0,z)=\underset{-a}{\overset{b}{\int }}f(x,z)dx$
is an integral that calculates the z-component of the electric field at point P situated above the x-axis where a charged rod of length (a+b) is located. The distance between point P and the x-axis is z=1.4 m. Evaluate $f(x,y)$ at x=1.1 m if a=0.69 m, b=2.2 m. The total charge on the rod is 6 nC.

a) 3.161E+00 V/m²

b) 3.477E+00 V/m²

c) 3.825E+00 V/m²

d) 4.208E+00 V/m²

e) 4.628E+00 V/m²

4)

A ring is uniformly charged with a net charge of 2 nC. The radius of the ring is R=1.8 m, with its center at the origin and oriented normal to the z axis as shown. what is the magnitude of the electric field at a distance z=1.3 m (on axis) away from the loop's center?

a) 1.764E+09 N/C²

b) 1.941E+09 N/C²

c) 2.135E+09 N/C²

d) 2.348E+09 N/C²

e) 2.583E+09 N/C²

5)  $E(z)=\underset{0}{\overset{R}{\int }}f(r^{\prime },z)d{r}^{\prime }$
is an integral that calculates the magnitude of the electric field at a distance $z$ fromthe center of a thin circular disk as measured along a line normal to the plane of the disk. The disk's radius is $R=2.0\text{ m}$ and the surface charge density is $\sigma =9{\text{ nC/m}}^3$. Evaluate $f(r^{\prime },z)$ at $r^{\prime }=1.2\text{ m}$.

a) 8.933E+00 V/m²

b) 9.826E+00 V/m²

c) 1.081E+01 V/m²

d) 1.189E+01 V/m²

e) 1.308E+01 V/m²

6) A large thin isolated square plate has an area of 9 m². It is uniformly charged with 5 nC of charge. What is the magnitude of the electric field 1 mm from the center of the plate's surface?

a) 2.357E+01 N/C

b) 2.593E+01 N/C

c) 2.852E+01 N/C

d) 3.137E+01 N/C

e) 3.451E+01 N/C

c05 D1

1)  $E(z)=\underset{0}{\overset{R}{\int }}f(r^{\prime },z)d{r}^{\prime }$
is an integral that calculates the magnitude of the electric field at a distance $z$ fromthe center of a thin circular disk as measured along a line normal to the plane of the disk. The disk's radius is $R=9.1\text{ m}$ and the surface charge density is $\sigma =2{\text{ nC/m}}^3$. Evaluate $f(r^{\prime },z)$ at $r^{\prime }=6.2\text{ m}$.

a) 4.961E-01 V/m²

b) 5.457E-01 V/m²

c) 6.002E-01 V/m²

d) 6.603E-01 V/m²

e) 7.263E-01 V/m²

2)

Three small charged objects are placed as shown, where $b=2a$, and $a=6\times 10^{-7}\text{m}$. What is the magnitude of the net force on $q_2$ if $q_1=3e$, $q_2=-7e$, and $q_3=6e$?

a) 1.028E-14 N

b) 1.130E-14 N

c) 1.244E-14 N

d) 1.368E-14 N

e) 1.505E-14 N

3)

 $E_z(x=0,z)=\underset{-a}{\overset{b}{\int }}f(x,z)dx$
is an integral that calculates the z-component of the electric field at point P situated above the x-axis where a charged rod of length (a+b) is located. The distance between point P and the x-axis is z=1.8 m. Evaluate $f(x,y)$ at x=1.0 m if a=1.0 m, b=1.8 m. The total charge on the rod is 6 nC.

a) 3.610E+00 V/m²

b) 3.971E+00 V/m²

c) 4.368E+00 V/m²

d) 4.804E+00 V/m²

e) 5.285E+00 V/m²

4) A large thin isolated square plate has an area of 6 m². It is uniformly charged with 9 nC of charge. What is the magnitude of the electric field 1 mm from the center of the plate's surface?

a) 7.701E+01 N/C

b) 8.471E+01 N/C

c) 9.318E+01 N/C

d) 1.025E+02 N/C

e) 1.127E+02 N/C

5)

A ring is uniformly charged with a net charge of 3 nC. The radius of the ring is R=1.8 m, with its center at the origin and oriented normal to the z axis as shown. what is the magnitude of the electric field at a distance z=1.1 m (on axis) away from the loop's center?

a) 3.159E+09 N/C²

b) 3.475E+09 N/C²

c) 3.823E+09 N/C²

d) 4.205E+09 N/C²

e) 4.626E+09 N/C²

6)

Three small charged objects are placed as shown, where $b=2a$, and $a=2\times 10^{-7}\text{m}$.what angle does the force on $q_2$ make above the $-x$ axis if $q_1=2e$, $q_2=-7e$, and $q_3=3e$?

a) 4.743E+01 degrees

b) 5.217E+01 degrees

c) 5.739E+01 degrees

d) 6.313E+01 degrees

e) 6.944E+01 degrees

c05 D2

1)

 $E_z(x=0,z)=\underset{-a}{\overset{b}{\int }}f(x,z)dx$
is an integral that calculates the z-component of the electric field at point P situated above the x-axis where a charged rod of length (a+b) is located. The distance between point P and the x-axis is z=1.8 m. Evaluate $f(x,y)$ at x=0.5 m if a=0.67 m, b=2.4 m. The total charge on the rod is 9 nC.

a) 5.465E+00 V/m²

b) 6.012E+00 V/m²

c) 6.613E+00 V/m²

d) 7.274E+00 V/m²

e) 8.002E+00 V/m²

2)  $E(z)=\underset{0}{\overset{R}{\int }}f(r^{\prime },z)d{r}^{\prime }$
is an integral that calculates the magnitude of the electric field at a distance $z$ fromthe center of a thin circular disk as measured along a line normal to the plane of the disk. The disk's radius is $R=6.9\text{ m}$ and the surface charge density is $\sigma =9{\text{ nC/m}}^3$. Evaluate $f(r^{\prime },z)$ at $r^{\prime }=4.3\text{ m}$.

a) 8.924E-01 V/m²

b) 9.816E-01 V/m²

c) 1.080E+00 V/m²

d) 1.188E+00 V/m²

e) 1.307E+00 V/m²

3)

Three small charged objects are placed as shown, where $b=2a$, and $a=6\times 10^{-7}\text{m}$.what angle does the force on $q_2$ make above the $-x$ axis if $q_1=3e$, $q_2=-7e$, and $q_3=6e$?

a) 6.343E+01 degrees

b) 6.978E+01 degrees

c) 7.676E+01 degrees

d) 8.443E+01 degrees

e) 9.288E+01 degrees

4)

Three small charged objects are placed as shown, where $b=2a$, and $a=2\times 10^{-7}\text{m}$. What is the magnitude of the net force on $q_2$ if $q_1=1e$, $q_2=-8e$, and $q_3=2e$?

a) 3.876E-14 N

b) 4.263E-14 N

c) 4.690E-14 N

d) 5.159E-14 N

e) 5.675E-14 N

5)

A ring is uniformly charged with a net charge of 9 nC. The radius of the ring is R=1.9 m, with its center at the origin and oriented normal to the z axis as shown. what is the magnitude of the electric field at a distance z=1.4 m (on axis) away from the loop's center?

a) 7.119E+09 N/C²

b) 7.831E+09 N/C²

c) 8.614E+09 N/C²

d) 9.476E+09 N/C²

e) 1.042E+10 N/C²

6) A large thin isolated square plate has an area of 9 m². It is uniformly charged with 5 nC of charge. What is the magnitude of the electric field 1 mm from the center of the plate's surface?

a) 2.357E+01 N/C

b) 2.593E+01 N/C

c) 2.852E+01 N/C

d) 3.137E+01 N/C

e) 3.451E+01 N/C

c05 E0

1)

Three small charged objects are placed as shown, where $b=2a$, and $a=2\times 10^{-7}\text{m}$. What is the magnitude of the net force on $q_2$ if $q_1=1e$, $q_2=-8e$, and $q_3=3e$?

a) 5.243E-14 N

b) 5.768E-14 N

c) 6.344E-14 N

d) 6.979E-14 N

e) 7.677E-14 N

2)

Three small charged objects are placed as shown, where $b=2a$, and $a=2\times 10^{-7}\text{m}$.what angle does the force on $q_2$ make above the $-x$ axis if $q_1=2e$, $q_2=-9e$, and $q_3=4e$?

a) 5.243E+01 degrees

b) 5.767E+01 degrees

c) 6.343E+01 degrees

d) 6.978E+01 degrees

e) 7.676E+01 degrees

3)

 $E_z(x=0,z)=\underset{-a}{\overset{b}{\int }}f(x,z)dx$
is an integral that calculates the z-component of the electric field at point P situated above the x-axis where a charged rod of length (a+b) is located. The distance between point P and the x-axis is z=1.5 m. Evaluate $f(x,y)$ at x=1.1 m if a=0.62 m, b=1.3 m. The total charge on the rod is 7 nC.

a) 6.311E+00 V/m²

b) 6.943E+00 V/m²

c) 7.637E+00 V/m²

d) 8.401E+00 V/m²

e) 9.241E+00 V/m²

4)

A ring is uniformly charged with a net charge of 6 nC. The radius of the ring is R=1.9 m, with its center at the origin and oriented normal to the z axis as shown. what is the magnitude of the electric field at a distance z=0.4 m (on axis) away from the loop's center?

a) 2.013E+09 N/C²

b) 2.214E+09 N/C²

c) 2.435E+09 N/C²

d) 2.679E+09 N/C²

e) 2.947E+09 N/C²

5)  $E(z)=\underset{0}{\overset{R}{\int }}f(r^{\prime },z)d{r}^{\prime }$
is an integral that calculates the magnitude of the electric field at a distance $z$ fromthe center of a thin circular disk as measured along a line normal to the plane of the disk. The disk's radius is $R=3.2\text{ m}$ and the surface charge density is $\sigma =2{\text{ nC/m}}^3$. Evaluate $f(r^{\prime },z)$ at $r^{\prime }=2.2\text{ m}$.

a) 3.228E+00 V/m²

b) 3.551E+00 V/m²

c) 3.906E+00 V/m²

d) 4.297E+00 V/m²

e) 4.727E+00 V/m²

6) A large thin isolated square plate has an area of 9 m². It is uniformly charged with 8 nC of charge. What is the magnitude of the electric field 3 mm from the center of the plate's surface?

a) 3.428E+01 N/C

b) 3.771E+01 N/C

c) 4.148E+01 N/C

d) 4.563E+01 N/C

e) 5.020E+01 N/C

c05 E1

1)

 $E_z(x=0,z)=\underset{-a}{\overset{b}{\int }}f(x,z)dx$
is an integral that calculates the z-component of the electric field at point P situated above the x-axis where a charged rod of length (a+b) is located. The distance between point P and the x-axis is z=1.7 m. Evaluate $f(x,y)$ at x=0.76 m if a=1.1 m, b=1.6 m. The total charge on the rod is 8 nC.

a) 5.267E+00 V/m²

b) 5.794E+00 V/m²

c) 6.374E+00 V/m²

d) 7.011E+00 V/m²

e) 7.712E+00 V/m²

2)

A ring is uniformly charged with a net charge of 8 nC. The radius of the ring is R=1.7 m, with its center at the origin and oriented normal to the z axis as shown. what is the magnitude of the electric field at a distance z=0.32 m (on axis) away from the loop's center?

a) 3.339E+09 N/C²

b) 3.673E+09 N/C²

c) 4.041E+09 N/C²

d) 4.445E+09 N/C²

e) 4.889E+09 N/C²

3)

Three small charged objects are placed as shown, where $b=2a$, and $a=2\times 10^{-7}\text{m}$. What is the magnitude of the net force on $q_2$ if $q_1=1e$, $q_2=-8e$, and $q_3=2e$?

a) 3.876E-14 N

b) 4.263E-14 N

c) 4.690E-14 N

d) 5.159E-14 N

e) 5.675E-14 N

4)  $E(z)=\underset{0}{\overset{R}{\int }}f(r^{\prime },z)d{r}^{\prime }$
is an integral that calculates the magnitude of the electric field at a distance $z$ fromthe center of a thin circular disk as measured along a line normal to the plane of the disk. The disk's radius is $R=1.8\text{ m}$ and the surface charge density is $\sigma =9{\text{ nC/m}}^3$. Evaluate $f(r^{\prime },z)$ at $r^{\prime }=0.83\text{ m}$.

a) 2.898E+01 V/m²

b) 3.188E+01 V/m²

c) 3.507E+01 V/m²

d) 3.857E+01 V/m²

e) 4.243E+01 V/m²

5)

Three small charged objects are placed as shown, where $b=2a$, and $a=4\times 10^{-7}\text{m}$.what angle does the force on $q_2$ make above the $-x$ axis if $q_1=3e$, $q_2=-7e$, and $q_3=5e$?

a) 5.569E+01 degrees

b) 6.125E+01 degrees

c) 6.738E+01 degrees

d) 7.412E+01 degrees

e) 8.153E+01 degrees

6) A large thin isolated square plate has an area of 6 m². It is uniformly charged with 9 nC of charge. What is the magnitude of the electric field 3 mm from the center of the plate's surface?

a) 8.471E+01 N/C

b) 9.318E+01 N/C

c) 1.025E+02 N/C

d) 1.127E+02 N/C

e) 1.240E+02 N/C

c05 E2

1)

 $E_z(x=0,z)=\underset{-a}{\overset{b}{\int }}f(x,z)dx$
is an integral that calculates the z-component of the electric field at point P situated above the x-axis where a charged rod of length (a+b) is located. The distance between point P and the x-axis is z=1.7 m. Evaluate $f(x,y)$ at x=0.52 m if a=0.88 m, b=1.3 m. The total charge on the rod is 6 nC.

a) 6.804E+00 V/m²

b) 7.485E+00 V/m²

c) 8.233E+00 V/m²

d) 9.056E+00 V/m²

e) 9.962E+00 V/m²

2)

Three small charged objects are placed as shown, where $b=2a$, and $a=4\times 10^{-7}\text{m}$. What is the magnitude of the net force on $q_2$ if $q_1=3e$, $q_2=-7e$, and $q_3=6e$?

a) 2.544E-14 N

b) 2.798E-14 N

c) 3.078E-14 N

d) 3.385E-14 N

e) 3.724E-14 N

3) A large thin isolated square plate has an area of 9 m². It is uniformly charged with 6 nC of charge. What is the magnitude of the electric field 1 mm from the center of the plate's surface?

a) 2.571E+01 N/C

b) 2.828E+01 N/C

c) 3.111E+01 N/C

d) 3.422E+01 N/C

e) 3.765E+01 N/C

4)

A ring is uniformly charged with a net charge of 3 nC. The radius of the ring is R=1.8 m, with its center at the origin and oriented normal to the z axis as shown. what is the magnitude of the electric field at a distance z=1.1 m (on axis) away from the loop's center?

a) 3.159E+09 N/C²

b) 3.475E+09 N/C²

c) 3.823E+09 N/C²

d) 4.205E+09 N/C²

e) 4.626E+09 N/C²

5)  $E(z)=\underset{0}{\overset{R}{\int }}f(r^{\prime },z)d{r}^{\prime }$
is an integral that calculates the magnitude of the electric field at a distance $z$ fromthe center of a thin circular disk as measured along a line normal to the plane of the disk. The disk's radius is $R=1.8\text{ m}$ and the surface charge density is $\sigma =3{\text{ nC/m}}^3$. Evaluate $f(r^{\prime },z)$ at $r^{\prime }=1.1\text{ m}$.

a) 7.517E+00 V/m²

b) 8.269E+00 V/m²

c) 9.096E+00 V/m²

d) 1.001E+01 V/m²

e) 1.101E+01 V/m²

6)

Three small charged objects are placed as shown, where $b=2a$, and $a=4\times 10^{-7}\text{m}$.what angle does the force on $q_2$ make above the $-x$ axis if $q_1=3e$, $q_2=-8e$, and $q_3=6e$?

a) 5.243E+01 degrees

b) 5.767E+01 degrees

c) 6.343E+01 degrees

d) 6.978E+01 degrees

e) 7.676E+01 degrees

c05 F0

1)

Three small charged objects are placed as shown, where $b=2a$, and $a=6\times 10^{-7}\text{m}$. What is the magnitude of the net force on $q_2$ if $q_1=3e$, $q_2=-7e$, and $q_3=5e$?

a) 9.958E-15 N

b) 1.095E-14 N

c) 1.205E-14 N

d) 1.325E-14 N

e) 1.458E-14 N

2)

Three small charged objects are placed as shown, where $b=2a$, and $a=2\times 10^{-7}\text{m}$.what angle does the force on $q_2$ make above the $-x$ axis if $q_1=2e$, $q_2=-9e$, and $q_3=4e$?

a) 5.243E+01 degrees

b) 5.767E+01 degrees

c) 6.343E+01 degrees

d) 6.978E+01 degrees

e) 7.676E+01 degrees

3)

 $E_z(x=0,z)=\underset{-a}{\overset{b}{\int }}f(x,z)dx$
is an integral that calculates the z-component of the electric field at point P situated above the x-axis where a charged rod of length (a+b) is located. The distance between point P and the x-axis is z=1.3 m. Evaluate $f(x,y)$ at x=0.83 m if a=0.82 m, b=1.3 m. The total charge on the rod is 7 nC.

a) 8.690E+00 V/m²

b) 9.559E+00 V/m²

c) 1.051E+01 V/m²

d) 1.157E+01 V/m²

e) 1.272E+01 V/m²

4)

A ring is uniformly charged with a net charge of 7 nC. The radius of the ring is R=1.6 m, with its center at the origin and oriented normal to the z axis as shown. what is the magnitude of the electric field at a distance z=0.35 m (on axis) away from the loop's center?

a) 4.142E+09 N/C²

b) 4.556E+09 N/C²

c) 5.012E+09 N/C²

d) 5.513E+09 N/C²

e) 6.064E+09 N/C²

5)  $E(z)=\underset{0}{\overset{R}{\int }}f(r^{\prime },z)d{r}^{\prime }$
is an integral that calculates the magnitude of the electric field at a distance $z$ fromthe center of a thin circular disk as measured along a line normal to the plane of the disk. The disk's radius is $R=1.4\text{ m}$ and the surface charge density is $\sigma =6{\text{ nC/m}}^3$. Evaluate $f(r^{\prime },z)$ at $r^{\prime }=0.56\text{ m}$.

a) 2.567E+01 V/m²

b) 2.824E+01 V/m²

c) 3.106E+01 V/m²

d) 3.417E+01 V/m²

e) 3.759E+01 V/m²

6) A large thin isolated square plate has an area of 8 m². It is uniformly charged with 7 nC of charge. What is the magnitude of the electric field 3 mm from the center of the plate's surface?

a) 4.492E+01 N/C

b) 4.941E+01 N/C

c) 5.435E+01 N/C

d) 5.979E+01 N/C

e) 6.577E+01 N/C

c05 F1

1)

Three small charged objects are placed as shown, where $b=2a$, and $a=2\times 10^{-7}\text{m}$. What is the magnitude of the net force on $q_2$ if $q_1=3e$, $q_2=-9e$, and $q_3=6e$?

a) 1.308E-13 N

b) 1.439E-13 N

c) 1.583E-13 N

d) 1.741E-13 N

e) 1.915E-13 N

2)  $E(z)=\underset{0}{\overset{R}{\int }}f(r^{\prime },z)d{r}^{\prime }$
is an integral that calculates the magnitude of the electric field at a distance $z$ fromthe center of a thin circular disk as measured along a line normal to the plane of the disk. The disk's radius is $R=7.2\text{ m}$ and the surface charge density is $\sigma =3{\text{ nC/m}}^3$. Evaluate $f(r^{\prime },z)$ at $r^{\prime }=3.6\text{ m}$.

a) 1.606E+00 V/m²

b) 1.767E+00 V/m²

c) 1.943E+00 V/m²

d) 2.138E+00 V/m²

e) 2.351E+00 V/m²

3) A large thin isolated square plate has an area of 6 m². It is uniformly charged with 9 nC of charge. What is the magnitude of the electric field 2 mm from the center of the plate's surface?

a) 7.000E+01 N/C

b) 7.701E+01 N/C

c) 8.471E+01 N/C

d) 9.318E+01 N/C

e) 1.025E+02 N/C

4)

A ring is uniformly charged with a net charge of 7 nC. The radius of the ring is R=1.6 m, with its center at the origin and oriented normal to the z axis as shown. what is the magnitude of the electric field at a distance z=0.35 m (on axis) away from the loop's center?

a) 4.142E+09 N/C²

b) 4.556E+09 N/C²

c) 5.012E+09 N/C²

d) 5.513E+09 N/C²

e) 6.064E+09 N/C²

5)

 $E_z(x=0,z)=\underset{-a}{\overset{b}{\int }}f(x,z)dx$
is an integral that calculates the z-component of the electric field at point P situated above the x-axis where a charged rod of length (a+b) is located. The distance between point P and the x-axis is z=1.8 m. Evaluate $f(x,y)$ at x=1.0 m if a=1.0 m, b=1.8 m. The total charge on the rod is 6 nC.

a) 3.610E+00 V/m²

b) 3.971E+00 V/m²

c) 4.368E+00 V/m²

d) 4.804E+00 V/m²

e) 5.285E+00 V/m²

6)

Three small charged objects are placed as shown, where $b=2a$, and $a=6\times 10^{-7}\text{m}$.what angle does the force on $q_2$ make above the $-x$ axis if $q_1=3e$, $q_2=-7e$, and $q_3=4e$?

a) 5.377E+01 degrees

b) 5.914E+01 degrees

c) 6.506E+01 degrees

d) 7.157E+01 degrees

e) 7.872E+01 degrees

c05 F2

1)

A ring is uniformly charged with a net charge of 2 nC. The radius of the ring is R=1.5 m, with its center at the origin and oriented normal to the z axis as shown. what is the magnitude of the electric field at a distance z=0.33 m (on axis) away from the loop's center?

a) 1.353E+09 N/C²

b) 1.488E+09 N/C²

c) 1.637E+09 N/C²

d) 1.801E+09 N/C²

e) 1.981E+09 N/C²

2)

Three small charged objects are placed as shown, where $b=2a$, and $a=2\times 10^{-7}\text{m}$. What is the magnitude of the net force on $q_2$ if $q_1=1e$, $q_2=-7e$, and $q_3=2e$?

a) 3.391E-14 N

b) 3.731E-14 N

c) 4.104E-14 N

d) 4.514E-14 N

e) 4.965E-14 N

3)

 $E_z(x=0,z)=\underset{-a}{\overset{b}{\int }}f(x,z)dx$
is an integral that calculates the z-component of the electric field at point P situated above the x-axis where a charged rod of length (a+b) is located. The distance between point P and the x-axis is z=1.9 m. Evaluate $f(x,y)$ at x=0.96 m if a=0.95 m, b=1.8 m. The total charge on the rod is 7 nC.

a) 3.385E+00 V/m²

b) 3.724E+00 V/m²

c) 4.096E+00 V/m²

d) 4.506E+00 V/m²

e) 4.957E+00 V/m²

4)

Three small charged objects are placed as shown, where $b=2a$, and $a=4\times 10^{-7}\text{m}$.what angle does the force on $q_2$ make above the $-x$ axis if $q_1=1e$, $q_2=-8e$, and $q_3=4e$?

a) 3.719E+01 degrees

b) 4.091E+01 degrees

c) 4.500E+01 degrees

d) 4.950E+01 degrees

e) 5.445E+01 degrees

5) A large thin isolated square plate has an area of 6 m². It is uniformly charged with 6 nC of charge. What is the magnitude of the electric field 2 mm from the center of the plate's surface?

a) 5.647E+01 N/C

b) 6.212E+01 N/C

c) 6.833E+01 N/C

d) 7.516E+01 N/C

e) 8.268E+01 N/C

6)  $E(z)=\underset{0}{\overset{R}{\int }}f(r^{\prime },z)d{r}^{\prime }$
is an integral that calculates the magnitude of the electric field at a distance $z$ fromthe center of a thin circular disk as measured along a line normal to the plane of the disk. The disk's radius is $R=6.9\text{ m}$ and the surface charge density is $\sigma =9{\text{ nC/m}}^3$. Evaluate $f(r^{\prime },z)$ at $r^{\prime }=4.3\text{ m}$.

a) 8.924E-01 V/m²

b) 9.816E-01 V/m²

c) 1.080E+00 V/m²

d) 1.188E+00 V/m²

e) 1.307E+00 V/m²

c05 G0

1)

Three small charged objects are placed as shown, where $b=2a$, and $a=2\times 10^{-7}\text{m}$. What is the magnitude of the net force on $q_2$ if $q_1=1e$, $q_2=-7e$, and $q_3=2e$?

a) 3.391E-14 N

b) 3.731E-14 N

c) 4.104E-14 N

d) 4.514E-14 N

e) 4.965E-14 N

2)

Three small charged objects are placed as shown, where $b=2a$, and $a=6\times 10^{-7}\text{m}$.what angle does the force on $q_2$ make above the $-x$ axis if $q_1=3e$, $q_2=-7e$, and $q_3=4e$?

a) 5.914E+01 degrees

b) 6.506E+01 degrees

c) 7.157E+01 degrees

d) 7.872E+01 degrees

e) 8.659E+01 degrees

3)

 $E_z(x=0,z)=\underset{-a}{\overset{b}{\int }}f(x,z)dx$
is an integral that calculates the z-component of the electric field at point P situated above the x-axis where a charged rod of length (a+b) is located. The distance between point P and the x-axis is z=1.3 m. Evaluate $f(x,y)$ at x=0.83 m if a=0.82 m, b=1.3 m. The total charge on the rod is 7 nC.

a) 8.690E+00 V/m²

b) 9.559E+00 V/m²

c) 1.051E+01 V/m²

d) 1.157E+01 V/m²

e) 1.272E+01 V/m²

4)

A ring is uniformly charged with a net charge of 7 nC. The radius of the ring is R=1.7 m, with its center at the origin and oriented normal to the z axis as shown. what is the magnitude of the electric field at a distance z=1.1 m (on axis) away from the loop's center?

a) 8.336E+09 N/C²

b) 9.170E+09 N/C²

c) 1.009E+10 N/C²

d) 1.110E+10 N/C²

e) 1.220E+10 N/C²

5)  $E(z)=\underset{0}{\overset{R}{\int }}f(r^{\prime },z)d{r}^{\prime }$
is an integral that calculates the magnitude of the electric field at a distance $z$ fromthe center of a thin circular disk as measured along a line normal to the plane of the disk. The disk's radius is $R=3.0\text{ m}$ and the surface charge density is $\sigma =8{\text{ nC/m}}^3$. Evaluate $f(r^{\prime },z)$ at $r^{\prime }=2.0\text{ m}$.

a) 9.459E+00 V/m²

b) 1.040E+01 V/m²

c) 1.145E+01 V/m²

d) 1.259E+01 V/m²

e) 1.385E+01 V/m²

6) A large thin isolated square plate has an area of 6 m². It is uniformly charged with 5 nC of charge. What is the magnitude of the electric field 1 mm from the center of the plate's surface?

a) 3.214E+01 N/C

b) 3.536E+01 N/C

c) 3.889E+01 N/C

d) 4.278E+01 N/C

e) 4.706E+01 N/C

c05 G1

1)  $E(z)=\underset{0}{\overset{R}{\int }}f(r^{\prime },z)d{r}^{\prime }$
is an integral that calculates the magnitude of the electric field at a distance $z$ fromthe center of a thin circular disk as measured along a line normal to the plane of the disk. The disk's radius is $R=2.8\text{ m}$ and the surface charge density is $\sigma =3{\text{ nC/m}}^3$. Evaluate $f(r^{\prime },z)$ at $r^{\prime }=1.9\text{ m}$.

a) 4.295E+00 V/m²

b) 4.724E+00 V/m²

c) 5.196E+00 V/m²

d) 5.716E+00 V/m²

e) 6.288E+00 V/m²

2)

Three small charged objects are placed as shown, where $b=2a$, and $a=6\times 10^{-7}\text{m}$.what angle does the force on $q_2$ make above the $-x$ axis if $q_1=2e$, $q_2=-9e$, and $q_3=5e$?

a) 5.272E+01 degrees

b) 5.799E+01 degrees

c) 6.379E+01 degrees

d) 7.017E+01 degrees

e) 7.719E+01 degrees

3)

Three small charged objects are placed as shown, where $b=2a$, and $a=4\times 10^{-7}\text{m}$. What is the magnitude of the net force on $q_2$ if $q_1=2e$, $q_2=-8e$, and $q_3=3e$?

a) 2.036E-14 N

b) 2.240E-14 N

c) 2.464E-14 N

d) 2.710E-14 N

e) 2.981E-14 N

4) A large thin isolated square plate has an area of 9 m². It is uniformly charged with 8 nC of charge. What is the magnitude of the electric field 3 mm from the center of the plate's surface?

a) 3.428E+01 N/C

b) 3.771E+01 N/C

c) 4.148E+01 N/C

d) 4.563E+01 N/C

e) 5.020E+01 N/C

5)

 $E_z(x=0,z)=\underset{-a}{\overset{b}{\int }}f(x,z)dx$
is an integral that calculates the z-component of the electric field at point P situated above the x-axis where a charged rod of length (a+b) is located. The distance between point P and the x-axis is z=1.4 m. Evaluate $f(x,y)$ at x=1.1 m if a=0.69 m, b=2.2 m. The total charge on the rod is 6 nC.

a) 3.161E+00 V/m²

b) 3.477E+00 V/m²

c) 3.825E+00 V/m²

d) 4.208E+00 V/m²

e) 4.628E+00 V/m²

6)

A ring is uniformly charged with a net charge of 2 nC. The radius of the ring is R=1.5 m, with its center at the origin and oriented normal to the z axis as shown. what is the magnitude of the electric field at a distance z=0.33 m (on axis) away from the loop's center?

a) 1.353E+09 N/C²

b) 1.488E+09 N/C²

c) 1.637E+09 N/C²

d) 1.801E+09 N/C²

e) 1.981E+09 N/C²

c05 G2

1)

A ring is uniformly charged with a net charge of 4 nC. The radius of the ring is R=1.6 m, with its center at the origin and oriented normal to the z axis as shown. what is the magnitude of the electric field at a distance z=1.0 m (on axis) away from the loop's center?

a) 5.352E+09 N/C²

b) 5.887E+09 N/C²

c) 6.476E+09 N/C²

d) 7.124E+09 N/C²

e) 7.836E+09 N/C²

2) A large thin isolated square plate has an area of 9 m². It is uniformly charged with 8 nC of charge. What is the magnitude of the electric field 3 mm from the center of the plate's surface?

a) 3.428E+01 N/C

b) 3.771E+01 N/C

c) 4.148E+01 N/C

d) 4.563E+01 N/C

e) 5.020E+01 N/C

3)

Three small charged objects are placed as shown, where $b=2a$, and $a=2\times 10^{-7}\text{m}$. What is the magnitude of the net force on $q_2$ if $q_1=1e$, $q_2=-8e$, and $q_3=3e$?

a) 5.243E-14 N

b) 5.768E-14 N

c) 6.344E-14 N

d) 6.979E-14 N

e) 7.677E-14 N

4)  $E(z)=\underset{0}{\overset{R}{\int }}f(r^{\prime },z)d{r}^{\prime }$
is an integral that calculates the magnitude of the electric field at a distance $z$ fromthe center of a thin circular disk as measured along a line normal to the plane of the disk. The disk's radius is $R=3.0\text{ m}$ and the surface charge density is $\sigma =8{\text{ nC/m}}^3$. Evaluate $f(r^{\prime },z)$ at $r^{\prime }=2.0\text{ m}$.

a) 9.459E+00 V/m²

b) 1.040E+01 V/m²

c) 1.145E+01 V/m²

d) 1.259E+01 V/m²

e) 1.385E+01 V/m²

5)

Three small charged objects are placed as shown, where $b=2a$, and $a=4\times 10^{-7}\text{m}$.what angle does the force on $q_2$ make above the $-x$ axis if $q_1=3e$, $q_2=-8e$, and $q_3=6e$?

a) 5.243E+01 degrees

b) 5.767E+01 degrees

c) 6.343E+01 degrees

d) 6.978E+01 degrees

e) 7.676E+01 degrees

6)

 $E_z(x=0,z)=\underset{-a}{\overset{b}{\int }}f(x,z)dx$
is an integral that calculates the z-component of the electric field at point P situated above the x-axis where a charged rod of length (a+b) is located. The distance between point P and the x-axis is z=1.8 m. Evaluate $f(x,y)$ at x=0.5 m if a=0.67 m, b=2.4 m. The total charge on the rod is 9 nC.

a) 5.465E+00 V/m²

b) 6.012E+00 V/m²

c) 6.613E+00 V/m²

d) 7.274E+00 V/m²

e) 8.002E+00 V/m²

c05 H0

1)

Three small charged objects are placed as shown, where $b=2a$, and $a=6\times 10^{-7}\text{m}$. What is the magnitude of the net force on $q_2$ if $q_1=2e$, $q_2=-8e$, and $q_3=4e$?

a) 8.613E-15 N

b) 9.474E-15 N

c) 1.042E-14 N

d) 1.146E-14 N

e) 1.261E-14 N

2)

Three small charged objects are placed as shown, where $b=2a$, and $a=6\times 10^{-7}\text{m}$.what angle does the force on $q_2$ make above the $-x$ axis if $q_1=2e$, $q_2=-9e$, and $q_3=4e$?

a) 4.766E+01 degrees

b) 5.243E+01 degrees

c) 5.767E+01 degrees

d) 6.343E+01 degrees

e) 6.978E+01 degrees

3)

 $E_z(x=0,z)=\underset{-a}{\overset{b}{\int }}f(x,z)dx$
is an integral that calculates the z-component of the electric field at point P situated above the x-axis where a charged rod of length (a+b) is located. The distance between point P and the x-axis is z=1.2 m. Evaluate $f(x,y)$ at x=0.73 m if a=0.52 m, b=1.6 m. The total charge on the rod is 7 nC.

a) 9.655E+00 V/m²

b) 1.062E+01 V/m²

c) 1.168E+01 V/m²

d) 1.285E+01 V/m²

e) 1.414E+01 V/m²

4)

A ring is uniformly charged with a net charge of 4 nC. The radius of the ring is R=1.6 m, with its center at the origin and oriented normal to the z axis as shown. what is the magnitude of the electric field at a distance z=1.0 m (on axis) away from the loop's center?

a) 5.352E+09 N/C²

b) 5.887E+09 N/C²

c) 6.476E+09 N/C²

d) 7.124E+09 N/C²

e) 7.836E+09 N/C²

5)  $E(z)=\underset{0}{\overset{R}{\int }}f(r^{\prime },z)d{r}^{\prime }$
is an integral that calculates the magnitude of the electric field at a distance $z$ fromthe center of a thin circular disk as measured along a line normal to the plane of the disk. The disk's radius is $R=8.7\text{ m}$ and the surface charge density is $\sigma =7{\text{ nC/m}}^3$. Evaluate $f(r^{\prime },z)$ at $r^{\prime }=5.8\text{ m}$.

a) 3.722E-01 V/m²

b) 4.094E-01 V/m²

c) 4.504E-01 V/m²

d) 4.954E-01 V/m²

e) 5.450E-01 V/m²

6) A large thin isolated square plate has an area of 9 m². It is uniformly charged with 5 nC of charge. What is the magnitude of the electric field 1 mm from the center of the plate's surface?

a) 2.357E+01 N/C

b) 2.593E+01 N/C

c) 2.852E+01 N/C

d) 3.137E+01 N/C

e) 3.451E+01 N/C

c05 H1

1) A large thin isolated square plate has an area of 5 m². It is uniformly charged with 7 nC of charge. What is the magnitude of the electric field 1 mm from the center of the plate's surface?

a) 6.534E+01 N/C

b) 7.187E+01 N/C

c) 7.906E+01 N/C

d) 8.696E+01 N/C

e) 9.566E+01 N/C

2)

Three small charged objects are placed as shown, where $b=2a$, and $a=6\times 10^{-7}\text{m}$. What is the magnitude of the net force on $q_2$ if $q_1=3e$, $q_2=-7e$, and $q_3=5e$?

a) 9.958E-15 N

b) 1.095E-14 N

c) 1.205E-14 N

d) 1.325E-14 N

e) 1.458E-14 N

3)

 $E_z(x=0,z)=\underset{-a}{\overset{b}{\int }}f(x,z)dx$
is an integral that calculates the z-component of the electric field at point P situated above the x-axis where a charged rod of length (a+b) is located. The distance between point P and the x-axis is z=1.6 m. Evaluate $f(x,y)$ at x=0.73 m if a=0.64 m, b=1.8 m. The total charge on the rod is 3 nC.

a) 2.955E+00 V/m²

b) 3.250E+00 V/m²

c) 3.575E+00 V/m²

d) 3.933E+00 V/m²

e) 4.326E+00 V/m²

4)  $E(z)=\underset{0}{\overset{R}{\int }}f(r^{\prime },z)d{r}^{\prime }$
is an integral that calculates the magnitude of the electric field at a distance $z$ fromthe center of a thin circular disk as measured along a line normal to the plane of the disk. The disk's radius is $R=8.7\text{ m}$ and the surface charge density is $\sigma =7{\text{ nC/m}}^3$. Evaluate $f(r^{\prime },z)$ at $r^{\prime }=5.8\text{ m}$.

a) 3.722E-01 V/m²

b) 4.094E-01 V/m²

c) 4.504E-01 V/m²

d) 4.954E-01 V/m²

e) 5.450E-01 V/m²

5)

Three small charged objects are placed as shown, where $b=2a$, and $a=4\times 10^{-7}\text{m}$.what angle does the force on $q_2$ make above the $-x$ axis if $q_1=3e$, $q_2=-8e$, and $q_3=6e$?

a) 5.243E+01 degrees

b) 5.767E+01 degrees

c) 6.343E+01 degrees

d) 6.978E+01 degrees

e) 7.676E+01 degrees

6)

A ring is uniformly charged with a net charge of 6 nC. The radius of the ring is R=1.9 m, with its center at the origin and oriented normal to the z axis as shown. what is the magnitude of the electric field at a distance z=0.4 m (on axis) away from the loop's center?

a) 2.013E+09 N/C²

b) 2.214E+09 N/C²

c) 2.435E+09 N/C²

d) 2.679E+09 N/C²

e) 2.947E+09 N/C²

c05 H2

1)

 $E_z(x=0,z)=\underset{-a}{\overset{b}{\int }}f(x,z)dx$
is an integral that calculates the z-component of the electric field at point P situated above the x-axis where a charged rod of length (a+b) is located. The distance between point P and the x-axis is z=1.2 m. Evaluate $f(x,y)$ at x=0.54 m if a=0.76 m, b=1.7 m. The total charge on the rod is 8 nC.

a) 1.399E+01 V/m²

b) 1.539E+01 V/m²

c) 1.693E+01 V/m²

d) 1.862E+01 V/m²

e) 2.049E+01 V/m²

2)

Three small charged objects are placed as shown, where $b=2a$, and $a=2\times 10^{-7}\text{m}$.what angle does the force on $q_2$ make above the $-x$ axis if $q_1=2e$, $q_2=-7e$, and $q_3=3e$?

a) 4.743E+01 degrees

b) 5.217E+01 degrees

c) 5.739E+01 degrees

d) 6.313E+01 degrees

e) 6.944E+01 degrees

3)  $E(z)=\underset{0}{\overset{R}{\int }}f(r^{\prime },z)d{r}^{\prime }$
is an integral that calculates the magnitude of the electric field at a distance $z$ fromthe center of a thin circular disk as measured along a line normal to the plane of the disk. The disk's radius is $R=6.9\text{ m}$ and the surface charge density is $\sigma =9{\text{ nC/m}}^3$. Evaluate $f(r^{\prime },z)$ at $r^{\prime }=4.3\text{ m}$.

a) 8.924E-01 V/m²

b) 9.816E-01 V/m²

c) 1.080E+00 V/m²

d) 1.188E+00 V/m²

e) 1.307E+00 V/m²

4)

Three small charged objects are placed as shown, where $b=2a$, and $a=6\times 10^{-7}\text{m}$. What is the magnitude of the net force on $q_2$ if $q_1=2e$, $q_2=-8e$, and $q_3=4e$?

a) 8.613E-15 N

b) 9.474E-15 N

c) 1.042E-14 N

d) 1.146E-14 N

e) 1.261E-14 N

5) A large thin isolated square plate has an area of 8 m². It is uniformly charged with 6 nC of charge. What is the magnitude of the electric field 1 mm from the center of the plate's surface?

a) 3.500E+01 N/C

b) 3.850E+01 N/C

c) 4.235E+01 N/C

d) 4.659E+01 N/C

e) 5.125E+01 N/C

6)

A ring is uniformly charged with a net charge of 3 nC. The radius of the ring is R=1.7 m, with its center at the origin and oriented normal to the z axis as shown. what is the magnitude of the electric field at a distance z=0.34 m (on axis) away from the loop's center?

a) 1.202E+09 N/C²

b) 1.322E+09 N/C²

c) 1.454E+09 N/C²

d) 1.599E+09 N/C²

e) 1.759E+09 N/C²

c05 I0

1)

Three small charged objects are placed as shown, where $b=2a$, and $a=2\times 10^{-7}\text{m}$. What is the magnitude of the net force on $q_2$ if $q_1=3e$, $q_2=-9e$, and $q_3=6e$?

a) 1.308E-13 N

b) 1.439E-13 N

c) 1.583E-13 N

d) 1.741E-13 N

e) 1.915E-13 N

2)

Three small charged objects are placed as shown, where $b=2a$, and $a=6\times 10^{-7}\text{m}$.what angle does the force on $q_2$ make above the $-x$ axis if $q_1=3e$, $q_2=-8e$, and $q_3=5e$?

a) 5.062E+01 degrees

b) 5.569E+01 degrees

c) 6.125E+01 degrees

d) 6.738E+01 degrees

e) 7.412E+01 degrees

3)

 $E_z(x=0,z)=\underset{-a}{\overset{b}{\int }}f(x,z)dx$
is an integral that calculates the z-component of the electric field at point P situated above the x-axis where a charged rod of length (a+b) is located. The distance between point P and the x-axis is z=1.6 m. Evaluate $f(x,y)$ at x=0.73 m if a=0.64 m, b=1.8 m. The total charge on the rod is 3 nC.

a) 2.955E+00 V/m²

b) 3.250E+00 V/m²

c) 3.575E+00 V/m²

d) 3.933E+00 V/m²

e) 4.326E+00 V/m²

4)

A ring is uniformly charged with a net charge of 7 nC. The radius of the ring is R=1.7 m, with its center at the origin and oriented normal to the z axis as shown. what is the magnitude of the electric field at a distance z=1.2 m (on axis) away from the loop's center?

a) 6.925E+09 N/C²

b) 7.617E+09 N/C²

c) 8.379E+09 N/C²

d) 9.217E+09 N/C²

e) 1.014E+10 N/C²

5)  $E(z)=\underset{0}{\overset{R}{\int }}f(r^{\prime },z)d{r}^{\prime }$
is an integral that calculates the magnitude of the electric field at a distance $z$ fromthe center of a thin circular disk as measured along a line normal to the plane of the disk. The disk's radius is $R=4.3\text{ m}$ and the surface charge density is $\sigma =2{\text{ nC/m}}^3$. Evaluate $f(r^{\prime },z)$ at $r^{\prime }=2.4\text{ m}$.

a) 5.647E+00 V/m²

b) 6.212E+00 V/m²

c) 6.833E+00 V/m²

d) 7.517E+00 V/m²

e) 8.268E+00 V/m²

6) A large thin isolated square plate has an area of 5 m². It is uniformly charged with 8 nC of charge. What is the magnitude of the electric field 3 mm from the center of the plate's surface?

a) 6.171E+01 N/C

b) 6.788E+01 N/C

c) 7.467E+01 N/C

d) 8.214E+01 N/C

e) 9.035E+01 N/C

c05 I1

1)

 $E_z(x=0,z)=\underset{-a}{\overset{b}{\int }}f(x,z)dx$
is an integral that calculates the z-component of the electric field at point P situated above the x-axis where a charged rod of length (a+b) is located. The distance between point P and the x-axis is z=1.8 m. Evaluate $f(x,y)$ at x=0.5 m if a=0.67 m, b=2.4 m. The total charge on the rod is 9 nC.

a) 5.465E+00 V/m²

b) 6.012E+00 V/m²

c) 6.613E+00 V/m²

d) 7.274E+00 V/m²

e) 8.002E+00 V/m²

2)

Three small charged objects are placed as shown, where $b=2a$, and $a=6\times 10^{-7}\text{m}$. What is the magnitude of the net force on $q_2$ if $q_1=2e$, $q_2=-8e$, and $q_3=4e$?

a) 8.613E-15 N

b) 9.474E-15 N

c) 1.042E-14 N

d) 1.146E-14 N

e) 1.261E-14 N

3)

Three small charged objects are placed as shown, where $b=2a$, and $a=4\times 10^{-7}\text{m}$.what angle does the force on $q_2$ make above the $-x$ axis if $q_1=2e$, $q_2=-9e$, and $q_3=5e$?

a) 3.961E+01 degrees

b) 4.357E+01 degrees

c) 4.793E+01 degrees

d) 5.272E+01 degrees

e) 5.799E+01 degrees

4)

A ring is uniformly charged with a net charge of 7 nC. The radius of the ring is R=1.7 m, with its center at the origin and oriented normal to the z axis as shown. what is the magnitude of the electric field at a distance z=1.2 m (on axis) away from the loop's center?

a) 6.925E+09 N/C²

b) 7.617E+09 N/C²

c) 8.379E+09 N/C²

d) 9.217E+09 N/C²

e) 1.014E+10 N/C²

5)  $E(z)=\underset{0}{\overset{R}{\int }}f(r^{\prime },z)d{r}^{\prime }$
is an integral that calculates the magnitude of the electric field at a distance $z$ fromthe center of a thin circular disk as measured along a line normal to the plane of the disk. The disk's radius is $R=9.1\text{ m}$ and the surface charge density is $\sigma =2{\text{ nC/m}}^3$. Evaluate $f(r^{\prime },z)$ at $r^{\prime }=6.2\text{ m}$.

a) 4.961E-01 V/m²

b) 5.457E-01 V/m²

c) 6.002E-01 V/m²

d) 6.603E-01 V/m²

e) 7.263E-01 V/m²

6) A large thin isolated square plate has an area of 4 m². It is uniformly charged with 5 nC of charge. What is the magnitude of the electric field 1 mm from the center of the plate's surface?

a) 4.821E+01 N/C

b) 5.303E+01 N/C

c) 5.834E+01 N/C

d) 6.417E+01 N/C

e) 7.059E+01 N/C

c05 I2

1)  $E(z)=\underset{0}{\overset{R}{\int }}f(r^{\prime },z)d{r}^{\prime }$
is an integral that calculates the magnitude of the electric field at a distance $z$ fromthe center of a thin circular disk as measured along a line normal to the plane of the disk. The disk's radius is $R=4.3\text{ m}$ and the surface charge density is $\sigma =2{\text{ nC/m}}^3$. Evaluate $f(r^{\prime },z)$ at $r^{\prime }=2.4\text{ m}$.

a) 5.647E+00 V/m²

b) 6.212E+00 V/m²

c) 6.833E+00 V/m²

d) 7.517E+00 V/m²

e) 8.268E+00 V/m²

2)

Three small charged objects are placed as shown, where $b=2a$, and $a=6\times 10^{-7}\text{m}$.what angle does the force on $q_2$ make above the $-x$ axis if $q_1=3e$, $q_2=-7e$, and $q_3=4e$?

a) 5.914E+01 degrees

b) 6.506E+01 degrees

c) 7.157E+01 degrees

d) 7.872E+01 degrees

e) 8.659E+01 degrees

3)

Three small charged objects are placed as shown, where $b=2a$, and $a=4\times 10^{-7}\text{m}$. What is the magnitude of the net force on $q_2$ if $q_1=2e$, $q_2=-8e$, and $q_3=5e$?

a) 2.248E-14 N

b) 2.473E-14 N

c) 2.721E-14 N

d) 2.993E-14 N

e) 3.292E-14 N

4)

A ring is uniformly charged with a net charge of 2 nC. The radius of the ring is R=1.6 m, with its center at the origin and oriented normal to the z axis as shown. what is the magnitude of the electric field at a distance z=0.99 m (on axis) away from the loop's center?

a) 2.429E+09 N/C²

b) 2.672E+09 N/C²

c) 2.939E+09 N/C²

d) 3.233E+09 N/C²

e) 3.556E+09 N/C²

5) A large thin isolated square plate has an area of 9 m². It is uniformly charged with 6 nC of charge. What is the magnitude of the electric field 1 mm from the center of the plate's surface?

a) 2.571E+01 N/C

b) 2.828E+01 N/C

c) 3.111E+01 N/C

d) 3.422E+01 N/C

e) 3.765E+01 N/C

6)

 $E_z(x=0,z)=\underset{-a}{\overset{b}{\int }}f(x,z)dx$
is an integral that calculates the z-component of the electric field at point P situated above the x-axis where a charged rod of length (a+b) is located. The distance between point P and the x-axis is z=1.9 m. Evaluate $f(x,y)$ at x=0.96 m if a=0.95 m, b=1.8 m. The total charge on the rod is 7 nC.

a) 3.385E+00 V/m²

b) 3.724E+00 V/m²

c) 4.096E+00 V/m²

d) 4.506E+00 V/m²

e) 4.957E+00 V/m²

c05 J0

1)

Three small charged objects are placed as shown, where $b=2a$, and $a=4\times 10^{-7}\text{m}$. What is the magnitude of the net force on $q_2$ if $q_1=2e$, $q_2=-8e$, and $q_3=5e$?

a) 2.248E-14 N

b) 2.473E-14 N

c) 2.721E-14 N

d) 2.993E-14 N

e) 3.292E-14 N

2)

Three small charged objects are placed as shown, where $b=2a$, and $a=2\times 10^{-7}\text{m}$.what angle does the force on $q_2$ make above the $-x$ axis if $q_1=3e$, $q_2=-9e$, and $q_3=5e$?

a) 6.125E+01 degrees

b) 6.738E+01 degrees

c) 7.412E+01 degrees

d) 8.153E+01 degrees

e) 8.968E+01 degrees

3)

 $E_z(x=0,z)=\underset{-a}{\overset{b}{\int }}f(x,z)dx$
is an integral that calculates the z-component of the electric field at point P situated above the x-axis where a charged rod of length (a+b) is located. The distance between point P and the x-axis is z=1.9 m. Evaluate $f(x,y)$ at x=0.54 m if a=1.0 m, b=2.0 m. The total charge on the rod is 3 nC.

a) 1.665E+00 V/m²

b) 1.831E+00 V/m²

c) 2.014E+00 V/m²

d) 2.216E+00 V/m²

e) 2.437E+00 V/m²

4)

A ring is uniformly charged with a net charge of 7 nC. The radius of the ring is R=1.6 m, with its center at the origin and oriented normal to the z axis as shown. what is the magnitude of the electric field at a distance z=0.35 m (on axis) away from the loop's center?

a) 4.142E+09 N/C²

b) 4.556E+09 N/C²

c) 5.012E+09 N/C²

d) 5.513E+09 N/C²

e) 6.064E+09 N/C²

5)  $E(z)=\underset{0}{\overset{R}{\int }}f(r^{\prime },z)d{r}^{\prime }$
is an integral that calculates the magnitude of the electric field at a distance $z$ fromthe center of a thin circular disk as measured along a line normal to the plane of the disk. The disk's radius is $R=9.1\text{ m}$ and the surface charge density is $\sigma =2{\text{ nC/m}}^3$. Evaluate $f(r^{\prime },z)$ at $r^{\prime }=6.2\text{ m}$.

a) 4.961E-01 V/m²

b) 5.457E-01 V/m²

c) 6.002E-01 V/m²

d) 6.603E-01 V/m²

e) 7.263E-01 V/m²

6) A large thin isolated square plate has an area of 4 m². It is uniformly charged with 5 nC of charge. What is the magnitude of the electric field 1 mm from the center of the plate's surface?

a) 4.821E+01 N/C

b) 5.303E+01 N/C

c) 5.834E+01 N/C

d) 6.417E+01 N/C

e) 7.059E+01 N/C

c05 J1

1)

 $E_z(x=0,z)=\underset{-a}{\overset{b}{\int }}f(x,z)dx$
is an integral that calculates the z-component of the electric field at point P situated above the x-axis where a charged rod of length (a+b) is located. The distance between point P and the x-axis is z=1.5 m. Evaluate $f(x,y)$ at x=1.1 m if a=0.61 m, b=1.7 m. The total charge on the rod is 8 nC.

a) 5.995E+00 V/m²

b) 6.595E+00 V/m²

c) 7.254E+00 V/m²

d) 7.980E+00 V/m²

e) 8.778E+00 V/m²

2) A large thin isolated square plate has an area of 3 m². It is uniformly charged with 5 nC of charge. What is the magnitude of the electric field 3 mm from the center of the plate's surface?

a) 9.412E+01 N/C

b) 1.035E+02 N/C

c) 1.139E+02 N/C

d) 1.253E+02 N/C

e) 1.378E+02 N/C

3)  $E(z)=\underset{0}{\overset{R}{\int }}f(r^{\prime },z)d{r}^{\prime }$
is an integral that calculates the magnitude of the electric field at a distance $z$ fromthe center of a thin circular disk as measured along a line normal to the plane of the disk. The disk's radius is $R=7.2\text{ m}$ and the surface charge density is $\sigma =3{\text{ nC/m}}^3$. Evaluate $f(r^{\prime },z)$ at $r^{\prime }=3.6\text{ m}$.

a) 1.606E+00 V/m²

b) 1.767E+00 V/m²

c) 1.943E+00 V/m²

d) 2.138E+00 V/m²

e) 2.351E+00 V/m²

4)

Three small charged objects are placed as shown, where $b=2a$, and $a=4\times 10^{-7}\text{m}$. What is the magnitude of the net force on $q_2$ if $q_1=2e$, $q_2=-8e$, and $q_3=3e$?

a) 2.036E-14 N

b) 2.240E-14 N

c) 2.464E-14 N

d) 2.710E-14 N

e) 2.981E-14 N

5)

A ring is uniformly charged with a net charge of 2 nC. The radius of the ring is R=1.5 m, with its center at the origin and oriented normal to the z axis as shown. what is the magnitude of the electric field at a distance z=0.33 m (on axis) away from the loop's center?

a) 1.353E+09 N/C²

b) 1.488E+09 N/C²

c) 1.637E+09 N/C²

d) 1.801E+09 N/C²

e) 1.981E+09 N/C²

6)

Three small charged objects are placed as shown, where $b=2a$, and $a=4\times 10^{-7}\text{m}$.what angle does the force on $q_2$ make above the $-x$ axis if $q_1=2e$, $q_2=-9e$, and $q_3=5e$?

a) 3.961E+01 degrees

b) 4.357E+01 degrees

c) 4.793E+01 degrees

d) 5.272E+01 degrees

e) 5.799E+01 degrees

c05 J2

1)  $E(z)=\underset{0}{\overset{R}{\int }}f(r^{\prime },z)d{r}^{\prime }$
is an integral that calculates the magnitude of the electric field at a distance $z$ fromthe center of a thin circular disk as measured along a line normal to the plane of the disk. The disk's radius is $R=8.3\text{ m}$ and the surface charge density is $\sigma =5{\text{ nC/m}}^3$. Evaluate $f(r^{\prime },z)$ at $r^{\prime }=5.3\text{ m}$.

a) 1.022E+00 V/m²

b) 1.125E+00 V/m²

c) 1.237E+00 V/m²

d) 1.361E+00 V/m²

e) 1.497E+00 V/m²

2) A large thin isolated square plate has an area of 3 m². It is uniformly charged with 9 nC of charge. What is the magnitude of the electric field 3 mm from the center of the plate's surface?

a) 1.694E+02 N/C

b) 1.864E+02 N/C

c) 2.050E+02 N/C

d) 2.255E+02 N/C

e) 2.480E+02 N/C

3)

Three small charged objects are placed as shown, where $b=2a$, and $a=6\times 10^{-7}\text{m}$. What is the magnitude of the net force on $q_2$ if $q_1=1e$, $q_2=-7e$, and $q_3=2e$?

a) 3.426E-15 N

b) 3.768E-15 N

c) 4.145E-15 N

d) 4.560E-15 N

e) 5.015E-15 N

4)

 $E_z(x=0,z)=\underset{-a}{\overset{b}{\int }}f(x,z)dx$
is an integral that calculates the z-component of the electric field at point P situated above the x-axis where a charged rod of length (a+b) is located. The distance between point P and the x-axis is z=1.8 m. Evaluate $f(x,y)$ at x=0.65 m if a=0.85 m, b=1.8 m. The total charge on the rod is 5 nC.

a) 3.959E+00 V/m²

b) 4.355E+00 V/m²

c) 4.790E+00 V/m²

d) 5.269E+00 V/m²

e) 5.796E+00 V/m²

5)

Three small charged objects are placed as shown, where $b=2a$, and $a=4\times 10^{-7}\text{m}$.what angle does the force on $q_2$ make above the $-x$ axis if $q_1=3e$, $q_2=-9e$, and $q_3=6e$?

a) 5.767E+01 degrees

b) 6.343E+01 degrees

c) 6.978E+01 degrees

d) 7.676E+01 degrees

e) 8.443E+01 degrees

6)

A ring is uniformly charged with a net charge of 8 nC. The radius of the ring is R=1.7 m, with its center at the origin and oriented normal to the z axis as shown. what is the magnitude of the electric field at a distance z=0.32 m (on axis) away from the loop's center?

a) 3.339E+09 N/C²

b) 3.673E+09 N/C²

c) 4.041E+09 N/C²

d) 4.445E+09 N/C²

e) 4.889E+09 N/C²

c05 K0

1)

Three small charged objects are placed as shown, where $b=2a$, and $a=4\times 10^{-7}\text{m}$. What is the magnitude of the net force on $q_2$ if $q_1=2e$, $q_2=-8e$, and $q_3=5e$?

a) 2.248E-14 N

b) 2.473E-14 N

c) 2.721E-14 N

d) 2.993E-14 N

e) 3.292E-14 N

2)

Three small charged objects are placed as shown, where $b=2a$, and $a=4\times 10^{-7}\text{m}$.what angle does the force on $q_2$ make above the $-x$ axis if $q_1=3e$, $q_2=-7e$, and $q_3=5e$?

a) 5.569E+01 degrees

b) 6.125E+01 degrees

c) 6.738E+01 degrees

d) 7.412E+01 degrees

e) 8.153E+01 degrees

3)

 $E_z(x=0,z)=\underset{-a}{\overset{b}{\int }}f(x,z)dx$
is an integral that calculates the z-component of the electric field at point P situated above the x-axis where a charged rod of length (a+b) is located. The distance between point P and the x-axis is z=1.7 m. Evaluate $f(x,y)$ at x=0.52 m if a=0.88 m, b=1.3 m. The total charge on the rod is 6 nC.

a) 6.804E+00 V/m²

b) 7.485E+00 V/m²

c) 8.233E+00 V/m²

d) 9.056E+00 V/m²

e) 9.962E+00 V/m²

4)

A ring is uniformly charged with a net charge of 4 nC. The radius of the ring is R=1.6 m, with its center at the origin and oriented normal to the z axis as shown. what is the magnitude of the electric field at a distance z=1.0 m (on axis) away from the loop's center?

a) 5.352E+09 N/C²

b) 5.887E+09 N/C²

c) 6.476E+09 N/C²

d) 7.124E+09 N/C²

e) 7.836E+09 N/C²

5)  $E(z)=\underset{0}{\overset{R}{\int }}f(r^{\prime },z)d{r}^{\prime }$
is an integral that calculates the magnitude of the electric field at a distance $z$ fromthe center of a thin circular disk as measured along a line normal to the plane of the disk. The disk's radius is $R=3.3\text{ m}$ and the surface charge density is $\sigma =4{\text{ nC/m}}^3$. Evaluate $f(r^{\prime },z)$ at $r^{\prime }=2.0\text{ m}$.

a) 6.877E+00 V/m²

b) 7.565E+00 V/m²

c) 8.321E+00 V/m²

d) 9.153E+00 V/m²

e) 1.007E+01 V/m²

6) A large thin isolated square plate has an area of 4 m². It is uniformly charged with 5 nC of charge. What is the magnitude of the electric field 1 mm from the center of the plate's surface?

a) 4.821E+01 N/C

b) 5.303E+01 N/C

c) 5.834E+01 N/C

d) 6.417E+01 N/C

e) 7.059E+01 N/C

c05 K1

1) A large thin isolated square plate has an area of 4 m². It is uniformly charged with 5 nC of charge. What is the magnitude of the electric field 1 mm from the center of the plate's surface?

a) 4.821E+01 N/C

b) 5.303E+01 N/C

c) 5.834E+01 N/C

d) 6.417E+01 N/C

e) 7.059E+01 N/C

2)  $E(z)=\underset{0}{\overset{R}{\int }}f(r^{\prime },z)d{r}^{\prime }$
is an integral that calculates the magnitude of the electric field at a distance $z$ fromthe center of a thin circular disk as measured along a line normal to the plane of the disk. The disk's radius is $R=2.8\text{ m}$ and the surface charge density is $\sigma =3{\text{ nC/m}}^3$. Evaluate $f(r^{\prime },z)$ at $r^{\prime }=1.9\text{ m}$.

a) 4.295E+00 V/m²

b) 4.724E+00 V/m²

c) 5.196E+00 V/m²

d) 5.716E+00 V/m²

e) 6.288E+00 V/m²

3)

 $E_z(x=0,z)=\underset{-a}{\overset{b}{\int }}f(x,z)dx$
is an integral that calculates the z-component of the electric field at point P situated above the x-axis where a charged rod of length (a+b) is located. The distance between point P and the x-axis is z=1.8 m. Evaluate $f(x,y)$ at x=0.65 m if a=0.85 m, b=1.8 m. The total charge on the rod is 5 nC.

a) 3.959E+00 V/m²

b) 4.355E+00 V/m²

c) 4.790E+00 V/m²

d) 5.269E+00 V/m²

e) 5.796E+00 V/m²

4)

A ring is uniformly charged with a net charge of 5 nC. The radius of the ring is R=1.9 m, with its center at the origin and oriented normal to the z axis as shown. what is the magnitude of the electric field at a distance z=1.3 m (on axis) away from the loop's center?

a) 4.788E+09 N/C²

b) 5.267E+09 N/C²

c) 5.793E+09 N/C²

d) 6.373E+09 N/C²

e) 7.010E+09 N/C²

5)

Three small charged objects are placed as shown, where $b=2a$, and $a=6\times 10^{-7}\text{m}$. What is the magnitude of the net force on $q_2$ if $q_1=1e$, $q_2=-8e$, and $q_3=2e$?

a) 5.732E-15 N

b) 6.305E-15 N

c) 6.936E-15 N

d) 7.629E-15 N

e) 8.392E-15 N

6)

Three small charged objects are placed as shown, where $b=2a$, and $a=2\times 10^{-7}\text{m}$.what angle does the force on $q_2$ make above the $-x$ axis if $q_1=3e$, $q_2=-9e$, and $q_3=5e$?

a) 6.125E+01 degrees

b) 6.738E+01 degrees

c) 7.412E+01 degrees

d) 8.153E+01 degrees

e) 8.968E+01 degrees

c05 K2

1) A large thin isolated square plate has an area of 6 m². It is uniformly charged with 9 nC of charge. What is the magnitude of the electric field 3 mm from the center of the plate's surface?

a) 8.471E+01 N/C

b) 9.318E+01 N/C

c) 1.025E+02 N/C

d) 1.127E+02 N/C

e) 1.240E+02 N/C

2)

Three small charged objects are placed as shown, where $b=2a$, and $a=2\times 10^{-7}\text{m}$. What is the magnitude of the net force on $q_2$ if $q_1=1e$, $q_2=-8e$, and $q_3=3e$?

a) 5.243E-14 N

b) 5.768E-14 N

c) 6.344E-14 N

d) 6.979E-14 N

e) 7.677E-14 N

3)

Three small charged objects are placed as shown, where $b=2a$, and $a=6\times 10^{-7}\text{m}$.what angle does the force on $q_2$ make above the $-x$ axis if $q_1=2e$, $q_2=-9e$, and $q_3=4e$?

a) 4.766E+01 degrees

b) 5.243E+01 degrees

c) 5.767E+01 degrees

d) 6.343E+01 degrees

e) 6.978E+01 degrees

4)  $E(z)=\underset{0}{\overset{R}{\int }}f(r^{\prime },z)d{r}^{\prime }$
is an integral that calculates the magnitude of the electric field at a distance $z$ fromthe center of a thin circular disk as measured along a line normal to the plane of the disk. The disk's radius is $R=1.8\text{ m}$ and the surface charge density is $\sigma =3{\text{ nC/m}}^3$. Evaluate $f(r^{\prime },z)$ at $r^{\prime }=1.1\text{ m}$.

a) 7.517E+00 V/m²

b) 8.269E+00 V/m²

c) 9.096E+00 V/m²

d) 1.001E+01 V/m²

e) 1.101E+01 V/m²

5)

A ring is uniformly charged with a net charge of 5 nC. The radius of the ring is R=1.9 m, with its center at the origin and oriented normal to the z axis as shown. what is the magnitude of the electric field at a distance z=1.3 m (on axis) away from the loop's center?

a) 4.788E+09 N/C²

b) 5.267E+09 N/C²

c) 5.793E+09 N/C²

d) 6.373E+09 N/C²

e) 7.010E+09 N/C²

6)

 $E_z(x=0,z)=\underset{-a}{\overset{b}{\int }}f(x,z)dx$
is an integral that calculates the z-component of the electric field at point P situated above the x-axis where a charged rod of length (a+b) is located. The distance between point P and the x-axis is z=1.8 m. Evaluate $f(x,y)$ at x=1.0 m if a=1.0 m, b=1.8 m. The total charge on the rod is 6 nC.

a) 3.610E+00 V/m²

b) 3.971E+00 V/m²

c) 4.368E+00 V/m²

d) 4.804E+00 V/m²

e) 5.285E+00 V/m²

c05 L0

1)

Three small charged objects are placed as shown, where $b=2a$, and $a=4\times 10^{-7}\text{m}$. What is the magnitude of the net force on $q_2$ if $q_1=3e$, $q_2=-7e$, and $q_3=6e$?

a) 2.544E-14 N

b) 2.798E-14 N

c) 3.078E-14 N

d) 3.385E-14 N

e) 3.724E-14 N

2)

Three small charged objects are placed as shown, where $b=2a$, and $a=4\times 10^{-7}\text{m}$.what angle does the force on $q_2$ make above the $-x$ axis if $q_1=3e$, $q_2=-8e$, and $q_3=6e$?

a) 5.243E+01 degrees

b) 5.767E+01 degrees

c) 6.343E+01 degrees

d) 6.978E+01 degrees

e) 7.676E+01 degrees

3)

 $E_z(x=0,z)=\underset{-a}{\overset{b}{\int }}f(x,z)dx$
is an integral that calculates the z-component of the electric field at point P situated above the x-axis where a charged rod of length (a+b) is located. The distance between point P and the x-axis is z=1.8 m. Evaluate $f(x,y)$ at x=0.65 m if a=0.85 m, b=1.8 m. The total charge on the rod is 5 nC.

a) 3.959E+00 V/m²

b) 4.355E+00 V/m²

c) 4.790E+00 V/m²

d) 5.269E+00 V/m²

e) 5.796E+00 V/m²

4)

A ring is uniformly charged with a net charge of 2 nC. The radius of the ring is R=1.5 m, with its center at the origin and oriented normal to the z axis as shown. what is the magnitude of the electric field at a distance z=0.33 m (on axis) away from the loop's center?

a) 1.353E+09 N/C²

b) 1.488E+09 N/C²

c) 1.637E+09 N/C²

d) 1.801E+09 N/C²

e) 1.981E+09 N/C²

5)  $E(z)=\underset{0}{\overset{R}{\int }}f(r^{\prime },z)d{r}^{\prime }$
is an integral that calculates the magnitude of the electric field at a distance $z$ fromthe center of a thin circular disk as measured along a line normal to the plane of the disk. The disk's radius is $R=2.8\text{ m}$ and the surface charge density is $\sigma =3{\text{ nC/m}}^3$. Evaluate $f(r^{\prime },z)$ at $r^{\prime }=1.9\text{ m}$.

a) 4.295E+00 V/m²

b) 4.724E+00 V/m²

c) 5.196E+00 V/m²

d) 5.716E+00 V/m²

e) 6.288E+00 V/m²

6) A large thin isolated square plate has an area of 6 m². It is uniformly charged with 9 nC of charge. What is the magnitude of the electric field 2 mm from the center of the plate's surface?

a) 7.000E+01 N/C

b) 7.701E+01 N/C

c) 8.471E+01 N/C

d) 9.318E+01 N/C

e) 1.025E+02 N/C

c05 L1

1)

Three small charged objects are placed as shown, where $b=2a$, and $a=2\times 10^{-7}\text{m}$.what angle does the force on $q_2$ make above the $-x$ axis if $q_1=2e$, $q_2=-9e$, and $q_3=4e$?

a) 5.243E+01 degrees

b) 5.767E+01 degrees

c) 6.343E+01 degrees

d) 6.978E+01 degrees

e) 7.676E+01 degrees

2)

 $E_z(x=0,z)=\underset{-a}{\overset{b}{\int }}f(x,z)dx$
is an integral that calculates the z-component of the electric field at point P situated above the x-axis where a charged rod of length (a+b) is located. The distance between point P and the x-axis is z=1.7 m. Evaluate $f(x,y)$ at x=0.76 m if a=1.1 m, b=1.6 m. The total charge on the rod is 8 nC.

a) 5.267E+00 V/m²

b) 5.794E+00 V/m²

c) 6.374E+00 V/m²

d) 7.011E+00 V/m²

e) 7.712E+00 V/m²

3)

A ring is uniformly charged with a net charge of 8 nC. The radius of the ring is R=1.7 m, with its center at the origin and oriented normal to the z axis as shown. what is the magnitude of the electric field at a distance z=0.32 m (on axis) away from the loop's center?

a) 3.339E+09 N/C²

b) 3.673E+09 N/C²

c) 4.041E+09 N/C²

d) 4.445E+09 N/C²

e) 4.889E+09 N/C²

4)

Three small charged objects are placed as shown, where $b=2a$, and $a=6\times 10^{-7}\text{m}$. What is the magnitude of the net force on $q_2$ if $q_1=1e$, $q_2=-8e$, and $q_3=2e$?

a) 5.732E-15 N

b) 6.305E-15 N

c) 6.936E-15 N

d) 7.629E-15 N

e) 8.392E-15 N

5)  $E(z)=\underset{0}{\overset{R}{\int }}f(r^{\prime },z)d{r}^{\prime }$
is an integral that calculates the magnitude of the electric field at a distance $z$ fromthe center of a thin circular disk as measured along a line normal to the plane of the disk. The disk's radius is $R=7.9\text{ m}$ and the surface charge density is $\sigma =2{\text{ nC/m}}^3$. Evaluate $f(r^{\prime },z)$ at $r^{\prime }=5.1\text{ m}$.

a) 8.253E-01 V/m²

b) 9.079E-01 V/m²

c) 9.987E-01 V/m²

d) 1.099E+00 V/m²

e) 1.208E+00 V/m²

6) A large thin isolated square plate has an area of 4 m². It is uniformly charged with 5 nC of charge. What is the magnitude of the electric field 1 mm from the center of the plate's surface?

a) 4.821E+01 N/C

b) 5.303E+01 N/C

c) 5.834E+01 N/C

d) 6.417E+01 N/C

e) 7.059E+01 N/C

c05 L2

1)

 $E_z(x=0,z)=\underset{-a}{\overset{b}{\int }}f(x,z)dx$
is an integral that calculates the z-component of the electric field at point P situated above the x-axis where a charged rod of length (a+b) is located. The distance between point P and the x-axis is z=1.9 m. Evaluate $f(x,y)$ at x=0.83 m if a=0.7 m, b=1.8 m. The total charge on the rod is 9 nC.

a) 6.897E+00 V/m²

b) 7.587E+00 V/m²

c) 8.345E+00 V/m²

d) 9.180E+00 V/m²

e) 1.010E+01 V/m²

2)

Three small charged objects are placed as shown, where $b=2a$, and $a=2\times 10^{-7}\text{m}$.what angle does the force on $q_2$ make above the $-x$ axis if $q_1=1e$, $q_2=-7e$, and $q_3=4e$?

a) 4.091E+01 degrees

b) 4.500E+01 degrees

c) 4.950E+01 degrees

d) 5.445E+01 degrees

e) 5.990E+01 degrees

3) A large thin isolated square plate has an area of 6 m². It is uniformly charged with 5 nC of charge. What is the magnitude of the electric field 1 mm from the center of the plate's surface?

a) 3.214E+01 N/C

b) 3.536E+01 N/C

c) 3.889E+01 N/C

d) 4.278E+01 N/C

e) 4.706E+01 N/C

4)

Three small charged objects are placed as shown, where $b=2a$, and $a=6\times 10^{-7}\text{m}$. What is the magnitude of the net force on $q_2$ if $q_1=1e$, $q_2=-8e$, and $q_3=2e$?

a) 5.732E-15 N

b) 6.305E-15 N

c) 6.936E-15 N

d) 7.629E-15 N

e) 8.392E-15 N

5)  $E(z)=\underset{0}{\overset{R}{\int }}f(r^{\prime },z)d{r}^{\prime }$
is an integral that calculates the magnitude of the electric field at a distance $z$ fromthe center of a thin circular disk as measured along a line normal to the plane of the disk. The disk's radius is $R=8.7\text{ m}$ and the surface charge density is $\sigma =7{\text{ nC/m}}^3$. Evaluate $f(r^{\prime },z)$ at $r^{\prime }=5.8\text{ m}$.

a) 3.722E-01 V/m²

b) 4.094E-01 V/m²

c) 4.504E-01 V/m²

d) 4.954E-01 V/m²

e) 5.450E-01 V/m²

6)

A ring is uniformly charged with a net charge of 6 nC. The radius of the ring is R=1.9 m, with its center at the origin and oriented normal to the z axis as shown. what is the magnitude of the electric field at a distance z=0.4 m (on axis) away from the loop's center?

a) 2.013E+09 N/C²

b) 2.214E+09 N/C²

c) 2.435E+09 N/C²

d) 2.679E+09 N/C²

e) 2.947E+09 N/C²

c05 M0

1)

Three small charged objects are placed as shown, where $b=2a$, and $a=2\times 10^{-7}\text{m}$. What is the magnitude of the net force on $q_2$ if $q_1=1e$, $q_2=-7e$, and $q_3=2e$?

a) 3.391E-14 N

b) 3.731E-14 N

c) 4.104E-14 N

d) 4.514E-14 N

e) 4.965E-14 N

2)

Three small charged objects are placed as shown, where $b=2a$, and $a=2\times 10^{-7}\text{m}$.what angle does the force on $q_2$ make above the $-x$ axis if $q_1=2e$, $q_2=-7e$, and $q_3=3e$?

a) 4.743E+01 degrees

b) 5.217E+01 degrees

c) 5.739E+01 degrees

d) 6.313E+01 degrees

e) 6.944E+01 degrees

3)

 $E_z(x=0,z)=\underset{-a}{\overset{b}{\int }}f(x,z)dx$
is an integral that calculates the z-component of the electric field at point P situated above the x-axis where a charged rod of length (a+b) is located. The distance between point P and the x-axis is z=1.5 m. Evaluate $f(x,y)$ at x=1.1 m if a=0.62 m, b=1.3 m. The total charge on the rod is 7 nC.

a) 6.311E+00 V/m²

b) 6.943E+00 V/m²

c) 7.637E+00 V/m²

d) 8.401E+00 V/m²

e) 9.241E+00 V/m²

4)

A ring is uniformly charged with a net charge of 4 nC. The radius of the ring is R=1.6 m, with its center at the origin and oriented normal to the z axis as shown. what is the magnitude of the electric field at a distance z=1.0 m (on axis) away from the loop's center?

a) 5.352E+09 N/C²

b) 5.887E+09 N/C²

c) 6.476E+09 N/C²

d) 7.124E+09 N/C²

e) 7.836E+09 N/C²

5)  $E(z)=\underset{0}{\overset{R}{\int }}f(r^{\prime },z)d{r}^{\prime }$
is an integral that calculates the magnitude of the electric field at a distance $z$ fromthe center of a thin circular disk as measured along a line normal to the plane of the disk. The disk's radius is $R=2.0\text{ m}$ and the surface charge density is $\sigma =9{\text{ nC/m}}^3$. Evaluate $f(r^{\prime },z)$ at $r^{\prime }=1.2\text{ m}$.

a) 8.933E+00 V/m²

b) 9.826E+00 V/m²

c) 1.081E+01 V/m²

d) 1.189E+01 V/m²

e) 1.308E+01 V/m²

6) A large thin isolated square plate has an area of 3 m². It is uniformly charged with 9 nC of charge. What is the magnitude of the electric field 3 mm from the center of the plate's surface?

a) 1.694E+02 N/C

b) 1.864E+02 N/C

c) 2.050E+02 N/C

d) 2.255E+02 N/C

e) 2.480E+02 N/C

c05 M1

1)

A ring is uniformly charged with a net charge of 3 nC. The radius of the ring is R=1.8 m, with its center at the origin and oriented normal to the z axis as shown. what is the magnitude of the electric field at a distance z=1.1 m (on axis) away from the loop's center?

a) 3.159E+09 N/C²

b) 3.475E+09 N/C²

c) 3.823E+09 N/C²

d) 4.205E+09 N/C²

e) 4.626E+09 N/C²

2)  $E(z)=\underset{0}{\overset{R}{\int }}f(r^{\prime },z)d{r}^{\prime }$
is an integral that calculates the magnitude of the electric field at a distance $z$ fromthe center of a thin circular disk as measured along a line normal to the plane of the disk. The disk's radius is $R=7.5\text{ m}$ and the surface charge density is $\sigma =3{\text{ nC/m}}^3$. Evaluate $f(r^{\prime },z)$ at $r^{\prime }=2.6\text{ m}$.

a) 7.820E-01 V/m²

b) 8.602E-01 V/m²

c) 9.462E-01 V/m²

d) 1.041E+00 V/m²

e) 1.145E+00 V/m²

3)

Three small charged objects are placed as shown, where $b=2a$, and $a=6\times 10^{-7}\text{m}$. What is the magnitude of the net force on $q_2$ if $q_1=2e$, $q_2=-8e$, and $q_3=4e$?

a) 8.613E-15 N

b) 9.474E-15 N

c) 1.042E-14 N

d) 1.146E-14 N

e) 1.261E-14 N

4)

 $E_z(x=0,z)=\underset{-a}{\overset{b}{\int }}f(x,z)dx$
is an integral that calculates the z-component of the electric field at point P situated above the x-axis where a charged rod of length (a+b) is located. The distance between point P and the x-axis is z=1.8 m. Evaluate $f(x,y)$ at x=1.0 m if a=1.0 m, b=1.8 m. The total charge on the rod is 6 nC.

a) 3.610E+00 V/m²

b) 3.971E+00 V/m²

c) 4.368E+00 V/m²

d) 4.804E+00 V/m²

e) 5.285E+00 V/m²

5)

Three small charged objects are placed as shown, where $b=2a$, and $a=4\times 10^{-7}\text{m}$.what angle does the force on $q_2$ make above the $-x$ axis if $q_1=1e$, $q_2=-8e$, and $q_3=4e$?

a) 3.719E+01 degrees

b) 4.091E+01 degrees

c) 4.500E+01 degrees

d) 4.950E+01 degrees

e) 5.445E+01 degrees

6) A large thin isolated square plate has an area of 6 m². It is uniformly charged with 9 nC of charge. What is the magnitude of the electric field 2 mm from the center of the plate's surface?

a) 7.000E+01 N/C

b) 7.701E+01 N/C

c) 8.471E+01 N/C

d) 9.318E+01 N/C

e) 1.025E+02 N/C

c05 M2

1)  $E(z)=\underset{0}{\overset{R}{\int }}f(r^{\prime },z)d{r}^{\prime }$
is an integral that calculates the magnitude of the electric field at a distance $z$ fromthe center of a thin circular disk as measured along a line normal to the plane of the disk. The disk's radius is $R=6.9\text{ m}$ and the surface charge density is $\sigma =9{\text{ nC/m}}^3$. Evaluate $f(r^{\prime },z)$ at $r^{\prime }=4.3\text{ m}$.

a) 8.924E-01 V/m²

b) 9.816E-01 V/m²

c) 1.080E+00 V/m²

d) 1.188E+00 V/m²

e) 1.307E+00 V/m²

2)

 $E_z(x=0,z)=\underset{-a}{\overset{b}{\int }}f(x,z)dx$
is an integral that calculates the z-component of the electric field at point P situated above the x-axis where a charged rod of length (a+b) is located. The distance between point P and the x-axis is z=1.5 m. Evaluate $f(x,y)$ at x=0.79 m if a=0.75 m, b=2.1 m. The total charge on the rod is 6 nC.

a) 5.825E+00 V/m²

b) 6.407E+00 V/m²

c) 7.048E+00 V/m²

d) 7.753E+00 V/m²

e) 8.528E+00 V/m²

3)

Three small charged objects are placed as shown, where $b=2a$, and $a=2\times 10^{-7}\text{m}$.what angle does the force on $q_2$ make above the $-x$ axis if $q_1=2e$, $q_2=-9e$, and $q_3=4e$?

a) 5.243E+01 degrees

b) 5.767E+01 degrees

c) 6.343E+01 degrees

d) 6.978E+01 degrees

e) 7.676E+01 degrees

4) A large thin isolated square plate has an area of 8 m². It is uniformly charged with 7 nC of charge. What is the magnitude of the electric field 3 mm from the center of the plate's surface?

a) 4.492E+01 N/C

b) 4.941E+01 N/C

c) 5.435E+01 N/C

d) 5.979E+01 N/C

e) 6.577E+01 N/C

5)

Three small charged objects are placed as shown, where $b=2a$, and $a=4\times 10^{-7}\text{m}$. What is the magnitude of the net force on $q_2$ if $q_1=3e$, $q_2=-7e$, and $q_3=6e$?

a) 2.544E-14 N

b) 2.798E-14 N

c) 3.078E-14 N

d) 3.385E-14 N

e) 3.724E-14 N

6)

A ring is uniformly charged with a net charge of 2 nC. The radius of the ring is R=1.5 m, with its center at the origin and oriented normal to the z axis as shown. what is the magnitude of the electric field at a distance z=0.33 m (on axis) away from the loop's center?

a) 1.353E+09 N/C²

b) 1.488E+09 N/C²

c) 1.637E+09 N/C²

d) 1.801E+09 N/C²

e) 1.981E+09 N/C²

c05 N0

1)

Three small charged objects are placed as shown, where $b=2a$, and $a=4\times 10^{-7}\text{m}$. What is the magnitude of the net force on $q_2$ if $q_1=2e$, $q_2=-7e$, and $q_3=3e$?

a) 1.473E-14 N

b) 1.620E-14 N

c) 1.782E-14 N

d) 1.960E-14 N

e) 2.156E-14 N

2)

Three small charged objects are placed as shown, where $b=2a$, and $a=2\times 10^{-7}\text{m}$.what angle does the force on $q_2$ make above the $-x$ axis if $q_1=2e$, $q_2=-7e$, and $q_3=5e$?

a) 4.357E+01 degrees

b) 4.793E+01 degrees

c) 5.272E+01 degrees

d) 5.799E+01 degrees

e) 6.379E+01 degrees

3)

 $E_z(x=0,z)=\underset{-a}{\overset{b}{\int }}f(x,z)dx$
is an integral that calculates the z-component of the electric field at point P situated above the x-axis where a charged rod of length (a+b) is located. The distance between point P and the x-axis is z=1.5 m. Evaluate $f(x,y)$ at x=0.79 m if a=0.75 m, b=2.1 m. The total charge on the rod is 6 nC.

a) 5.825E+00 V/m²

b) 6.407E+00 V/m²

c) 7.048E+00 V/m²

d) 7.753E+00 V/m²

e) 8.528E+00 V/m²

4)

A ring is uniformly charged with a net charge of 3 nC. The radius of the ring is R=1.8 m, with its center at the origin and oriented normal to the z axis as shown. what is the magnitude of the electric field at a distance z=1.1 m (on axis) away from the loop's center?

a) 3.159E+09 N/C²

b) 3.475E+09 N/C²

c) 3.823E+09 N/C²

d) 4.205E+09 N/C²

e) 4.626E+09 N/C²

5)  $E(z)=\underset{0}{\overset{R}{\int }}f(r^{\prime },z)d{r}^{\prime }$
is an integral that calculates the magnitude of the electric field at a distance $z$ fromthe center of a thin circular disk as measured along a line normal to the plane of the disk. The disk's radius is $R=7.5\text{ m}$ and the surface charge density is $\sigma =3{\text{ nC/m}}^3$. Evaluate $f(r^{\prime },z)$ at $r^{\prime }=2.6\text{ m}$.

a) 7.820E-01 V/m²

b) 8.602E-01 V/m²

c) 9.462E-01 V/m²

d) 1.041E+00 V/m²

e) 1.145E+00 V/m²

6) A large thin isolated square plate has an area of 4 m². It is uniformly charged with 5 nC of charge. What is the magnitude of the electric field 1 mm from the center of the plate's surface?

a) 4.821E+01 N/C

b) 5.303E+01 N/C

c) 5.834E+01 N/C

d) 6.417E+01 N/C

e) 7.059E+01 N/C

c05 N1

1)

A ring is uniformly charged with a net charge of 7 nC. The radius of the ring is R=1.7 m, with its center at the origin and oriented normal to the z axis as shown. what is the magnitude of the electric field at a distance z=1.1 m (on axis) away from the loop's center?

a) 8.336E+09 N/C²

b) 9.170E+09 N/C²

c) 1.009E+10 N/C²

d) 1.110E+10 N/C²

e) 1.220E+10 N/C²

2)

Three small charged objects are placed as shown, where $b=2a$, and $a=2\times 10^{-7}\text{m}$. What is the magnitude of the net force on $q_2$ if $q_1=1e$, $q_2=-9e$, and $q_3=4e$?

a) 5.014E-14 N

b) 5.515E-14 N

c) 6.067E-14 N

d) 6.674E-14 N

e) 7.341E-14 N

3)  $E(z)=\underset{0}{\overset{R}{\int }}f(r^{\prime },z)d{r}^{\prime }$
is an integral that calculates the magnitude of the electric field at a distance $z$ fromthe center of a thin circular disk as measured along a line normal to the plane of the disk. The disk's radius is $R=9.1\text{ m}$ and the surface charge density is $\sigma =2{\text{ nC/m}}^3$. Evaluate $f(r^{\prime },z)$ at $r^{\prime }=6.2\text{ m}$.

a) 4.961E-01 V/m²

b) 5.457E-01 V/m²

c) 6.002E-01 V/m²

d) 6.603E-01 V/m²

e) 7.263E-01 V/m²

4) A large thin isolated square plate has an area of 9 m². It is uniformly charged with 6 nC of charge. What is the magnitude of the electric field 1 mm from the center of the plate's surface?

a) 2.571E+01 N/C

b) 2.828E+01 N/C

c) 3.111E+01 N/C

d) 3.422E+01 N/C

e) 3.765E+01 N/C

5)

Three small charged objects are placed as shown, where $b=2a$, and $a=2\times 10^{-7}\text{m}$.what angle does the force on $q_2$ make above the $-x$ axis if $q_1=2e$, $q_2=-7e$, and $q_3=5e$?

a) 4.357E+01 degrees

b) 4.793E+01 degrees

c) 5.272E+01 degrees

d) 5.799E+01 degrees

e) 6.379E+01 degrees

6)

 $E_z(x=0,z)=\underset{-a}{\overset{b}{\int }}f(x,z)dx$
is an integral that calculates the z-component of the electric field at point P situated above the x-axis where a charged rod of length (a+b) is located. The distance between point P and the x-axis is z=1.9 m. Evaluate $f(x,y)$ at x=0.96 m if a=0.95 m, b=1.8 m. The total charge on the rod is 7 nC.

a) 3.385E+00 V/m²

b) 3.724E+00 V/m²

c) 4.096E+00 V/m²

d) 4.506E+00 V/m²

e) 4.957E+00 V/m²

c05 N2

1) A large thin isolated square plate has an area of 3 m². It is uniformly charged with 5 nC of charge. What is the magnitude of the electric field 3 mm from the center of the plate's surface?

a) 9.412E+01 N/C

b) 1.035E+02 N/C

c) 1.139E+02 N/C

d) 1.253E+02 N/C

e) 1.378E+02 N/C

2)  $E(z)=\underset{0}{\overset{R}{\int }}f(r^{\prime },z)d{r}^{\prime }$
is an integral that calculates the magnitude of the electric field at a distance $z$ fromthe center of a thin circular disk as measured along a line normal to the plane of the disk. The disk's radius is $R=3.3\text{ m}$ and the surface charge density is $\sigma =4{\text{ nC/m}}^3$. Evaluate $f(r^{\prime },z)$ at $r^{\prime }=2.0\text{ m}$.

a) 6.877E+00 V/m²

b) 7.565E+00 V/m²

c) 8.321E+00 V/m²

d) 9.153E+00 V/m²

e) 1.007E+01 V/m²

3)

A ring is uniformly charged with a net charge of 5 nC. The radius of the ring is R=1.6 m, with its center at the origin and oriented normal to the z axis as shown. what is the magnitude of the electric field at a distance z=1.1 m (on axis) away from the loop's center?

a) 5.581E+09 N/C²

b) 6.139E+09 N/C²

c) 6.753E+09 N/C²

d) 7.428E+09 N/C²

e) 8.171E+09 N/C²

4)

Three small charged objects are placed as shown, where $b=2a$, and $a=4\times 10^{-7}\text{m}$. What is the magnitude of the net force on $q_2$ if $q_1=2e$, $q_2=-7e$, and $q_3=3e$?

a) 1.473E-14 N

b) 1.620E-14 N

c) 1.782E-14 N

d) 1.960E-14 N

e) 2.156E-14 N

5)

Three small charged objects are placed as shown, where $b=2a$, and $a=6\times 10^{-7}\text{m}$.what angle does the force on $q_2$ make above the $-x$ axis if $q_1=3e$, $q_2=-7e$, and $q_3=4e$?

a) 5.914E+01 degrees

b) 6.506E+01 degrees

c) 7.157E+01 degrees

d) 7.872E+01 degrees

e) 8.659E+01 degrees

6)

 $E_z(x=0,z)=\underset{-a}{\overset{b}{\int }}f(x,z)dx$
is an integral that calculates the z-component of the electric field at point P situated above the x-axis where a charged rod of length (a+b) is located. The distance between point P and the x-axis is z=1.2 m. Evaluate $f(x,y)$ at x=0.54 m if a=0.76 m, b=1.7 m. The total charge on the rod is 8 nC.

a) 1.399E+01 V/m²

b) 1.539E+01 V/m²

c) 1.693E+01 V/m²

d) 1.862E+01 V/m²

e) 2.049E+01 V/m²

c05 O0

1)

Three small charged objects are placed as shown, where $b=2a$, and $a=2\times 10^{-7}\text{m}$. What is the magnitude of the net force on $q_2$ if $q_1=1e$, $q_2=-7e$, and $q_3=2e$?

a) 3.391E-14 N

b) 3.731E-14 N

c) 4.104E-14 N

d) 4.514E-14 N

e) 4.965E-14 N

2)

Three small charged objects are placed as shown, where $b=2a$, and $a=6\times 10^{-7}\text{m}$.what angle does the force on $q_2$ make above the $-x$ axis if $q_1=2e$, $q_2=-9e$, and $q_3=4e$?

a) 4.766E+01 degrees

b) 5.243E+01 degrees

c) 5.767E+01 degrees

d) 6.343E+01 degrees

e) 6.978E+01 degrees

3)

 $E_z(x=0,z)=\underset{-a}{\overset{b}{\int }}f(x,z)dx$
is an integral that calculates the z-component of the electric field at point P situated above the x-axis where a charged rod of length (a+b) is located. The distance between point P and the x-axis is z=1.8 m. Evaluate $f(x,y)$ at x=1.0 m if a=1.0 m, b=1.8 m. The total charge on the rod is 6 nC.

a) 3.610E+00 V/m²

b) 3.971E+00 V/m²

c) 4.368E+00 V/m²

d) 4.804E+00 V/m²

e) 5.285E+00 V/m²

4)

A ring is uniformly charged with a net charge of 7 nC. The radius of the ring is R=1.6 m, with its center at the origin and oriented normal to the z axis as shown. what is the magnitude of the electric field at a distance z=0.35 m (on axis) away from the loop's center?

a) 4.142E+09 N/C²

b) 4.556E+09 N/C²

c) 5.012E+09 N/C²

d) 5.513E+09 N/C²

e) 6.064E+09 N/C²

5)  $E(z)=\underset{0}{\overset{R}{\int }}f(r^{\prime },z)d{r}^{\prime }$
is an integral that calculates the magnitude of the electric field at a distance $z$ fromthe center of a thin circular disk as measured along a line normal to the plane of the disk. The disk's radius is $R=1.4\text{ m}$ and the surface charge density is $\sigma =6{\text{ nC/m}}^3$. Evaluate $f(r^{\prime },z)$ at $r^{\prime }=0.56\text{ m}$.

a) 2.567E+01 V/m²

b) 2.824E+01 V/m²

c) 3.106E+01 V/m²

d) 3.417E+01 V/m²

e) 3.759E+01 V/m²

6) A large thin isolated square plate has an area of 6 m². It is uniformly charged with 9 nC of charge. What is the magnitude of the electric field 3 mm from the center of the plate's surface?

a) 8.471E+01 N/C

b) 9.318E+01 N/C

c) 1.025E+02 N/C

d) 1.127E+02 N/C

e) 1.240E+02 N/C

c05 O1

1)

Three small charged objects are placed as shown, where $b=2a$, and $a=2\times 10^{-7}\text{m}$. What is the magnitude of the net force on $q_2$ if $q_1=1e$, $q_2=-7e$, and $q_3=2e$?

a) 3.391E-14 N

b) 3.731E-14 N

c) 4.104E-14 N

d) 4.514E-14 N

e) 4.965E-14 N

2)

A ring is uniformly charged with a net charge of 6 nC. The radius of the ring is R=1.9 m, with its center at the origin and oriented normal to the z axis as shown. what is the magnitude of the electric field at a distance z=0.4 m (on axis) away from the loop's center?

a) 2.013E+09 N/C²

b) 2.214E+09 N/C²

c) 2.435E+09 N/C²

d) 2.679E+09 N/C²

e) 2.947E+09 N/C²

3)

Three small charged objects are placed as shown, where $b=2a$, and $a=4\times 10^{-7}\text{m}$.what angle does the force on $q_2$ make above the $-x$ axis if $q_1=2e$, $q_2=-9e$, and $q_3=5e$?

a) 3.961E+01 degrees

b) 4.357E+01 degrees

c) 4.793E+01 degrees

d) 5.272E+01 degrees

e) 5.799E+01 degrees

4)

 $E_z(x=0,z)=\underset{-a}{\overset{b}{\int }}f(x,z)dx$
is an integral that calculates the z-component of the electric field at point P situated above the x-axis where a charged rod of length (a+b) is located. The distance between point P and the x-axis is z=1.7 m. Evaluate $f(x,y)$ at x=0.52 m if a=0.88 m, b=1.3 m. The total charge on the rod is 6 nC.

a) 6.804E+00 V/m²

b) 7.485E+00 V/m²

c) 8.233E+00 V/m²

d) 9.056E+00 V/m²

e) 9.962E+00 V/m²

5) A large thin isolated square plate has an area of 6 m². It is uniformly charged with 6 nC of charge. What is the magnitude of the electric field 2 mm from the center of the plate's surface?

a) 5.647E+01 N/C

b) 6.212E+01 N/C

c) 6.833E+01 N/C

d) 7.516E+01 N/C

e) 8.268E+01 N/C

6)  $E(z)=\underset{0}{\overset{R}{\int }}f(r^{\prime },z)d{r}^{\prime }$
is an integral that calculates the magnitude of the electric field at a distance $z$ fromthe center of a thin circular disk as measured along a line normal to the plane of the disk. The disk's radius is $R=8.1\text{ m}$ and the surface charge density is $\sigma =3{\text{ nC/m}}^3$. Evaluate $f(r^{\prime },z)$ at $r^{\prime }=4.2\text{ m}$.

a) 5.134E-01 V/m²

b) 5.648E-01 V/m²

c) 6.212E-01 V/m²

d) 6.834E-01 V/m²

e) 7.517E-01 V/m²

c05 O2

1)

Three small charged objects are placed as shown, where $b=2a$, and $a=4\times 10^{-7}\text{m}$.what angle does the force on $q_2$ make above the $-x$ axis if $q_1=3e$, $q_2=-7e$, and $q_3=5e$?

a) 5.569E+01 degrees

b) 6.125E+01 degrees

c) 6.738E+01 degrees

d) 7.412E+01 degrees

e) 8.153E+01 degrees

2) A large thin isolated square plate has an area of 9 m². It is uniformly charged with 8 nC of charge. What is the magnitude of the electric field 3 mm from the center of the plate's surface?

a) 3.428E+01 N/C

b) 3.771E+01 N/C

c) 4.148E+01 N/C

d) 4.563E+01 N/C

e) 5.020E+01 N/C

3)

 $E_z(x=0,z)=\underset{-a}{\overset{b}{\int }}f(x,z)dx$
is an integral that calculates the z-component of the electric field at point P situated above the x-axis where a charged rod of length (a+b) is located. The distance between point P and the x-axis is z=1.9 m. Evaluate $f(x,y)$ at x=0.54 m if a=1.0 m, b=2.0 m. The total charge on the rod is 3 nC.

a) 1.665E+00 V/m²

b) 1.831E+00 V/m²

c) 2.014E+00 V/m²

d) 2.216E+00 V/m²

e) 2.437E+00 V/m²

4)  $E(z)=\underset{0}{\overset{R}{\int }}f(r^{\prime },z)d{r}^{\prime }$
is an integral that calculates the magnitude of the electric field at a distance $z$ fromthe center of a thin circular disk as measured along a line normal to the plane of the disk. The disk's radius is $R=6.8\text{ m}$ and the surface charge density is $\sigma =6{\text{ nC/m}}^3$. Evaluate $f(r^{\prime },z)$ at $r^{\prime }=3.6\text{ m}$.

a) 1.258E+00 V/m²

b) 1.384E+00 V/m²

c) 1.522E+00 V/m²

d) 1.674E+00 V/m²

e) 1.842E+00 V/m²

5)

Three small charged objects are placed as shown, where $b=2a$, and $a=6\times 10^{-7}\text{m}$. What is the magnitude of the net force on $q_2$ if $q_1=3e$, $q_2=-7e$, and $q_3=5e$?

a) 9.958E-15 N

b) 1.095E-14 N

c) 1.205E-14 N

d) 1.325E-14 N

e) 1.458E-14 N

6)

A ring is uniformly charged with a net charge of 7 nC. The radius of the ring is R=1.7 m, with its center at the origin and oriented normal to the z axis as shown. what is the magnitude of the electric field at a distance z=1.2 m (on axis) away from the loop's center?

a) 6.925E+09 N/C²

b) 7.617E+09 N/C²

c) 8.379E+09 N/C²

d) 9.217E+09 N/C²

e) 1.014E+10 N/C²

c05 P0

1)

Three small charged objects are placed as shown, where $b=2a$, and $a=2\times 10^{-7}\text{m}$. What is the magnitude of the net force on $q_2$ if $q_1=1e$, $q_2=-8e$, and $q_3=3e$?

a) 5.243E-14 N

b) 5.768E-14 N

c) 6.344E-14 N

d) 6.979E-14 N

e) 7.677E-14 N

2)

Three small charged objects are placed as shown, where $b=2a$, and $a=2\times 10^{-7}\text{m}$.what angle does the force on $q_2$ make above the $-x$ axis if $q_1=1e$, $q_2=-8e$, and $q_3=3e$?

a) 3.629E+01 degrees

b) 3.992E+01 degrees

c) 4.391E+01 degrees

d) 4.830E+01 degrees

e) 5.313E+01 degrees

3)

 $E_z(x=0,z)=\underset{-a}{\overset{b}{\int }}f(x,z)dx$
is an integral that calculates the z-component of the electric field at point P situated above the x-axis where a charged rod of length (a+b) is located. The distance between point P and the x-axis is z=1.6 m. Evaluate $f(x,y)$ at x=0.73 m if a=0.64 m, b=1.8 m. The total charge on the rod is 3 nC.

a) 2.955E+00 V/m²

b) 3.250E+00 V/m²

c) 3.575E+00 V/m²

d) 3.933E+00 V/m²

e) 4.326E+00 V/m²

4)

A ring is uniformly charged with a net charge of 3 nC. The radius of the ring is R=1.8 m, with its center at the origin and oriented normal to the z axis as shown. what is the magnitude of the electric field at a distance z=1.1 m (on axis) away from the loop's center?

a) 3.159E+09 N/C²

b) 3.475E+09 N/C²

c) 3.823E+09 N/C²

d) 4.205E+09 N/C²

e) 4.626E+09 N/C²

5)  $E(z)=\underset{0}{\overset{R}{\int }}f(r^{\prime },z)d{r}^{\prime }$
is an integral that calculates the magnitude of the electric field at a distance $z$ fromthe center of a thin circular disk as measured along a line normal to the plane of the disk. The disk's radius is $R=1.8\text{ m}$ and the surface charge density is $\sigma =3{\text{ nC/m}}^3$. Evaluate $f(r^{\prime },z)$ at $r^{\prime }=1.1\text{ m}$.

a) 7.517E+00 V/m²

b) 8.269E+00 V/m²

c) 9.096E+00 V/m²

d) 1.001E+01 V/m²

e) 1.101E+01 V/m²

6) A large thin isolated square plate has an area of 6 m². It is uniformly charged with 9 nC of charge. What is the magnitude of the electric field 2 mm from the center of the plate's surface?

a) 7.000E+01 N/C

b) 7.701E+01 N/C

c) 8.471E+01 N/C

d) 9.318E+01 N/C

e) 1.025E+02 N/C

c05 P1

1)

 $E_z(x=0,z)=\underset{-a}{\overset{b}{\int }}f(x,z)dx$
is an integral that calculates the z-component of the electric field at point P situated above the x-axis where a charged rod of length (a+b) is located. The distance between point P and the x-axis is z=1.8 m. Evaluate $f(x,y)$ at x=0.65 m if a=0.85 m, b=1.8 m. The total charge on the rod is 5 nC.

a) 3.959E+00 V/m²

b) 4.355E+00 V/m²

c) 4.790E+00 V/m²

d) 5.269E+00 V/m²

e) 5.796E+00 V/m²

2) A large thin isolated square plate has an area of 8 m². It is uniformly charged with 5 nC of charge. What is the magnitude of the electric field 1 mm from the center of the plate's surface?

a) 2.652E+01 N/C

b) 2.917E+01 N/C

c) 3.209E+01 N/C

d) 3.529E+01 N/C

e) 3.882E+01 N/C

3)

A ring is uniformly charged with a net charge of 5 nC. The radius of the ring is R=1.6 m, with its center at the origin and oriented normal to the z axis as shown. what is the magnitude of the electric field at a distance z=1.1 m (on axis) away from the loop's center?

a) 5.581E+09 N/C²

b) 6.139E+09 N/C²

c) 6.753E+09 N/C²

d) 7.428E+09 N/C²

e) 8.171E+09 N/C²

4)

Three small charged objects are placed as shown, where $b=2a$, and $a=4\times 10^{-7}\text{m}$. What is the magnitude of the net force on $q_2$ if $q_1=3e$, $q_2=-7e$, and $q_3=6e$?

a) 2.544E-14 N

b) 2.798E-14 N

c) 3.078E-14 N

d) 3.385E-14 N

e) 3.724E-14 N

5)

Three small charged objects are placed as shown, where $b=2a$, and $a=6\times 10^{-7}\text{m}$.what angle does the force on $q_2$ make above the $-x$ axis if $q_1=2e$, $q_2=-9e$, and $q_3=5e$?

a) 5.272E+01 degrees

b) 5.799E+01 degrees

c) 6.379E+01 degrees

d) 7.017E+01 degrees

e) 7.719E+01 degrees

6)  $E(z)=\underset{0}{\overset{R}{\int }}f(r^{\prime },z)d{r}^{\prime }$
is an integral that calculates the magnitude of the electric field at a distance $z$ fromthe center of a thin circular disk as measured along a line normal to the plane of the disk. The disk's radius is $R=8.7\text{ m}$ and the surface charge density is $\sigma =7{\text{ nC/m}}^3$. Evaluate $f(r^{\prime },z)$ at $r^{\prime }=5.8\text{ m}$.

a) 3.722E-01 V/m²

b) 4.094E-01 V/m²

c) 4.504E-01 V/m²

d) 4.954E-01 V/m²

e) 5.450E-01 V/m²

c05 P2

1)

A ring is uniformly charged with a net charge of 7 nC. The radius of the ring is R=1.7 m, with its center at the origin and oriented normal to the z axis as shown. what is the magnitude of the electric field at a distance z=1.1 m (on axis) away from the loop's center?

a) 8.336E+09 N/C²

b) 9.170E+09 N/C²

c) 1.009E+10 N/C²

d) 1.110E+10 N/C²

e) 1.220E+10 N/C²

2)  $E(z)=\underset{0}{\overset{R}{\int }}f(r^{\prime },z)d{r}^{\prime }$
is an integral that calculates the magnitude of the electric field at a distance $z$ fromthe center of a thin circular disk as measured along a line normal to the plane of the disk. The disk's radius is $R=7.9\text{ m}$ and the surface charge density is $\sigma =2{\text{ nC/m}}^3$. Evaluate $f(r^{\prime },z)$ at $r^{\prime }=5.1\text{ m}$.

a) 8.253E-01 V/m²

b) 9.079E-01 V/m²

c) 9.987E-01 V/m²

d) 1.099E+00 V/m²

e) 1.208E+00 V/m²

3)

Three small charged objects are placed as shown, where $b=2a$, and $a=2\times 10^{-7}\text{m}$. What is the magnitude of the net force on $q_2$ if $q_1=1e$, $q_2=-8e$, and $q_3=2e$?

a) 3.876E-14 N

b) 4.263E-14 N

c) 4.690E-14 N

d) 5.159E-14 N

e) 5.675E-14 N

4) A large thin isolated square plate has an area of 6 m². It is uniformly charged with 5 nC of charge. What is the magnitude of the electric field 2 mm from the center of the plate's surface?

a) 3.214E+01 N/C

b) 3.536E+01 N/C

c) 3.889E+01 N/C

d) 4.278E+01 N/C

e) 4.706E+01 N/C

5)

Three small charged objects are placed as shown, where $b=2a$, and $a=4\times 10^{-7}\text{m}$.what angle does the force on $q_2$ make above the $-x$ axis if $q_1=1e$, $q_2=-8e$, and $q_3=4e$?

a) 3.719E+01 degrees

b) 4.091E+01 degrees

c) 4.500E+01 degrees

d) 4.950E+01 degrees

e) 5.445E+01 degrees

6)

 $E_z(x=0,z)=\underset{-a}{\overset{b}{\int }}f(x,z)dx$
is an integral that calculates the z-component of the electric field at point P situated above the x-axis where a charged rod of length (a+b) is located. The distance between point P and the x-axis is z=1.5 m. Evaluate $f(x,y)$ at x=0.79 m if a=0.75 m, b=2.1 m. The total charge on the rod is 6 nC.

a) 5.825E+00 V/m²

b) 6.407E+00 V/m²

c) 7.048E+00 V/m²

d) 7.753E+00 V/m²

e) 8.528E+00 V/m²

c05 Q0

1)

Three small charged objects are placed as shown, where $b=2a$, and $a=2\times 10^{-7}\text{m}$. What is the magnitude of the net force on $q_2$ if $q_1=3e$, $q_2=-9e$, and $q_3=6e$?

a) 1.308E-13 N

b) 1.439E-13 N

c) 1.583E-13 N

d) 1.741E-13 N

e) 1.915E-13 N

2)

Three small charged objects are placed as shown, where $b=2a$, and $a=6\times 10^{-7}\text{m}$.what angle does the force on $q_2$ make above the $-x$ axis if $q_1=3e$, $q_2=-7e$, and $q_3=6e$?

a) 6.343E+01 degrees

b) 6.978E+01 degrees

c) 7.676E+01 degrees

d) 8.443E+01 degrees

e) 9.288E+01 degrees

3)

 $E_z(x=0,z)=\underset{-a}{\overset{b}{\int }}f(x,z)dx$
is an integral that calculates the z-component of the electric field at point P situated above the x-axis where a charged rod of length (a+b) is located. The distance between point P and the x-axis is z=1.7 m. Evaluate $f(x,y)$ at x=0.76 m if a=1.1 m, b=1.6 m. The total charge on the rod is 8 nC.

a) 5.267E+00 V/m²

b) 5.794E+00 V/m²

c) 6.374E+00 V/m²

d) 7.011E+00 V/m²

e) 7.712E+00 V/m²

4)

A ring is uniformly charged with a net charge of 8 nC. The radius of the ring is R=1.7 m, with its center at the origin and oriented normal to the z axis as shown. what is the magnitude of the electric field at a distance z=0.32 m (on axis) away from the loop's center?

a) 3.339E+09 N/C²

b) 3.673E+09 N/C²

c) 4.041E+09 N/C²

d) 4.445E+09 N/C²

e) 4.889E+09 N/C²

5)  $E(z)=\underset{0}{\overset{R}{\int }}f(r^{\prime },z)d{r}^{\prime }$
is an integral that calculates the magnitude of the electric field at a distance $z$ fromthe center of a thin circular disk as measured along a line normal to the plane of the disk. The disk's radius is $R=7.5\text{ m}$ and the surface charge density is $\sigma =3{\text{ nC/m}}^3$. Evaluate $f(r^{\prime },z)$ at $r^{\prime }=2.6\text{ m}$.

a) 7.820E-01 V/m²

b) 8.602E-01 V/m²

c) 9.462E-01 V/m²

d) 1.041E+00 V/m²

e) 1.145E+00 V/m²

6) A large thin isolated square plate has an area of 5 m². It is uniformly charged with 8 nC of charge. What is the magnitude of the electric field 3 mm from the center of the plate's surface?

a) 6.171E+01 N/C

b) 6.788E+01 N/C

c) 7.467E+01 N/C

d) 8.214E+01 N/C

e) 9.035E+01 N/C

c05 Q1

1)  $E(z)=\underset{0}{\overset{R}{\int }}f(r^{\prime },z)d{r}^{\prime }$
is an integral that calculates the magnitude of the electric field at a distance $z$ fromthe center of a thin circular disk as measured along a line normal to the plane of the disk. The disk's radius is $R=2.8\text{ m}$ and the surface charge density is $\sigma =3{\text{ nC/m}}^3$. Evaluate $f(r^{\prime },z)$ at $r^{\prime }=1.9\text{ m}$.

a) 4.295E+00 V/m²

b) 4.724E+00 V/m²

c) 5.196E+00 V/m²

d) 5.716E+00 V/m²

e) 6.288E+00 V/m²

2)

A ring is uniformly charged with a net charge of 6 nC. The radius of the ring is R=1.9 m, with its center at the origin and oriented normal to the z axis as shown. what is the magnitude of the electric field at a distance z=0.4 m (on axis) away from the loop's center?

a) 2.013E+09 N/C²

b) 2.214E+09 N/C²

c) 2.435E+09 N/C²

d) 2.679E+09 N/C²

e) 2.947E+09 N/C²

3)

Three small charged objects are placed as shown, where $b=2a$, and $a=2\times 10^{-7}\text{m}$. What is the magnitude of the net force on $q_2$ if $q_1=1e$, $q_2=-8e$, and $q_3=3e$?

a) 5.243E-14 N

b) 5.768E-14 N

c) 6.344E-14 N

d) 6.979E-14 N

e) 7.677E-14 N

4)

Three small charged objects are placed as shown, where $b=2a$, and $a=2\times 10^{-7}\text{m}$.what angle does the force on $q_2$ make above the $-x$ axis if $q_1=1e$, $q_2=-8e$, and $q_3=3e$?

a) 3.629E+01 degrees

b) 3.992E+01 degrees

c) 4.391E+01 degrees

d) 4.830E+01 degrees

e) 5.313E+01 degrees

5)

 $E_z(x=0,z)=\underset{-a}{\overset{b}{\int }}f(x,z)dx$
is an integral that calculates the z-component of the electric field at point P situated above the x-axis where a charged rod of length (a+b) is located. The distance between point P and the x-axis is z=1.9 m. Evaluate $f(x,y)$ at x=0.54 m if a=1.0 m, b=2.0 m. The total charge on the rod is 3 nC.

a) 1.665E+00 V/m²

b) 1.831E+00 V/m²

c) 2.014E+00 V/m²

d) 2.216E+00 V/m²

e) 2.437E+00 V/m²

6) A large thin isolated square plate has an area of 8 m². It is uniformly charged with 5 nC of charge. What is the magnitude of the electric field 1 mm from the center of the plate's surface?

a) 2.652E+01 N/C

b) 2.917E+01 N/C

c) 3.209E+01 N/C

d) 3.529E+01 N/C

e) 3.882E+01 N/C

c05 Q2

1)

Three small charged objects are placed as shown, where $b=2a$, and $a=4\times 10^{-7}\text{m}$. What is the magnitude of the net force on $q_2$ if $q_1=2e$, $q_2=-7e$, and $q_3=3e$?

a) 1.473E-14 N

b) 1.620E-14 N

c) 1.782E-14 N

d) 1.960E-14 N

e) 2.156E-14 N

2)

 $E_z(x=0,z)=\underset{-a}{\overset{b}{\int }}f(x,z)dx$
is an integral that calculates the z-component of the electric field at point P situated above the x-axis where a charged rod of length (a+b) is located. The distance between point P and the x-axis is z=1.6 m. Evaluate $f(x,y)$ at x=0.73 m if a=0.64 m, b=1.8 m. The total charge on the rod is 3 nC.

a) 2.955E+00 V/m²

b) 3.250E+00 V/m²

c) 3.575E+00 V/m²

d) 3.933E+00 V/m²

e) 4.326E+00 V/m²

3)

Three small charged objects are placed as shown, where $b=2a$, and $a=4\times 10^{-7}\text{m}$.what angle does the force on $q_2$ make above the $-x$ axis if $q_1=1e$, $q_2=-8e$, and $q_3=4e$?

a) 3.719E+01 degrees

b) 4.091E+01 degrees

c) 4.500E+01 degrees

d) 4.950E+01 degrees

e) 5.445E+01 degrees

4) A large thin isolated square plate has an area of 6 m². It is uniformly charged with 5 nC of charge. What is the magnitude of the electric field 1 mm from the center of the plate's surface?

a) 3.214E+01 N/C

b) 3.536E+01 N/C

c) 3.889E+01 N/C

d) 4.278E+01 N/C

e) 4.706E+01 N/C

5)  $E(z)=\underset{0}{\overset{R}{\int }}f(r^{\prime },z)d{r}^{\prime }$
is an integral that calculates the magnitude of the electric field at a distance $z$ fromthe center of a thin circular disk as measured along a line normal to the plane of the disk. The disk's radius is $R=9.1\text{ m}$ and the surface charge density is $\sigma =2{\text{ nC/m}}^3$. Evaluate $f(r^{\prime },z)$ at $r^{\prime }=6.2\text{ m}$.

a) 4.961E-01 V/m²

b) 5.457E-01 V/m²

c) 6.002E-01 V/m²

d) 6.603E-01 V/m²

e) 7.263E-01 V/m²

6)

A ring is uniformly charged with a net charge of 9 nC. The radius of the ring is R=1.9 m, with its center at the origin and oriented normal to the z axis as shown. what is the magnitude of the electric field at a distance z=1.4 m (on axis) away from the loop's center?

a) 7.119E+09 N/C²

b) 7.831E+09 N/C²

c) 8.614E+09 N/C²

d) 9.476E+09 N/C²

e) 1.042E+10 N/C²

c05 R0

1)

Three small charged objects are placed as shown, where $b=2a$, and $a=4\times 10^{-7}\text{m}$. What is the magnitude of the net force on $q_2$ if $q_1=2e$, $q_2=-8e$, and $q_3=3e$?

a) 2.036E-14 N

b) 2.240E-14 N

c) 2.464E-14 N

d) 2.710E-14 N

e) 2.981E-14 N

2)

Three small charged objects are placed as shown, where $b=2a$, and $a=6\times 10^{-7}\text{m}$.what angle does the force on $q_2$ make above the $-x$ axis if $q_1=2e$, $q_2=-9e$, and $q_3=4e$?

a) 4.766E+01 degrees

b) 5.243E+01 degrees

c) 5.767E+01 degrees

d) 6.343E+01 degrees

e) 6.978E+01 degrees

3)

 $E_z(x=0,z)=\underset{-a}{\overset{b}{\int }}f(x,z)dx$
is an integral that calculates the z-component of the electric field at point P situated above the x-axis where a charged rod of length (a+b) is located. The distance between point P and the x-axis is z=1.2 m. Evaluate $f(x,y)$ at x=0.54 m if a=0.76 m, b=1.7 m. The total charge on the rod is 8 nC.

a) 1.399E+01 V/m²

b) 1.539E+01 V/m²

c) 1.693E+01 V/m²

d) 1.862E+01 V/m²

e) 2.049E+01 V/m²

4)

A ring is uniformly charged with a net charge of 3 nC. The radius of the ring is R=1.8 m, with its center at the origin and oriented normal to the z axis as shown. what is the magnitude of the electric field at a distance z=1.1 m (on axis) away from the loop's center?

a) 3.159E+09 N/C²

b) 3.475E+09 N/C²

c) 3.823E+09 N/C²

d) 4.205E+09 N/C²

e) 4.626E+09 N/C²

5)  $E(z)=\underset{0}{\overset{R}{\int }}f(r^{\prime },z)d{r}^{\prime }$
is an integral that calculates the magnitude of the electric field at a distance $z$ fromthe center of a thin circular disk as measured along a line normal to the plane of the disk. The disk's radius is $R=2.8\text{ m}$ and the surface charge density is $\sigma =3{\text{ nC/m}}^3$. Evaluate $f(r^{\prime },z)$ at $r^{\prime }=1.9\text{ m}$.

a) 4.295E+00 V/m²

b) 4.724E+00 V/m²

c) 5.196E+00 V/m²

d) 5.716E+00 V/m²

e) 6.288E+00 V/m²

6) A large thin isolated square plate has an area of 9 m². It is uniformly charged with 6 nC of charge. What is the magnitude of the electric field 1 mm from the center of the plate's surface?

a) 2.571E+01 N/C

b) 2.828E+01 N/C

c) 3.111E+01 N/C

d) 3.422E+01 N/C

e) 3.765E+01 N/C

c05 R1

1)  $E(z)=\underset{0}{\overset{R}{\int }}f(r^{\prime },z)d{r}^{\prime }$
is an integral that calculates the magnitude of the electric field at a distance $z$ fromthe center of a thin circular disk as measured along a line normal to the plane of the disk. The disk's radius is $R=3.3\text{ m}$ and the surface charge density is $\sigma =4{\text{ nC/m}}^3$. Evaluate $f(r^{\prime },z)$ at $r^{\prime }=2.0\text{ m}$.

a) 6.877E+00 V/m²

b) 7.565E+00 V/m²

c) 8.321E+00 V/m²

d) 9.153E+00 V/m²

e) 1.007E+01 V/m²

2)

Three small charged objects are placed as shown, where $b=2a$, and $a=2\times 10^{-7}\text{m}$.what angle does the force on $q_2$ make above the $-x$ axis if $q_1=2e$, $q_2=-7e$, and $q_3=5e$?

a) 4.357E+01 degrees

b) 4.793E+01 degrees

c) 5.272E+01 degrees

d) 5.799E+01 degrees

e) 6.379E+01 degrees

3) A large thin isolated square plate has an area of 5 m². It is uniformly charged with 8 nC of charge. What is the magnitude of the electric field 3 mm from the center of the plate's surface?

a) 6.171E+01 N/C

b) 6.788E+01 N/C

c) 7.467E+01 N/C

d) 8.214E+01 N/C

e) 9.035E+01 N/C

4)

 $E_z(x=0,z)=\underset{-a}{\overset{b}{\int }}f(x,z)dx$
is an integral that calculates the z-component of the electric field at point P situated above the x-axis where a charged rod of length (a+b) is located. The distance between point P and the x-axis is z=1.7 m. Evaluate $f(x,y)$ at x=0.76 m if a=1.1 m, b=1.6 m. The total charge on the rod is 8 nC.

a) 5.267E+00 V/m²

b) 5.794E+00 V/m²

c) 6.374E+00 V/m²

d) 7.011E+00 V/m²

e) 7.712E+00 V/m²

5)

Three small charged objects are placed as shown, where $b=2a$, and $a=6\times 10^{-7}\text{m}$. What is the magnitude of the net force on $q_2$ if $q_1=2e$, $q_2=-8e$, and $q_3=4e$?

a) 8.613E-15 N

b) 9.474E-15 N

c) 1.042E-14 N

d) 1.146E-14 N

e) 1.261E-14 N

6)

A ring is uniformly charged with a net charge of 5 nC. The radius of the ring is R=1.6 m, with its center at the origin and oriented normal to the z axis as shown. what is the magnitude of the electric field at a distance z=1.1 m (on axis) away from the loop's center?

a) 5.581E+09 N/C²

b) 6.139E+09 N/C²

c) 6.753E+09 N/C²

d) 7.428E+09 N/C²

e) 8.171E+09 N/C²

c05 R2

1)

A ring is uniformly charged with a net charge of 7 nC. The radius of the ring is R=1.7 m, with its center at the origin and oriented normal to the z axis as shown. what is the magnitude of the electric field at a distance z=1.1 m (on axis) away from the loop's center?

a) 8.336E+09 N/C²

b) 9.170E+09 N/C²

c) 1.009E+10 N/C²

d) 1.110E+10 N/C²

e) 1.220E+10 N/C²

2)

 $E_z(x=0,z)=\underset{-a}{\overset{b}{\int }}f(x,z)dx$
is an integral that calculates the z-component of the electric field at point P situated above the x-axis where a charged rod of length (a+b) is located. The distance between point P and the x-axis is z=1.9 m. Evaluate $f(x,y)$ at x=0.54 m if a=1.0 m, b=2.0 m. The total charge on the rod is 3 nC.

a) 1.665E+00 V/m²

b) 1.831E+00 V/m²

c) 2.014E+00 V/m²

d) 2.216E+00 V/m²

e) 2.437E+00 V/m²

3)

Three small charged objects are placed as shown, where $b=2a$, and $a=4\times 10^{-7}\text{m}$. What is the magnitude of the net force on $q_2$ if $q_1=1e$, $q_2=-8e$, and $q_3=2e$?

a) 1.172E-14 N

b) 1.290E-14 N

c) 1.419E-14 N

d) 1.561E-14 N

e) 1.717E-14 N

4) A large thin isolated square plate has an area of 6 m². It is uniformly charged with 5 nC of charge. What is the magnitude of the electric field 2 mm from the center of the plate's surface?

a) 3.214E+01 N/C

b) 3.536E+01 N/C

c) 3.889E+01 N/C

d) 4.278E+01 N/C

e) 4.706E+01 N/C

5)

Three small charged objects are placed as shown, where $b=2a$, and $a=2\times 10^{-7}\text{m}$.what angle does the force on $q_2$ make above the $-x$ axis if $q_1=2e$, $q_2=-7e$, and $q_3=3e$?

a) 4.743E+01 degrees

b) 5.217E+01 degrees

c) 5.739E+01 degrees

d) 6.313E+01 degrees

e) 6.944E+01 degrees

6)  $E(z)=\underset{0}{\overset{R}{\int }}f(r^{\prime },z)d{r}^{\prime }$
is an integral that calculates the magnitude of the electric field at a distance $z$ fromthe center of a thin circular disk as measured along a line normal to the plane of the disk. The disk's radius is $R=6.9\text{ m}$ and the surface charge density is $\sigma =9{\text{ nC/m}}^3$. Evaluate $f(r^{\prime },z)$ at $r^{\prime }=4.3\text{ m}$.

a) 8.924E-01 V/m²

b) 9.816E-01 V/m²

c) 1.080E+00 V/m²

d) 1.188E+00 V/m²

e) 1.307E+00 V/m²

c05 S0

1)

Three small charged objects are placed as shown, where $b=2a$, and $a=6\times 10^{-7}\text{m}$. What is the magnitude of the net force on $q_2$ if $q_1=3e$, $q_2=-7e$, and $q_3=5e$?

a) 9.958E-15 N

b) 1.095E-14 N

c) 1.205E-14 N

d) 1.325E-14 N

e) 1.458E-14 N

2)

Three small charged objects are placed as shown, where $b=2a$, and $a=6\times 10^{-7}\text{m}$.what angle does the force on $q_2$ make above the $-x$ axis if $q_1=2e$, $q_2=-9e$, and $q_3=4e$?

a) 4.766E+01 degrees

b) 5.243E+01 degrees

c) 5.767E+01 degrees

d) 6.343E+01 degrees

e) 6.978E+01 degrees

3)

 $E_z(x=0,z)=\underset{-a}{\overset{b}{\int }}f(x,z)dx$
is an integral that calculates the z-component of the electric field at point P situated above the x-axis where a charged rod of length (a+b) is located. The distance between point P and the x-axis is z=1.6 m. Evaluate $f(x,y)$ at x=0.73 m if a=0.64 m, b=1.8 m. The total charge on the rod is 3 nC.

a) 2.955E+00 V/m²

b) 3.250E+00 V/m²

c) 3.575E+00 V/m²

d) 3.933E+00 V/m²

e) 4.326E+00 V/m²

4)

A ring is uniformly charged with a net charge of 5 nC. The radius of the ring is R=1.9 m, with its center at the origin and oriented normal to the z axis as shown. what is the magnitude of the electric field at a distance z=1.3 m (on axis) away from the loop's center?

a) 4.788E+09 N/C²

b) 5.267E+09 N/C²

c) 5.793E+09 N/C²

d) 6.373E+09 N/C²

e) 7.010E+09 N/C²

5)  $E(z)=\underset{0}{\overset{R}{\int }}f(r^{\prime },z)d{r}^{\prime }$
is an integral that calculates the magnitude of the electric field at a distance $z$ fromthe center of a thin circular disk as measured along a line normal to the plane of the disk. The disk's radius is $R=2.8\text{ m}$ and the surface charge density is $\sigma =3{\text{ nC/m}}^3$. Evaluate $f(r^{\prime },z)$ at $r^{\prime }=1.9\text{ m}$.

a) 4.295E+00 V/m²

b) 4.724E+00 V/m²

c) 5.196E+00 V/m²

d) 5.716E+00 V/m²

e) 6.288E+00 V/m²

6) A large thin isolated square plate has an area of 5 m². It is uniformly charged with 8 nC of charge. What is the magnitude of the electric field 3 mm from the center of the plate's surface?

a) 6.171E+01 N/C

b) 6.788E+01 N/C

c) 7.467E+01 N/C

d) 8.214E+01 N/C

e) 9.035E+01 N/C

c05 S1

1)

A ring is uniformly charged with a net charge of 3 nC. The radius of the ring is R=1.8 m, with its center at the origin and oriented normal to the z axis as shown. what is the magnitude of the electric field at a distance z=1.1 m (on axis) away from the loop's center?

a) 3.159E+09 N/C²

b) 3.475E+09 N/C²

c) 3.823E+09 N/C²

d) 4.205E+09 N/C²

e) 4.626E+09 N/C²

2)  $E(z)=\underset{0}{\overset{R}{\int }}f(r^{\prime },z)d{r}^{\prime }$
is an integral that calculates the magnitude of the electric field at a distance $z$ fromthe center of a thin circular disk as measured along a line normal to the plane of the disk. The disk's radius is $R=9.1\text{ m}$ and the surface charge density is $\sigma =2{\text{ nC/m}}^3$. Evaluate $f(r^{\prime },z)$ at $r^{\prime }=6.2\text{ m}$.

a) 4.961E-01 V/m²

b) 5.457E-01 V/m²

c) 6.002E-01 V/m²

d) 6.603E-01 V/m²

e) 7.263E-01 V/m²

3)

Three small charged objects are placed as shown, where $b=2a$, and $a=2\times 10^{-7}\text{m}$.what angle does the force on $q_2$ make above the $-x$ axis if $q_1=2e$, $q_2=-7e$, and $q_3=5e$?

a) 4.357E+01 degrees

b) 4.793E+01 degrees

c) 5.272E+01 degrees

d) 5.799E+01 degrees

e) 6.379E+01 degrees

4) A large thin isolated square plate has an area of 3 m². It is uniformly charged with 9 nC of charge. What is the magnitude of the electric field 3 mm from the center of the plate's surface?

a) 1.694E+02 N/C

b) 1.864E+02 N/C

c) 2.050E+02 N/C

d) 2.255E+02 N/C

e) 2.480E+02 N/C

5)

Three small charged objects are placed as shown, where $b=2a$, and $a=6\times 10^{-7}\text{m}$. What is the magnitude of the net force on $q_2$ if $q_1=3e$, $q_2=-7e$, and $q_3=6e$?

a) 1.028E-14 N

b) 1.130E-14 N

c) 1.244E-14 N

d) 1.368E-14 N

e) 1.505E-14 N

6)

 $E_z(x=0,z)=\underset{-a}{\overset{b}{\int }}f(x,z)dx$
is an integral that calculates the z-component of the electric field at point P situated above the x-axis where a charged rod of length (a+b) is located. The distance between point P and the x-axis is z=1.2 m. Evaluate $f(x,y)$ at x=0.54 m if a=0.76 m, b=1.7 m. The total charge on the rod is 8 nC.

a) 1.399E+01 V/m²

b) 1.539E+01 V/m²

c) 1.693E+01 V/m²

d) 1.862E+01 V/m²

e) 2.049E+01 V/m²

c05 S2

1)

Three small charged objects are placed as shown, where $b=2a$, and $a=2\times 10^{-7}\text{m}$. What is the magnitude of the net force on $q_2$ if $q_1=1e$, $q_2=-9e$, and $q_3=4e$?

a) 5.014E-14 N

b) 5.515E-14 N

c) 6.067E-14 N

d) 6.674E-14 N

e) 7.341E-14 N

2)  $E(z)=\underset{0}{\overset{R}{\int }}f(r^{\prime },z)d{r}^{\prime }$
is an integral that calculates the magnitude of the electric field at a distance $z$ fromthe center of a thin circular disk as measured along a line normal to the plane of the disk. The disk's radius is $R=1.4\text{ m}$ and the surface charge density is $\sigma =6{\text{ nC/m}}^3$. Evaluate $f(r^{\prime },z)$ at $r^{\prime }=0.56\text{ m}$.

a) 2.567E+01 V/m²

b) 2.824E+01 V/m²

c) 3.106E+01 V/m²

d) 3.417E+01 V/m²

e) 3.759E+01 V/m²

3)

 $E_z(x=0,z)=\underset{-a}{\overset{b}{\int }}f(x,z)dx$
is an integral that calculates the z-component of the electric field at point P situated above the x-axis where a charged rod of length (a+b) is located. The distance between point P and the x-axis is z=1.8 m. Evaluate $f(x,y)$ at x=0.65 m if a=0.85 m, b=1.8 m. The total charge on the rod is 5 nC.

a) 3.959E+00 V/m²

b) 4.355E+00 V/m²

c) 4.790E+00 V/m²

d) 5.269E+00 V/m²

e) 5.796E+00 V/m²

4)

A ring is uniformly charged with a net charge of 6 nC. The radius of the ring is R=1.9 m, with its center at the origin and oriented normal to the z axis as shown. what is the magnitude of the electric field at a distance z=0.4 m (on axis) away from the loop's center?

a) 2.013E+09 N/C²

b) 2.214E+09 N/C²

c) 2.435E+09 N/C²

d) 2.679E+09 N/C²

e) 2.947E+09 N/C²

5) A large thin isolated square plate has an area of 6 m². It is uniformly charged with 9 nC of charge. What is the magnitude of the electric field 3 mm from the center of the plate's surface?

a) 8.471E+01 N/C

b) 9.318E+01 N/C

c) 1.025E+02 N/C

d) 1.127E+02 N/C

e) 1.240E+02 N/C

6)

Three small charged objects are placed as shown, where $b=2a$, and $a=6\times 10^{-7}\text{m}$.what angle does the force on $q_2$ make above the $-x$ axis if $q_1=3e$, $q_2=-7e$, and $q_3=6e$?

a) 6.343E+01 degrees

b) 6.978E+01 degrees

c) 7.676E+01 degrees

d) 8.443E+01 degrees

e) 9.288E+01 degrees

c05 T0

1)

Three small charged objects are placed as shown, where $b=2a$, and $a=4\times 10^{-7}\text{m}$. What is the magnitude of the net force on $q_2$ if $q_1=2e$, $q_2=-8e$, and $q_3=5e$?

a) 2.248E-14 N

b) 2.473E-14 N

c) 2.721E-14 N

d) 2.993E-14 N

e) 3.292E-14 N

2)

Three small charged objects are placed as shown, where $b=2a$, and $a=4\times 10^{-7}\text{m}$.what angle does the force on $q_2$ make above the $-x$ axis if $q_1=1e$, $q_2=-8e$, and $q_3=4e$?

a) 3.719E+01 degrees

b) 4.091E+01 degrees

c) 4.500E+01 degrees

d) 4.950E+01 degrees

e) 5.445E+01 degrees

3)

 $E_z(x=0,z)=\underset{-a}{\overset{b}{\int }}f(x,z)dx$
is an integral that calculates the z-component of the electric field at point P situated above the x-axis where a charged rod of length (a+b) is located. The distance between point P and the x-axis is z=1.3 m. Evaluate $f(x,y)$ at x=0.83 m if a=0.82 m, b=1.3 m. The total charge on the rod is 7 nC.

a) 8.690E+00 V/m²

b) 9.559E+00 V/m²

c) 1.051E+01 V/m²

d) 1.157E+01 V/m²

e) 1.272E+01 V/m²

4)

A ring is uniformly charged with a net charge of 2 nC. The radius of the ring is R=1.5 m, with its center at the origin and oriented normal to the z axis as shown. what is the magnitude of the electric field at a distance z=0.33 m (on axis) away from the loop's center?

a) 1.353E+09 N/C²

b) 1.488E+09 N/C²

c) 1.637E+09 N/C²

d) 1.801E+09 N/C²

e) 1.981E+09 N/C²

5)  $E(z)=\underset{0}{\overset{R}{\int }}f(r^{\prime },z)d{r}^{\prime }$
is an integral that calculates the magnitude of the electric field at a distance $z$ fromthe center of a thin circular disk as measured along a line normal to the plane of the disk. The disk's radius is $R=8.1\text{ m}$ and the surface charge density is $\sigma =3{\text{ nC/m}}^3$. Evaluate $f(r^{\prime },z)$ at $r^{\prime }=4.2\text{ m}$.

a) 5.134E-01 V/m²

b) 5.648E-01 V/m²

c) 6.212E-01 V/m²

d) 6.834E-01 V/m²

e) 7.517E-01 V/m²

6) A large thin isolated square plate has an area of 3 m². It is uniformly charged with 9 nC of charge. What is the magnitude of the electric field 3 mm from the center of the plate's surface?

a) 1.694E+02 N/C

b) 1.864E+02 N/C

c) 2.050E+02 N/C

d) 2.255E+02 N/C

e) 2.480E+02 N/C

c05 T1

1)

A ring is uniformly charged with a net charge of 7 nC. The radius of the ring is R=1.6 m, with its center at the origin and oriented normal to the z axis as shown. what is the magnitude of the electric field at a distance z=0.34 m (on axis) away from the loop's center?

a) 3.672E+09 N/C²

b) 4.039E+09 N/C²

c) 4.443E+09 N/C²

d) 4.887E+09 N/C²

e) 5.376E+09 N/C²

2) A large thin isolated square plate has an area of 4 m². It is uniformly charged with 5 nC of charge. What is the magnitude of the electric field 1 mm from the center of the plate's surface?

a) 4.821E+01 N/C

b) 5.303E+01 N/C

c) 5.834E+01 N/C

d) 6.417E+01 N/C

e) 7.059E+01 N/C

3)

Three small charged objects are placed as shown, where $b=2a$, and $a=6\times 10^{-7}\text{m}$. What is the magnitude of the net force on $q_2$ if $q_1=3e$, $q_2=-7e$, and $q_3=5e$?

a) 9.958E-15 N

b) 1.095E-14 N

c) 1.205E-14 N

d) 1.325E-14 N

e) 1.458E-14 N

4)

Three small charged objects are placed as shown, where $b=2a$, and $a=2\times 10^{-7}\text{m}$.what angle does the force on $q_2$ make above the $-x$ axis if $q_1=1e$, $q_2=-7e$, and $q_3=4e$?

a) 4.091E+01 degrees

b) 4.500E+01 degrees

c) 4.950E+01 degrees

d) 5.445E+01 degrees

e) 5.990E+01 degrees

5)

 $E_z(x=0,z)=\underset{-a}{\overset{b}{\int }}f(x,z)dx$
is an integral that calculates the z-component of the electric field at point P situated above the x-axis where a charged rod of length (a+b) is located. The distance between point P and the x-axis is z=1.2 m. Evaluate $f(x,y)$ at x=0.73 m if a=0.52 m, b=1.6 m. The total charge on the rod is 7 nC.

a) 9.655E+00 V/m²

b) 1.062E+01 V/m²

c) 1.168E+01 V/m²

d) 1.285E+01 V/m²

e) 1.414E+01 V/m²

6)  $E(z)=\underset{0}{\overset{R}{\int }}f(r^{\prime },z)d{r}^{\prime }$
is an integral that calculates the magnitude of the electric field at a distance $z$ fromthe center of a thin circular disk as measured along a line normal to the plane of the disk. The disk's radius is $R=8.7\text{ m}$ and the surface charge density is $\sigma =7{\text{ nC/m}}^3$. Evaluate $f(r^{\prime },z)$ at $r^{\prime }=5.8\text{ m}$.

a) 3.722E-01 V/m²

b) 4.094E-01 V/m²

c) 4.504E-01 V/m²

d) 4.954E-01 V/m²

e) 5.450E-01 V/m²

c05 T2

1) A large thin isolated square plate has an area of 6 m². It is uniformly charged with 9 nC of charge. What is the magnitude of the electric field 2 mm from the center of the plate's surface?

a) 7.000E+01 N/C

b) 7.701E+01 N/C

c) 8.471E+01 N/C

d) 9.318E+01 N/C

e) 1.025E+02 N/C

2)  $E(z)=\underset{0}{\overset{R}{\int }}f(r^{\prime },z)d{r}^{\prime }$
is an integral that calculates the magnitude of the electric field at a distance $z$ fromthe center of a thin circular disk as measured along a line normal to the plane of the disk. The disk's radius is $R=1.8\text{ m}$ and the surface charge density is $\sigma =3{\text{ nC/m}}^3$. Evaluate $f(r^{\prime },z)$ at $r^{\prime }=1.1\text{ m}$.

a) 7.517E+00 V/m²

b) 8.269E+00 V/m²

c) 9.096E+00 V/m²

d) 1.001E+01 V/m²

e) 1.101E+01 V/m²

3)

A ring is uniformly charged with a net charge of 9 nC. The radius of the ring is R=1.6 m, with its center at the origin and oriented normal to the z axis as shown. what is the magnitude of the electric field at a distance z=0.73 m (on axis) away from the loop's center?

a) 7.415E+09 N/C²

b) 8.156E+09 N/C²

c) 8.972E+09 N/C²

d) 9.869E+09 N/C²

e) 1.086E+10 N/C²

4)

Three small charged objects are placed as shown, where $b=2a$, and $a=4\times 10^{-7}\text{m}$. What is the magnitude of the net force on $q_2$ if $q_1=1e$, $q_2=-8e$, and $q_3=2e$?

a) 1.172E-14 N

b) 1.290E-14 N

c) 1.419E-14 N

d) 1.561E-14 N

e) 1.717E-14 N

5)

Three small charged objects are placed as shown, where $b=2a$, and $a=2\times 10^{-7}\text{m}$.what angle does the force on $q_2$ make above the $-x$ axis if $q_1=2e$, $q_2=-7e$, and $q_3=3e$?

a) 4.743E+01 degrees

b) 5.217E+01 degrees

c) 5.739E+01 degrees

d) 6.313E+01 degrees

e) 6.944E+01 degrees

6)

 $E_z(x=0,z)=\underset{-a}{\overset{b}{\int }}f(x,z)dx$
is an integral that calculates the z-component of the electric field at point P situated above the x-axis where a charged rod of length (a+b) is located. The distance between point P and the x-axis is z=1.8 m. Evaluate $f(x,y)$ at x=0.65 m if a=0.85 m, b=1.8 m. The total charge on the rod is 5 nC.

a) 3.959E+00 V/m²

b) 4.355E+00 V/m²

c) 4.790E+00 V/m²

d) 5.269E+00 V/m²

e) 5.796E+00 V/m²

c05 U0

1)

Three small charged objects are placed as shown, where $b=2a$, and $a=6\times 10^{-7}\text{m}$. What is the magnitude of the net force on $q_2$ if $q_1=1e$, $q_2=-7e$, and $q_3=2e$?

a) 3.426E-15 N

b) 3.768E-15 N

c) 4.145E-15 N

d) 4.560E-15 N

e) 5.015E-15 N

2)

Three small charged objects are placed as shown, where $b=2a$, and $a=4\times 10^{-7}\text{m}$.what angle does the force on $q_2$ make above the $-x$ axis if $q_1=1e$, $q_2=-8e$, and $q_3=4e$?

a) 3.719E+01 degrees

b) 4.091E+01 degrees

c) 4.500E+01 degrees

d) 4.950E+01 degrees

e) 5.445E+01 degrees

3)

 $E_z(x=0,z)=\underset{-a}{\overset{b}{\int }}f(x,z)dx$
is an integral that calculates the z-component of the electric field at point P situated above the x-axis where a charged rod of length (a+b) is located. The distance between point P and the x-axis is z=1.3 m. Evaluate $f(x,y)$ at x=0.83 m if a=0.82 m, b=1.3 m. The total charge on the rod is 7 nC.

a) 8.690E+00 V/m²

b) 9.559E+00 V/m²

c) 1.051E+01 V/m²

d) 1.157E+01 V/m²

e) 1.272E+01 V/m²

4)

A ring is uniformly charged with a net charge of 8 nC. The radius of the ring is R=1.7 m, with its center at the origin and oriented normal to the z axis as shown. what is the magnitude of the electric field at a distance z=0.32 m (on axis) away from the loop's center?

a) 3.339E+09 N/C²

b) 3.673E+09 N/C²

c) 4.041E+09 N/C²

d) 4.445E+09 N/C²

e) 4.889E+09 N/C²

5)  $E(z)=\underset{0}{\overset{R}{\int }}f(r^{\prime },z)d{r}^{\prime }$
is an integral that calculates the magnitude of the electric field at a distance $z$ fromthe center of a thin circular disk as measured along a line normal to the plane of the disk. The disk's radius is $R=3.0\text{ m}$ and the surface charge density is $\sigma =8{\text{ nC/m}}^3$. Evaluate $f(r^{\prime },z)$ at $r^{\prime }=2.0\text{ m}$.

a) 9.459E+00 V/m²

b) 1.040E+01 V/m²

c) 1.145E+01 V/m²

d) 1.259E+01 V/m²

e) 1.385E+01 V/m²

6) A large thin isolated square plate has an area of 6 m². It is uniformly charged with 9 nC of charge. What is the magnitude of the electric field 1 mm from the center of the plate's surface?

a) 7.701E+01 N/C

b) 8.471E+01 N/C

c) 9.318E+01 N/C

d) 1.025E+02 N/C

e) 1.127E+02 N/C

c05 U1

1) A large thin isolated square plate has an area of 9 m². It is uniformly charged with 5 nC of charge. What is the magnitude of the electric field 1 mm from the center of the plate's surface?

a) 2.357E+01 N/C

b) 2.593E+01 N/C

c) 2.852E+01 N/C

d) 3.137E+01 N/C

e) 3.451E+01 N/C

2)

A ring is uniformly charged with a net charge of 6 nC. The radius of the ring is R=1.9 m, with its center at the origin and oriented normal to the z axis as shown. what is the magnitude of the electric field at a distance z=0.4 m (on axis) away from the loop's center?

a) 2.013E+09 N/C²

b) 2.214E+09 N/C²

c) 2.435E+09 N/C²

d) 2.679E+09 N/C²

e) 2.947E+09 N/C²

3)

Three small charged objects are placed as shown, where $b=2a$, and $a=6\times 10^{-7}\text{m}$.what angle does the force on $q_2$ make above the $-x$ axis if $q_1=2e$, $q_2=-9e$, and $q_3=5e$?

a) 5.272E+01 degrees

b) 5.799E+01 degrees

c) 6.379E+01 degrees

d) 7.017E+01 degrees

e) 7.719E+01 degrees

4)

Three small charged objects are placed as shown, where $b=2a$, and $a=2\times 10^{-7}\text{m}$. What is the magnitude of the net force on $q_2$ if $q_1=3e$, $q_2=-9e$, and $q_3=6e$?

a) 1.308E-13 N

b) 1.439E-13 N

c) 1.583E-13 N

d) 1.741E-13 N

e) 1.915E-13 N

5)

 $E_z(x=0,z)=\underset{-a}{\overset{b}{\int }}f(x,z)dx$
is an integral that calculates the z-component of the electric field at point P situated above the x-axis where a charged rod of length (a+b) is located. The distance between point P and the x-axis is z=1.5 m. Evaluate $f(x,y)$ at x=1.1 m if a=0.61 m, b=1.7 m. The total charge on the rod is 8 nC.

a) 5.995E+00 V/m²

b) 6.595E+00 V/m²

c) 7.254E+00 V/m²

d) 7.980E+00 V/m²

e) 8.778E+00 V/m²

6)  $E(z)=\underset{0}{\overset{R}{\int }}f(r^{\prime },z)d{r}^{\prime }$
is an integral that calculates the magnitude of the electric field at a distance $z$ fromthe center of a thin circular disk as measured along a line normal to the plane of the disk. The disk's radius is $R=9.1\text{ m}$ and the surface charge density is $\sigma =2{\text{ nC/m}}^3$. Evaluate $f(r^{\prime },z)$ at $r^{\prime }=6.2\text{ m}$.

a) 4.961E-01 V/m²

b) 5.457E-01 V/m²

c) 6.002E-01 V/m²

d) 6.603E-01 V/m²

e) 7.263E-01 V/m²

c05 U2

1) A large thin isolated square plate has an area of 9 m². It is uniformly charged with 6 nC of charge. What is the magnitude of the electric field 1 mm from the center of the plate's surface?

a) 2.571E+01 N/C

b) 2.828E+01 N/C

c) 3.111E+01 N/C

d) 3.422E+01 N/C

e) 3.765E+01 N/C

2)

A ring is uniformly charged with a net charge of 8 nC. The radius of the ring is R=1.7 m, with its center at the origin and oriented normal to the z axis as shown. what is the magnitude of the electric field at a distance z=0.32 m (on axis) away from the loop's center?

a) 3.339E+09 N/C²

b) 3.673E+09 N/C²

c) 4.041E+09 N/C²

d) 4.445E+09 N/C²

e) 4.889E+09 N/C²

3)

Three small charged objects are placed as shown, where $b=2a$, and $a=6\times 10^{-7}\text{m}$.what angle does the force on $q_2$ make above the $-x$ axis if $q_1=3e$, $q_2=-7e$, and $q_3=6e$?

a) 6.343E+01 degrees

b) 6.978E+01 degrees

c) 7.676E+01 degrees

d) 8.443E+01 degrees

e) 9.288E+01 degrees

4)  $E(z)=\underset{0}{\overset{R}{\int }}f(r^{\prime },z)d{r}^{\prime }$
is an integral that calculates the magnitude of the electric field at a distance $z$ fromthe center of a thin circular disk as measured along a line normal to the plane of the disk. The disk's radius is $R=7.2\text{ m}$ and the surface charge density is $\sigma =3{\text{ nC/m}}^3$. Evaluate $f(r^{\prime },z)$ at $r^{\prime }=3.6\text{ m}$.

a) 1.606E+00 V/m²

b) 1.767E+00 V/m²

c) 1.943E+00 V/m²

d) 2.138E+00 V/m²

e) 2.351E+00 V/m²

5)

Three small charged objects are placed as shown, where $b=2a$, and $a=6\times 10^{-7}\text{m}$. What is the magnitude of the net force on $q_2$ if $q_1=3e$, $q_2=-7e$, and $q_3=5e$?

a) 9.958E-15 N

b) 1.095E-14 N

c) 1.205E-14 N

d) 1.325E-14 N

e) 1.458E-14 N

6)

 $E_z(x=0,z)=\underset{-a}{\overset{b}{\int }}f(x,z)dx$
is an integral that calculates the z-component of the electric field at point P situated above the x-axis where a charged rod of length (a+b) is located. The distance between point P and the x-axis is z=1.8 m. Evaluate $f(x,y)$ at x=1.0 m if a=1.0 m, b=1.8 m. The total charge on the rod is 6 nC.

a) 3.610E+00 V/m²

b) 3.971E+00 V/m²

c) 4.368E+00 V/m²

d) 4.804E+00 V/m²

e) 5.285E+00 V/m²

c05 V0

1)

Three small charged objects are placed as shown, where $b=2a$, and $a=2\times 10^{-7}\text{m}$. What is the magnitude of the net force on $q_2$ if $q_1=1e$, $q_2=-8e$, and $q_3=2e$?

a) 3.876E-14 N

b) 4.263E-14 N

c) 4.690E-14 N

d) 5.159E-14 N

e) 5.675E-14 N

2)

Three small charged objects are placed as shown, where $b=2a$, and $a=4\times 10^{-7}\text{m}$.what angle does the force on $q_2$ make above the $-x$ axis if $q_1=3e$, $q_2=-7e$, and $q_3=5e$?

a) 5.569E+01 degrees

b) 6.125E+01 degrees

c) 6.738E+01 degrees

d) 7.412E+01 degrees

e) 8.153E+01 degrees

3)

 $E_z(x=0,z)=\underset{-a}{\overset{b}{\int }}f(x,z)dx$
is an integral that calculates the z-component of the electric field at point P situated above the x-axis where a charged rod of length (a+b) is located. The distance between point P and the x-axis is z=1.5 m. Evaluate $f(x,y)$ at x=0.79 m if a=0.75 m, b=2.1 m. The total charge on the rod is 6 nC.

a) 5.825E+00 V/m²

b) 6.407E+00 V/m²

c) 7.048E+00 V/m²

d) 7.753E+00 V/m²

e) 8.528E+00 V/m²

4)

A ring is uniformly charged with a net charge of 4 nC. The radius of the ring is R=1.6 m, with its center at the origin and oriented normal to the z axis as shown. what is the magnitude of the electric field at a distance z=1.1 m (on axis) away from the loop's center?

a) 5.402E+09 N/C²

b) 5.943E+09 N/C²

c) 6.537E+09 N/C²

d) 7.191E+09 N/C²

e) 7.910E+09 N/C²

5)  $E(z)=\underset{0}{\overset{R}{\int }}f(r^{\prime },z)d{r}^{\prime }$
is an integral that calculates the magnitude of the electric field at a distance $z$ fromthe center of a thin circular disk as measured along a line normal to the plane of the disk. The disk's radius is $R=4.3\text{ m}$ and the surface charge density is $\sigma =2{\text{ nC/m}}^3$. Evaluate $f(r^{\prime },z)$ at $r^{\prime }=2.4\text{ m}$.

a) 5.647E+00 V/m²

b) 6.212E+00 V/m²

c) 6.833E+00 V/m²

d) 7.517E+00 V/m²

e) 8.268E+00 V/m²

6) A large thin isolated square plate has an area of 6 m². It is uniformly charged with 5 nC of charge. What is the magnitude of the electric field 1 mm from the center of the plate's surface?

a) 3.214E+01 N/C

b) 3.536E+01 N/C

c) 3.889E+01 N/C

d) 4.278E+01 N/C

e) 4.706E+01 N/C

c05 V1

1)

A ring is uniformly charged with a net charge of 5 nC. The radius of the ring is R=1.6 m, with its center at the origin and oriented normal to the z axis as shown. what is the magnitude of the electric field at a distance z=1.1 m (on axis) away from the loop's center?

a) 5.581E+09 N/C²

b) 6.139E+09 N/C²

c) 6.753E+09 N/C²

d) 7.428E+09 N/C²

e) 8.171E+09 N/C²

2)  $E(z)=\underset{0}{\overset{R}{\int }}f(r^{\prime },z)d{r}^{\prime }$
is an integral that calculates the magnitude of the electric field at a distance $z$ fromthe center of a thin circular disk as measured along a line normal to the plane of the disk. The disk's radius is $R=3.2\text{ m}$ and the surface charge density is $\sigma =2{\text{ nC/m}}^3$. Evaluate $f(r^{\prime },z)$ at $r^{\prime }=2.2\text{ m}$.

a) 3.228E+00 V/m²

b) 3.551E+00 V/m²

c) 3.906E+00 V/m²

d) 4.297E+00 V/m²

e) 4.727E+00 V/m²

3)

 $E_z(x=0,z)=\underset{-a}{\overset{b}{\int }}f(x,z)dx$
is an integral that calculates the z-component of the electric field at point P situated above the x-axis where a charged rod of length (a+b) is located. The distance between point P and the x-axis is z=1.9 m. Evaluate $f(x,y)$ at x=0.96 m if a=0.95 m, b=1.8 m. The total charge on the rod is 7 nC.

a) 3.385E+00 V/m²

b) 3.724E+00 V/m²

c) 4.096E+00 V/m²

d) 4.506E+00 V/m²

e) 4.957E+00 V/m²

4) A large thin isolated square plate has an area of 8 m². It is uniformly charged with 7 nC of charge. What is the magnitude of the electric field 3 mm from the center of the plate's surface?

a) 4.492E+01 N/C

b) 4.941E+01 N/C

c) 5.435E+01 N/C

d) 5.979E+01 N/C

e) 6.577E+01 N/C

5)

Three small charged objects are placed as shown, where $b=2a$, and $a=2\times 10^{-7}\text{m}$.what angle does the force on $q_2$ make above the $-x$ axis if $q_1=1e$, $q_2=-8e$, and $q_3=3e$?

a) 3.629E+01 degrees

b) 3.992E+01 degrees

c) 4.391E+01 degrees

d) 4.830E+01 degrees

e) 5.313E+01 degrees

6)

Three small charged objects are placed as shown, where $b=2a$, and $a=2\times 10^{-7}\text{m}$. What is the magnitude of the net force on $q_2$ if $q_1=1e$, $q_2=-8e$, and $q_3=3e$?

a) 5.243E-14 N

b) 5.768E-14 N

c) 6.344E-14 N

d) 6.979E-14 N

e) 7.677E-14 N

c05 V2

1)

 $E_z(x=0,z)=\underset{-a}{\overset{b}{\int }}f(x,z)dx$
is an integral that calculates the z-component of the electric field at point P situated above the x-axis where a charged rod of length (a+b) is located. The distance between point P and the x-axis is z=1.8 m. Evaluate $f(x,y)$ at x=0.5 m if a=0.67 m, b=2.4 m. The total charge on the rod is 9 nC.

a) 5.465E+00 V/m²

b) 6.012E+00 V/m²

c) 6.613E+00 V/m²

d) 7.274E+00 V/m²

e) 8.002E+00 V/m²

2)

A ring is uniformly charged with a net charge of 2 nC. The radius of the ring is R=1.6 m, with its center at the origin and oriented normal to the z axis as shown. what is the magnitude of the electric field at a distance z=0.99 m (on axis) away from the loop's center?

a) 2.429E+09 N/C²

b) 2.672E+09 N/C²

c) 2.939E+09 N/C²

d) 3.233E+09 N/C²

e) 3.556E+09 N/C²

3)

Three small charged objects are placed as shown, where $b=2a$, and $a=6\times 10^{-7}\text{m}$.what angle does the force on $q_2$ make above the $-x$ axis if $q_1=3e$, $q_2=-7e$, and $q_3=6e$?

a) 6.343E+01 degrees

b) 6.978E+01 degrees

c) 7.676E+01 degrees

d) 8.443E+01 degrees

e) 9.288E+01 degrees

4) A large thin isolated square plate has an area of 6 m². It is uniformly charged with 5 nC of charge. What is the magnitude of the electric field 2 mm from the center of the plate's surface?

a) 3.214E+01 N/C

b) 3.536E+01 N/C

c) 3.889E+01 N/C

d) 4.278E+01 N/C

e) 4.706E+01 N/C

5)

Three small charged objects are placed as shown, where $b=2a$, and $a=6\times 10^{-7}\text{m}$. What is the magnitude of the net force on $q_2$ if $q_1=3e$, $q_2=-7e$, and $q_3=6e$?

a) 1.028E-14 N

b) 1.130E-14 N

c) 1.244E-14 N

d) 1.368E-14 N

e) 1.505E-14 N

6)  $E(z)=\underset{0}{\overset{R}{\int }}f(r^{\prime },z)d{r}^{\prime }$
is an integral that calculates the magnitude of the electric field at a distance $z$ fromthe center of a thin circular disk as measured along a line normal to the plane of the disk. The disk's radius is $R=7.2\text{ m}$ and the surface charge density is $\sigma =3{\text{ nC/m}}^3$. Evaluate $f(r^{\prime },z)$ at $r^{\prime }=3.6\text{ m}$.

a) 1.606E+00 V/m²

b) 1.767E+00 V/m²

c) 1.943E+00 V/m²

d) 2.138E+00 V/m²

e) 2.351E+00 V/m²

c05 W0

1)

Three small charged objects are placed as shown, where $b=2a$, and $a=2\times 10^{-7}\text{m}$. What is the magnitude of the net force on $q_2$ if $q_1=1e$, $q_2=-9e$, and $q_3=4e$?

a) 5.014E-14 N

b) 5.515E-14 N

c) 6.067E-14 N

d) 6.674E-14 N

e) 7.341E-14 N

2)

Three small charged objects are placed as shown, where $b=2a$, and $a=2\times 10^{-7}\text{m}$.what angle does the force on $q_2$ make above the $-x$ axis if $q_1=2e$, $q_2=-7e$, and $q_3=3e$?

a) 4.743E+01 degrees

b) 5.217E+01 degrees

c) 5.739E+01 degrees

d) 6.313E+01 degrees

e) 6.944E+01 degrees

3)

 $E_z(x=0,z)=\underset{-a}{\overset{b}{\int }}f(x,z)dx$
is an integral that calculates the z-component of the electric field at point P situated above the x-axis where a charged rod of length (a+b) is located. The distance between point P and the x-axis is z=1.5 m. Evaluate $f(x,y)$ at x=1.1 m if a=0.62 m, b=1.3 m. The total charge on the rod is 7 nC.

a) 6.311E+00 V/m²

b) 6.943E+00 V/m²

c) 7.637E+00 V/m²

d) 8.401E+00 V/m²

e) 9.241E+00 V/m²

4)

A ring is uniformly charged with a net charge of 6 nC. The radius of the ring is R=1.9 m, with its center at the origin and oriented normal to the z axis as shown. what is the magnitude of the electric field at a distance z=0.4 m (on axis) away from the loop's center?

a) 2.013E+09 N/C²

b) 2.214E+09 N/C²

c) 2.435E+09 N/C²

d) 2.679E+09 N/C²

e) 2.947E+09 N/C²

5)  $E(z)=\underset{0}{\overset{R}{\int }}f(r^{\prime },z)d{r}^{\prime }$
is an integral that calculates the magnitude of the electric field at a distance $z$ fromthe center of a thin circular disk as measured along a line normal to the plane of the disk. The disk's radius is $R=2.8\text{ m}$ and the surface charge density is $\sigma =3{\text{ nC/m}}^3$. Evaluate $f(r^{\prime },z)$ at $r^{\prime }=1.9\text{ m}$.

a) 4.295E+00 V/m²

b) 4.724E+00 V/m²

c) 5.196E+00 V/m²

d) 5.716E+00 V/m²

e) 6.288E+00 V/m²

6) A large thin isolated square plate has an area of 5 m². It is uniformly charged with 8 nC of charge. What is the magnitude of the electric field 3 mm from the center of the plate's surface?

a) 6.171E+01 N/C

b) 6.788E+01 N/C

c) 7.467E+01 N/C

d) 8.214E+01 N/C

e) 9.035E+01 N/C

c05 W1

1)  $E(z)=\underset{0}{\overset{R}{\int }}f(r^{\prime },z)d{r}^{\prime }$
is an integral that calculates the magnitude of the electric field at a distance $z$ fromthe center of a thin circular disk as measured along a line normal to the plane of the disk. The disk's radius is $R=6.9\text{ m}$ and the surface charge density is $\sigma =9{\text{ nC/m}}^3$. Evaluate $f(r^{\prime },z)$ at $r^{\prime }=4.3\text{ m}$.

a) 8.924E-01 V/m²

b) 9.816E-01 V/m²

c) 1.080E+00 V/m²

d) 1.188E+00 V/m²

e) 1.307E+00 V/m²

2) A large thin isolated square plate has an area of 8 m². It is uniformly charged with 7 nC of charge. What is the magnitude of the electric field 3 mm from the center of the plate's surface?

a) 4.492E+01 N/C

b) 4.941E+01 N/C

c) 5.435E+01 N/C

d) 5.979E+01 N/C

e) 6.577E+01 N/C

3)

Three small charged objects are placed as shown, where $b=2a$, and $a=6\times 10^{-7}\text{m}$. What is the magnitude of the net force on $q_2$ if $q_1=3e$, $q_2=-7e$, and $q_3=5e$?

a) 9.958E-15 N

b) 1.095E-14 N

c) 1.205E-14 N

d) 1.325E-14 N

e) 1.458E-14 N

4)

 $E_z(x=0,z)=\underset{-a}{\overset{b}{\int }}f(x,z)dx$
is an integral that calculates the z-component of the electric field at point P situated above the x-axis where a charged rod of length (a+b) is located. The distance between point P and the x-axis is z=1.5 m. Evaluate $f(x,y)$ at x=1.1 m if a=0.62 m, b=1.3 m. The total charge on the rod is 7 nC.

a) 6.311E+00 V/m²

b) 6.943E+00 V/m²

c) 7.637E+00 V/m²

d) 8.401E+00 V/m²

e) 9.241E+00 V/m²

5)

Three small charged objects are placed as shown, where $b=2a$, and $a=6\times 10^{-7}\text{m}$.what angle does the force on $q_2$ make above the $-x$ axis if $q_1=3e$, $q_2=-7e$, and $q_3=4e$?

a) 5.377E+01 degrees

b) 5.914E+01 degrees

c) 6.506E+01 degrees

d) 7.157E+01 degrees

e) 7.872E+01 degrees

6)

A ring is uniformly charged with a net charge of 5 nC. The radius of the ring is R=1.6 m, with its center at the origin and oriented normal to the z axis as shown. what is the magnitude of the electric field at a distance z=1.1 m (on axis) away from the loop's center?

a) 5.581E+09 N/C²

b) 6.139E+09 N/C²

c) 6.753E+09 N/C²

d) 7.428E+09 N/C²

e) 8.171E+09 N/C²

c05 W2

1)

A ring is uniformly charged with a net charge of 8 nC. The radius of the ring is R=1.7 m, with its center at the origin and oriented normal to the z axis as shown. what is the magnitude of the electric field at a distance z=0.32 m (on axis) away from the loop's center?

a) 3.339E+09 N/C²

b) 3.673E+09 N/C²

c) 4.041E+09 N/C²

d) 4.445E+09 N/C²

e) 4.889E+09 N/C²

2) A large thin isolated square plate has an area of 9 m². It is uniformly charged with 6 nC of charge. What is the magnitude of the electric field 1 mm from the center of the plate's surface?

a) 2.571E+01 N/C

b) 2.828E+01 N/C

c) 3.111E+01 N/C

d) 3.422E+01 N/C

e) 3.765E+01 N/C

3)

Three small charged objects are placed as shown, where $b=2a$, and $a=2\times 10^{-7}\text{m}$.what angle does the force on $q_2$ make above the $-x$ axis if $q_1=2e$, $q_2=-9e$, and $q_3=4e$?

a) 5.243E+01 degrees

b) 5.767E+01 degrees

c) 6.343E+01 degrees

d) 6.978E+01 degrees

e) 7.676E+01 degrees

4)  $E(z)=\underset{0}{\overset{R}{\int }}f(r^{\prime },z)d{r}^{\prime }$
is an integral that calculates the magnitude of the electric field at a distance $z$ fromthe center of a thin circular disk as measured along a line normal to the plane of the disk. The disk's radius is $R=2.0\text{ m}$ and the surface charge density is $\sigma =9{\text{ nC/m}}^3$. Evaluate $f(r^{\prime },z)$ at $r^{\prime }=1.2\text{ m}$.

a) 8.933E+00 V/m²

b) 9.826E+00 V/m²

c) 1.081E+01 V/m²

d) 1.189E+01 V/m²

e) 1.308E+01 V/m²

5)

 $E_z(x=0,z)=\underset{-a}{\overset{b}{\int }}f(x,z)dx$
is an integral that calculates the z-component of the electric field at point P situated above the x-axis where a charged rod of length (a+b) is located. The distance between point P and the x-axis is z=1.9 m. Evaluate $f(x,y)$ at x=0.54 m if a=1.0 m, b=2.0 m. The total charge on the rod is 3 nC.

a) 1.665E+00 V/m²

b) 1.831E+00 V/m²

c) 2.014E+00 V/m²

d) 2.216E+00 V/m²

e) 2.437E+00 V/m²

6)

Three small charged objects are placed as shown, where $b=2a$, and $a=4\times 10^{-7}\text{m}$. What is the magnitude of the net force on $q_2$ if $q_1=2e$, $q_2=-8e$, and $q_3=3e$?

a) 2.036E-14 N

b) 2.240E-14 N

c) 2.464E-14 N

d) 2.710E-14 N

e) 2.981E-14 N

c05 X0

1)

Three small charged objects are placed as shown, where $b=2a$, and $a=4\times 10^{-7}\text{m}$. What is the magnitude of the net force on $q_2$ if $q_1=1e$, $q_2=-7e$, and $q_3=4e$?

a) 9.750E-15 N

b) 1.072E-14 N

c) 1.180E-14 N

d) 1.298E-14 N

e) 1.427E-14 N

2)

Three small charged objects are placed as shown, where $b=2a$, and $a=6\times 10^{-7}\text{m}$.what angle does the force on $q_2$ make above the $-x$ axis if $q_1=2e$, $q_2=-9e$, and $q_3=5e$?

a) 5.272E+01 degrees

b) 5.799E+01 degrees

c) 6.379E+01 degrees

d) 7.017E+01 degrees

e) 7.719E+01 degrees

3)

 $E_z(x=0,z)=\underset{-a}{\overset{b}{\int }}f(x,z)dx$
is an integral that calculates the z-component of the electric field at point P situated above the x-axis where a charged rod of length (a+b) is located. The distance between point P and the x-axis is z=1.5 m. Evaluate $f(x,y)$ at x=1.1 m if a=0.61 m, b=1.7 m. The total charge on the rod is 8 nC.

a) 5.995E+00 V/m²

b) 6.595E+00 V/m²

c) 7.254E+00 V/m²

d) 7.980E+00 V/m²

e) 8.778E+00 V/m²

4)

A ring is uniformly charged with a net charge of 5 nC. The radius of the ring is R=1.6 m, with its center at the origin and oriented normal to the z axis as shown. what is the magnitude of the electric field at a distance z=1.1 m (on axis) away from the loop's center?

a) 5.581E+09 N/C²

b) 6.139E+09 N/C²

c) 6.753E+09 N/C²

d) 7.428E+09 N/C²

e) 8.171E+09 N/C²

5)  $E(z)=\underset{0}{\overset{R}{\int }}f(r^{\prime },z)d{r}^{\prime }$
is an integral that calculates the magnitude of the electric field at a distance $z$ fromthe center of a thin circular disk as measured along a line normal to the plane of the disk. The disk's radius is $R=3.3\text{ m}$ and the surface charge density is $\sigma =4{\text{ nC/m}}^3$. Evaluate $f(r^{\prime },z)$ at $r^{\prime }=2.0\text{ m}$.

a) 6.877E+00 V/m²

b) 7.565E+00 V/m²

c) 8.321E+00 V/m²

d) 9.153E+00 V/m²

e) 1.007E+01 V/m²

6) A large thin isolated square plate has an area of 5 m². It is uniformly charged with 8 nC of charge. What is the magnitude of the electric field 3 mm from the center of the plate's surface?

a) 6.171E+01 N/C

b) 6.788E+01 N/C

c) 7.467E+01 N/C

d) 8.214E+01 N/C

e) 9.035E+01 N/C

c05 X1

1)  $E(z)=\underset{0}{\overset{R}{\int }}f(r^{\prime },z)d{r}^{\prime }$
is an integral that calculates the magnitude of the electric field at a distance $z$ fromthe center of a thin circular disk as measured along a line normal to the plane of the disk. The disk's radius is $R=7.5\text{ m}$ and the surface charge density is $\sigma =3{\text{ nC/m}}^3$. Evaluate $f(r^{\prime },z)$ at $r^{\prime }=2.6\text{ m}$.

a) 7.820E-01 V/m²

b) 8.602E-01 V/m²

c) 9.462E-01 V/m²

d) 1.041E+00 V/m²

e) 1.145E+00 V/m²

2)

Three small charged objects are placed as shown, where $b=2a$, and $a=6\times 10^{-7}\text{m}$. What is the magnitude of the net force on $q_2$ if $q_1=2e$, $q_2=-8e$, and $q_3=5e$?

a) 8.259E-15 N

b) 9.085E-15 N

c) 9.993E-15 N

d) 1.099E-14 N

e) 1.209E-14 N

3)

A ring is uniformly charged with a net charge of 3 nC. The radius of the ring is R=1.7 m, with its center at the origin and oriented normal to the z axis as shown. what is the magnitude of the electric field at a distance z=0.34 m (on axis) away from the loop's center?

a) 1.202E+09 N/C²

b) 1.322E+09 N/C²

c) 1.454E+09 N/C²

d) 1.599E+09 N/C²

e) 1.759E+09 N/C²

4)

Three small charged objects are placed as shown, where $b=2a$, and $a=6\times 10^{-7}\text{m}$.what angle does the force on $q_2$ make above the $-x$ axis if $q_1=3e$, $q_2=-7e$, and $q_3=6e$?

a) 6.343E+01 degrees

b) 6.978E+01 degrees

c) 7.676E+01 degrees

d) 8.443E+01 degrees

e) 9.288E+01 degrees

5)

 $E_z(x=0,z)=\underset{-a}{\overset{b}{\int }}f(x,z)dx$
is an integral that calculates the z-component of the electric field at point P situated above the x-axis where a charged rod of length (a+b) is located. The distance between point P and the x-axis is z=1.6 m. Evaluate $f(x,y)$ at x=0.73 m if a=0.64 m, b=1.8 m. The total charge on the rod is 3 nC.

a) 2.955E+00 V/m²

b) 3.250E+00 V/m²

c) 3.575E+00 V/m²

d) 3.933E+00 V/m²

e) 4.326E+00 V/m²

6) A large thin isolated square plate has an area of 6 m². It is uniformly charged with 9 nC of charge. What is the magnitude of the electric field 3 mm from the center of the plate's surface?

a) 8.471E+01 N/C

b) 9.318E+01 N/C

c) 1.025E+02 N/C

d) 1.127E+02 N/C

e) 1.240E+02 N/C

c05 X2

1)

A ring is uniformly charged with a net charge of 4 nC. The radius of the ring is R=1.6 m, with its center at the origin and oriented normal to the z axis as shown. what is the magnitude of the electric field at a distance z=1.0 m (on axis) away from the loop's center?

a) 5.352E+09 N/C²

b) 5.887E+09 N/C²

c) 6.476E+09 N/C²

d) 7.124E+09 N/C²

e) 7.836E+09 N/C²

2)

Three small charged objects are placed as shown, where $b=2a$, and $a=4\times 10^{-7}\text{m}$. What is the magnitude of the net force on $q_2$ if $q_1=2e$, $q_2=-8e$, and $q_3=5e$?

a) 2.248E-14 N

b) 2.473E-14 N

c) 2.721E-14 N

d) 2.993E-14 N

e) 3.292E-14 N

3)

Three small charged objects are placed as shown, where $b=2a$, and $a=4\times 10^{-7}\text{m}$.what angle does the force on $q_2$ make above the $-x$ axis if $q_1=2e$, $q_2=-9e$, and $q_3=5e$?

a) 3.961E+01 degrees

b) 4.357E+01 degrees

c) 4.793E+01 degrees

d) 5.272E+01 degrees

e) 5.799E+01 degrees

4)  $E(z)=\underset{0}{\overset{R}{\int }}f(r^{\prime },z)d{r}^{\prime }$
is an integral that calculates the magnitude of the electric field at a distance $z$ fromthe center of a thin circular disk as measured along a line normal to the plane of the disk. The disk's radius is $R=1.8\text{ m}$ and the surface charge density is $\sigma =3{\text{ nC/m}}^3$. Evaluate $f(r^{\prime },z)$ at $r^{\prime }=1.1\text{ m}$.

a) 7.517E+00 V/m²

b) 8.269E+00 V/m²

c) 9.096E+00 V/m²

d) 1.001E+01 V/m²

e) 1.101E+01 V/m²

5) A large thin isolated square plate has an area of 3 m². It is uniformly charged with 9 nC of charge. What is the magnitude of the electric field 3 mm from the center of the plate's surface?

a) 1.694E+02 N/C

b) 1.864E+02 N/C

c) 2.050E+02 N/C

d) 2.255E+02 N/C

e) 2.480E+02 N/C

6)

 $E_z(x=0,z)=\underset{-a}{\overset{b}{\int }}f(x,z)dx$
is an integral that calculates the z-component of the electric field at point P situated above the x-axis where a charged rod of length (a+b) is located. The distance between point P and the x-axis is z=1.5 m. Evaluate $f(x,y)$ at x=1.1 m if a=0.62 m, b=1.3 m. The total charge on the rod is 7 nC.

a) 6.311E+00 V/m²

b) 6.943E+00 V/m²

c) 7.637E+00 V/m²

d) 8.401E+00 V/m²

e) 9.241E+00 V/m²

c05 Y0

1)

Three small charged objects are placed as shown, where $b=2a$, and $a=6\times 10^{-7}\text{m}$. What is the magnitude of the net force on $q_2$ if $q_1=2e$, $q_2=-8e$, and $q_3=4e$?

a) 8.613E-15 N

b) 9.474E-15 N

c) 1.042E-14 N

d) 1.146E-14 N

e) 1.261E-14 N

2)

Three small charged objects are placed as shown, where $b=2a$, and $a=4\times 10^{-7}\text{m}$.what angle does the force on $q_2$ make above the $-x$ axis if $q_1=3e$, $q_2=-7e$, and $q_3=5e$?

a) 5.569E+01 degrees

b) 6.125E+01 degrees

c) 6.738E+01 degrees

d) 7.412E+01 degrees

e) 8.153E+01 degrees

3)

 $E_z(x=0,z)=\underset{-a}{\overset{b}{\int }}f(x,z)dx$
is an integral that calculates the z-component of the electric field at point P situated above the x-axis where a charged rod of length (a+b) is located. The distance between point P and the x-axis is z=1.5 m. Evaluate $f(x,y)$ at x=0.79 m if a=0.75 m, b=2.1 m. The total charge on the rod is 6 nC.

a) 5.825E+00 V/m²

b) 6.407E+00 V/m²

c) 7.048E+00 V/m²

d) 7.753E+00 V/m²

e) 8.528E+00 V/m²

4)

A ring is uniformly charged with a net charge of 7 nC. The radius of the ring is R=1.6 m, with its center at the origin and oriented normal to the z axis as shown. what is the magnitude of the electric field at a distance z=0.35 m (on axis) away from the loop's center?

a) 4.142E+09 N/C²

b) 4.556E+09 N/C²

c) 5.012E+09 N/C²

d) 5.513E+09 N/C²

e) 6.064E+09 N/C²

5)  $E(z)=\underset{0}{\overset{R}{\int }}f(r^{\prime },z)d{r}^{\prime }$
is an integral that calculates the magnitude of the electric field at a distance $z$ fromthe center of a thin circular disk as measured along a line normal to the plane of the disk. The disk's radius is $R=3.2\text{ m}$ and the surface charge density is $\sigma =2{\text{ nC/m}}^3$. Evaluate $f(r^{\prime },z)$ at $r^{\prime }=2.2\text{ m}$.

a) 3.228E+00 V/m²

b) 3.551E+00 V/m²

c) 3.906E+00 V/m²

d) 4.297E+00 V/m²

e) 4.727E+00 V/m²

6) A large thin isolated square plate has an area of 8 m². It is uniformly charged with 7 nC of charge. What is the magnitude of the electric field 3 mm from the center of the plate's surface?

a) 4.492E+01 N/C

b) 4.941E+01 N/C

c) 5.435E+01 N/C

d) 5.979E+01 N/C

e) 6.577E+01 N/C

c05 Y1

1) A large thin isolated square plate has an area of 8 m². It is uniformly charged with 7 nC of charge. What is the magnitude of the electric field 3 mm from the center of the plate's surface?

a) 4.492E+01 N/C

b) 4.941E+01 N/C

c) 5.435E+01 N/C

d) 5.979E+01 N/C

e) 6.577E+01 N/C

2)

A ring is uniformly charged with a net charge of 4 nC. The radius of the ring is R=1.6 m, with its center at the origin and oriented normal to the z axis as shown. what is the magnitude of the electric field at a distance z=1.1 m (on axis) away from the loop's center?

a) 5.402E+09 N/C²

b) 5.943E+09 N/C²

c) 6.537E+09 N/C²

d) 7.191E+09 N/C²

e) 7.910E+09 N/C²

3)

Three small charged objects are placed as shown, where $b=2a$, and $a=2\times 10^{-7}\text{m}$. What is the magnitude of the net force on $q_2$ if $q_1=1e$, $q_2=-7e$, and $q_3=2e$?

a) 3.391E-14 N

b) 3.731E-14 N

c) 4.104E-14 N

d) 4.514E-14 N

e) 4.965E-14 N

4)  $E(z)=\underset{0}{\overset{R}{\int }}f(r^{\prime },z)d{r}^{\prime }$
is an integral that calculates the magnitude of the electric field at a distance $z$ fromthe center of a thin circular disk as measured along a line normal to the plane of the disk. The disk's radius is $R=6.9\text{ m}$ and the surface charge density is $\sigma =9{\text{ nC/m}}^3$. Evaluate $f(r^{\prime },z)$ at $r^{\prime }=4.3\text{ m}$.

a) 8.924E-01 V/m²

b) 9.816E-01 V/m²

c) 1.080E+00 V/m²

d) 1.188E+00 V/m²

e) 1.307E+00 V/m²

5)

 $E_z(x=0,z)=\underset{-a}{\overset{b}{\int }}f(x,z)dx$
is an integral that calculates the z-component of the electric field at point P situated above the x-axis where a charged rod of length (a+b) is located. The distance between point P and the x-axis is z=1.5 m. Evaluate $f(x,y)$ at x=1.0 m if a=1.1 m, b=1.4 m. The total charge on the rod is 5 nC.

a) 4.602E+00 V/m²

b) 5.062E+00 V/m²

c) 5.568E+00 V/m²

d) 6.125E+00 V/m²

e) 6.738E+00 V/m²

6)

Three small charged objects are placed as shown, where $b=2a$, and $a=4\times 10^{-7}\text{m}$.what angle does the force on $q_2$ make above the $-x$ axis if $q_1=1e$, $q_2=-8e$, and $q_3=4e$?

a) 3.719E+01 degrees

b) 4.091E+01 degrees

c) 4.500E+01 degrees

d) 4.950E+01 degrees

e) 5.445E+01 degrees

c05 Y2

1)

 $E_z(x=0,z)=\underset{-a}{\overset{b}{\int }}f(x,z)dx$
is an integral that calculates the z-component of the electric field at point P situated above the x-axis where a charged rod of length (a+b) is located. The distance between point P and the x-axis is z=1.8 m. Evaluate $f(x,y)$ at x=0.5 m if a=0.67 m, b=2.4 m. The total charge on the rod is 9 nC.

a) 5.465E+00 V/m²

b) 6.012E+00 V/m²

c) 6.613E+00 V/m²

d) 7.274E+00 V/m²

e) 8.002E+00 V/m²

2)

A ring is uniformly charged with a net charge of 2 nC. The radius of the ring is R=1.6 m, with its center at the origin and oriented normal to the z axis as shown. what is the magnitude of the electric field at a distance z=0.99 m (on axis) away from the loop's center?

a) 2.429E+09 N/C²

b) 2.672E+09 N/C²

c) 2.939E+09 N/C²

d) 3.233E+09 N/C²

e) 3.556E+09 N/C²

3)

Three small charged objects are placed as shown, where $b=2a$, and $a=6\times 10^{-7}\text{m}$.what angle does the force on $q_2$ make above the $-x$ axis if $q_1=3e$, $q_2=-7e$, and $q_3=6e$?

a) 6.343E+01 degrees

b) 6.978E+01 degrees

c) 7.676E+01 degrees

d) 8.443E+01 degrees

e) 9.288E+01 degrees

4)

Three small charged objects are placed as shown, where $b=2a$, and $a=4\times 10^{-7}\text{m}$. What is the magnitude of the net force on $q_2$ if $q_1=2e$, $q_2=-8e$, and $q_3=5e$?

a) 2.248E-14 N

b) 2.473E-14 N

c) 2.721E-14 N

d) 2.993E-14 N

e) 3.292E-14 N

5)  $E(z)=\underset{0}{\overset{R}{\int }}f(r^{\prime },z)d{r}^{\prime }$
is an integral that calculates the magnitude of the electric field at a distance $z$ fromthe center of a thin circular disk as measured along a line normal to the plane of the disk. The disk's radius is $R=7.5\text{ m}$ and the surface charge density is $\sigma =3{\text{ nC/m}}^3$. Evaluate $f(r^{\prime },z)$ at $r^{\prime }=2.6\text{ m}$.

a) 7.820E-01 V/m²

b) 8.602E-01 V/m²

c) 9.462E-01 V/m²

d) 1.041E+00 V/m²

e) 1.145E+00 V/m²

6) A large thin isolated square plate has an area of 4 m². It is uniformly charged with 5 nC of charge. What is the magnitude of the electric field 1 mm from the center of the plate's surface?

a) 4.821E+01 N/C

b) 5.303E+01 N/C

c) 5.834E+01 N/C

d) 6.417E+01 N/C

e) 7.059E+01 N/C

c05 Z0

1)

Three small charged objects are placed as shown, where $b=2a$, and $a=6\times 10^{-7}\text{m}$. What is the magnitude of the net force on $q_2$ if $q_1=1e$, $q_2=-7e$, and $q_3=2e$?

a) 3.426E-15 N

b) 3.768E-15 N

c) 4.145E-15 N

d) 4.560E-15 N

e) 5.015E-15 N

2)

Three small charged objects are placed as shown, where $b=2a$, and $a=2\times 10^{-7}\text{m}$.what angle does the force on $q_2$ make above the $-x$ axis if $q_1=1e$, $q_2=-8e$, and $q_3=3e$?

a) 3.629E+01 degrees

b) 3.992E+01 degrees

c) 4.391E+01 degrees

d) 4.830E+01 degrees

e) 5.313E+01 degrees

3)

 $E_z(x=0,z)=\underset{-a}{\overset{b}{\int }}f(x,z)dx$
is an integral that calculates the z-component of the electric field at point P situated above the x-axis where a charged rod of length (a+b) is located. The distance between point P and the x-axis is z=1.3 m. Evaluate $f(x,y)$ at x=0.96 m if a=0.63 m, b=1.4 m. The total charge on the rod is 3 nC.

a) 3.719E+00 V/m²

b) 4.091E+00 V/m²

c) 4.500E+00 V/m²

d) 4.950E+00 V/m²

e) 5.445E+00 V/m²

4)

A ring is uniformly charged with a net charge of 3 nC. The radius of the ring is R=1.7 m, with its center at the origin and oriented normal to the z axis as shown. what is the magnitude of the electric field at a distance z=0.34 m (on axis) away from the loop's center?

a) 1.202E+09 N/C²

b) 1.322E+09 N/C²

c) 1.454E+09 N/C²

d) 1.599E+09 N/C²

e) 1.759E+09 N/C²

5)  $E(z)=\underset{0}{\overset{R}{\int }}f(r^{\prime },z)d{r}^{\prime }$
is an integral that calculates the magnitude of the electric field at a distance $z$ fromthe center of a thin circular disk as measured along a line normal to the plane of the disk. The disk's radius is $R=2.8\text{ m}$ and the surface charge density is $\sigma =3{\text{ nC/m}}^3$. Evaluate $f(r^{\prime },z)$ at $r^{\prime }=1.9\text{ m}$.

a) 4.295E+00 V/m²

b) 4.724E+00 V/m²

c) 5.196E+00 V/m²

d) 5.716E+00 V/m²

e) 6.288E+00 V/m²

6) A large thin isolated square plate has an area of 8 m². It is uniformly charged with 5 nC of charge. What is the magnitude of the electric field 1 mm from the center of the plate's surface?

a) 2.652E+01 N/C

b) 2.917E+01 N/C

c) 3.209E+01 N/C

d) 3.529E+01 N/C

e) 3.882E+01 N/C

c05 Z1

1)

Three small charged objects are placed as shown, where $b=2a$, and $a=4\times 10^{-7}\text{m}$. What is the magnitude of the net force on $q_2$ if $q_1=2e$, $q_2=-8e$, and $q_3=3e$?

a) 2.036E-14 N

b) 2.240E-14 N

c) 2.464E-14 N

d) 2.710E-14 N

e) 2.981E-14 N

2)

Three small charged objects are placed as shown, where $b=2a$, and $a=4\times 10^{-7}\text{m}$.what angle does the force on $q_2$ make above the $-x$ axis if $q_1=2e$, $q_2=-9e$, and $q_3=5e$?

a) 3.961E+01 degrees

b) 4.357E+01 degrees

c) 4.793E+01 degrees

d) 5.272E+01 degrees

e) 5.799E+01 degrees

3)

A ring is uniformly charged with a net charge of 2 nC. The radius of the ring is R=1.8 m, with its center at the origin and oriented normal to the z axis as shown. what is the magnitude of the electric field at a distance z=1.3 m (on axis) away from the loop's center?

a) 1.764E+09 N/C²

b) 1.941E+09 N/C²

c) 2.135E+09 N/C²

d) 2.348E+09 N/C²

e) 2.583E+09 N/C²

4)  $E(z)=\underset{0}{\overset{R}{\int }}f(r^{\prime },z)d{r}^{\prime }$
is an integral that calculates the magnitude of the electric field at a distance $z$ fromthe center of a thin circular disk as measured along a line normal to the plane of the disk. The disk's radius is $R=8.1\text{ m}$ and the surface charge density is $\sigma =3{\text{ nC/m}}^3$. Evaluate $f(r^{\prime },z)$ at $r^{\prime }=4.2\text{ m}$.

a) 5.134E-01 V/m²

b) 5.648E-01 V/m²

c) 6.212E-01 V/m²

d) 6.834E-01 V/m²

e) 7.517E-01 V/m²

5)

 $E_z(x=0,z)=\underset{-a}{\overset{b}{\int }}f(x,z)dx$
is an integral that calculates the z-component of the electric field at point P situated above the x-axis where a charged rod of length (a+b) is located. The distance between point P and the x-axis is z=1.9 m. Evaluate $f(x,y)$ at x=0.54 m if a=1.0 m, b=2.0 m. The total charge on the rod is 3 nC.

a) 1.665E+00 V/m²

b) 1.831E+00 V/m²

c) 2.014E+00 V/m²

d) 2.216E+00 V/m²

e) 2.437E+00 V/m²

6) A large thin isolated square plate has an area of 5 m². It is uniformly charged with 7 nC of charge. What is the magnitude of the electric field 1 mm from the center of the plate's surface?

a) 6.534E+01 N/C

b) 7.187E+01 N/C

c) 7.906E+01 N/C

d) 8.696E+01 N/C

e) 9.566E+01 N/C

c05 Z2

1)

Three small charged objects are placed as shown, where $b=2a$, and $a=6\times 10^{-7}\text{m}$. What is the magnitude of the net force on $q_2$ if $q_1=3e$, $q_2=-7e$, and $q_3=6e$?

a) 1.028E-14 N

b) 1.130E-14 N

c) 1.244E-14 N

d) 1.368E-14 N

e) 1.505E-14 N

2)

 $E_z(x=0,z)=\underset{-a}{\overset{b}{\int }}f(x,z)dx$
is an integral that calculates the z-component of the electric field at point P situated above the x-axis where a charged rod of length (a+b) is located. The distance between point P and the x-axis is z=1.9 m. Evaluate $f(x,y)$ at x=0.54 m if a=1.0 m, b=2.0 m. The total charge on the rod is 3 nC.

a) 1.665E+00 V/m²

b) 1.831E+00 V/m²

c) 2.014E+00 V/m²

d) 2.216E+00 V/m²

e) 2.437E+00 V/m²

3)

A ring is uniformly charged with a net charge of 3 nC. The radius of the ring is R=1.8 m, with its center at the origin and oriented normal to the z axis as shown. what is the magnitude of the electric field at a distance z=1.1 m (on axis) away from the loop's center?

a) 3.159E+09 N/C²

b) 3.475E+09 N/C²

c) 3.823E+09 N/C²

d) 4.205E+09 N/C²

e) 4.626E+09 N/C²

4)

Three small charged objects are placed as shown, where $b=2a$, and $a=6\times 10^{-7}\text{m}$.what angle does the force on $q_2$ make above the $-x$ axis if $q_1=3e$, $q_2=-7e$, and $q_3=4e$?

a) 5.377E+01 degrees

b) 5.914E+01 degrees

c) 6.506E+01 degrees

d) 7.157E+01 degrees

e) 7.872E+01 degrees

5) A large thin isolated square plate has an area of 6 m². It is uniformly charged with 5 nC of charge. What is the magnitude of the electric field 2 mm from the center of the plate's surface?

a) 3.214E+01 N/C

b) 3.536E+01 N/C

c) 3.889E+01 N/C

d) 4.278E+01 N/C

e) 4.706E+01 N/C

6)  $E(z)=\underset{0}{\overset{R}{\int }}f(r^{\prime },z)d{r}^{\prime }$
is an integral that calculates the magnitude of the electric field at a distance $z$ fromthe center of a thin circular disk as measured along a line normal to the plane of the disk. The disk's radius is $R=3.0\text{ m}$ and the surface charge density is $\sigma =8{\text{ nC/m}}^3$. Evaluate $f(r^{\prime },z)$ at $r^{\prime }=2.0\text{ m}$.

a) 9.459E+00 V/m²

b) 1.040E+01 V/m²

c) 1.145E+01 V/m²

d) 1.259E+01 V/m²

e) 1.385E+01 V/m²

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1. of 10 blank lines to separate exams from keys
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Key: A0

1)

Three small charged objects are placed as shown, where $b=2a$, and $a=2\times 10^{-7}\text{m}$. What is the magnitude of the net force on $q_2$ if $q_1=1e$, $q_2=-7e$, and $q_3=2e$?

-a) 3.391E-14 N

-b) 3.731E-14 N

-c) 4.104E-14 N

+d) 4.514E-14 N

-e) 4.965E-14 N

2)

Three small charged objects are placed as shown, where $b=2a$, and $a=2\times 10^{-7}\text{m}$.what angle does the force on $q_2$ make above the $-x$ axis if $q_1=2e$, $q_2=-9e$, and $q_3=4e$?

-a) 5.243E+01 degrees

-b) 5.767E+01 degrees

+c) 6.343E+01 degrees

-d) 6.978E+01 degrees

-e) 7.676E+01 degrees

3)

 $E_z(x=0,z)=\underset{-a}{\overset{b}{\int }}f(x,z)dx$
is an integral that calculates the z-component of the electric field at point P situated above the x-axis where a charged rod of length (a+b) is located. The distance between point P and the x-axis is z=1.4 m. Evaluate $f(x,y)$ at x=1.1 m if a=0.69 m, b=2.2 m. The total charge on the rod is 6 nC.

-a) 3.161E+00 V/m²

-b) 3.477E+00 V/m²

-c) 3.825E+00 V/m²

-d) 4.208E+00 V/m²

+e) 4.628E+00 V/m²

4)

A ring is uniformly charged with a net charge of 9 nC. The radius of the ring is R=1.9 m, with its center at the origin and oriented normal to the z axis as shown. what is the magnitude of the electric field at a distance z=1.4 m (on axis) away from the loop's center?

-a) 7.119E+09 N/C²

-b) 7.831E+09 N/C²

+c) 8.614E+09 N/C²

-d) 9.476E+09 N/C²

-e) 1.042E+10 N/C²

5)  $E(z)=\underset{0}{\overset{R}{\int }}f(r^{\prime },z)d{r}^{\prime }$
is an integral that calculates the magnitude of the electric field at a distance $z$ fromthe center of a thin circular disk as measured along a line normal to the plane of the disk. The disk's radius is $R=7.2\text{ m}$ and the surface charge density is $\sigma =3{\text{ nC/m}}^3$. Evaluate $f(r^{\prime },z)$ at $r^{\prime }=3.6\text{ m}$.

+a) 1.606E+00 V/m²

-b) 1.767E+00 V/m²

-c) 1.943E+00 V/m²

-d) 2.138E+00 V/m²

-e) 2.351E+00 V/m²

6) A large thin isolated square plate has an area of 6 m². It is uniformly charged with 6 nC of charge. What is the magnitude of the electric field 2 mm from the center of the plate's surface?

+a) 5.647E+01 N/C

-b) 6.212E+01 N/C

-c) 6.833E+01 N/C

-d) 7.516E+01 N/C

-e) 8.268E+01 N/C

Key: A1

1) A large thin isolated square plate has an area of 8 m². It is uniformly charged with 6 nC of charge. What is the magnitude of the electric field 1 mm from the center of the plate's surface?

-a) 3.500E+01 N/C

-b) 3.850E+01 N/C

+c) 4.235E+01 N/C

-d) 4.659E+01 N/C

-e) 5.125E+01 N/C

2)

Three small charged objects are placed as shown, where $b=2a$, and $a=4\times 10^{-7}\text{m}$. What is the magnitude of the net force on $q_2$ if $q_1=1e$, $q_2=-7e$, and $q_3=4e$?

-a) 9.750E-15 N

-b) 1.072E-14 N

-c) 1.180E-14 N

-d) 1.298E-14 N

+e) 1.427E-14 N

3)  $E(z)=\underset{0}{\overset{R}{\int }}f(r^{\prime },z)d{r}^{\prime }$
is an integral that calculates the magnitude of the electric field at a distance $z$ fromthe center of a thin circular disk as measured along a line normal to the plane of the disk. The disk's radius is $R=3.0\text{ m}$ and the surface charge density is $\sigma =8{\text{ nC/m}}^3$. Evaluate $f(r^{\prime },z)$ at $r^{\prime }=2.0\text{ m}$.

-a) 9.459E+00 V/m²

+b) 1.040E+01 V/m²

-c) 1.145E+01 V/m²

-d) 1.259E+01 V/m²

-e) 1.385E+01 V/m²

4)

A ring is uniformly charged with a net charge of 4 nC. The radius of the ring is R=1.6 m, with its center at the origin and oriented normal to the z axis as shown. what is the magnitude of the electric field at a distance z=1.0 m (on axis) away from the loop's center?

+a) 5.352E+09 N/C²

-b) 5.887E+09 N/C²

-c) 6.476E+09 N/C²

-d) 7.124E+09 N/C²

-e) 7.836E+09 N/C²

5)

 $E_z(x=0,z)=\underset{-a}{\overset{b}{\int }}f(x,z)dx$
is an integral that calculates the z-component of the electric field at point P situated above the x-axis where a charged rod of length (a+b) is located. The distance between point P and the x-axis is z=1.5 m. Evaluate $f(x,y)$ at x=1.0 m if a=1.1 m, b=1.4 m. The total charge on the rod is 5 nC.

+a) 4.602E+00 V/m²

-b) 5.062E+00 V/m²

-c) 5.568E+00 V/m²

-d) 6.125E+00 V/m²

-e) 6.738E+00 V/m²

6)

Three small charged objects are placed as shown, where $b=2a$, and $a=6\times 10^{-7}\text{m}$.what angle does the force on $q_2$ make above the $-x$ axis if $q_1=2e$, $q_2=-9e$, and $q_3=4e$?

-a) 4.766E+01 degrees

-b) 5.243E+01 degrees

-c) 5.767E+01 degrees

+d) 6.343E+01 degrees

-e) 6.978E+01 degrees

Key: A2

1)  $E(z)=\underset{0}{\overset{R}{\int }}f(r^{\prime },z)d{r}^{\prime }$
is an integral that calculates the magnitude of the electric field at a distance $z$ fromthe center of a thin circular disk as measured along a line normal to the plane of the disk. The disk's radius is $R=8.1\text{ m}$ and the surface charge density is $\sigma =3{\text{ nC/m}}^3$. Evaluate $f(r^{\prime },z)$ at $r^{\prime }=4.2\text{ m}$.

-a) 5.134E-01 V/m²

+b) 5.648E-01 V/m²

-c) 6.212E-01 V/m²

-d) 6.834E-01 V/m²

-e) 7.517E-01 V/m²

2)

Three small charged objects are placed as shown, where $b=2a$, and $a=2\times 10^{-7}\text{m}$.what angle does the force on $q_2$ make above the $-x$ axis if $q_1=2e$, $q_2=-7e$, and $q_3=5e$?

-a) 4.357E+01 degrees

-b) 4.793E+01 degrees

-c) 5.272E+01 degrees

+d) 5.799E+01 degrees

-e) 6.379E+01 degrees

3) A large thin isolated square plate has an area of 5 m². It is uniformly charged with 8 nC of charge. What is the magnitude of the electric field 3 mm from the center of the plate's surface?

-a) 6.171E+01 N/C

-b) 6.788E+01 N/C

-c) 7.467E+01 N/C

-d) 8.214E+01 N/C

+e) 9.035E+01 N/C

4)

 $E_z(x=0,z)=\underset{-a}{\overset{b}{\int }}f(x,z)dx$
is an integral that calculates the z-component of the electric field at point P situated above the x-axis where a charged rod of length (a+b) is located. The distance between point P and the x-axis is z=1.2 m. Evaluate $f(x,y)$ at x=0.73 m if a=0.52 m, b=1.6 m. The total charge on the rod is 7 nC.

-a) 9.655E+00 V/m²

-b) 1.062E+01 V/m²

-c) 1.168E+01 V/m²

+d) 1.285E+01 V/m²

-e) 1.414E+01 V/m²

5)

A ring is uniformly charged with a net charge of 6 nC. The radius of the ring is R=1.9 m, with its center at the origin and oriented normal to the z axis as shown. what is the magnitude of the electric field at a distance z=0.4 m (on axis) away from the loop's center?

-a) 2.013E+09 N/C²

-b) 2.214E+09 N/C²

-c) 2.435E+09 N/C²

-d) 2.679E+09 N/C²

+e) 2.947E+09 N/C²

6)

Three small charged objects are placed as shown, where $b=2a$, and $a=6\times 10^{-7}\text{m}$. What is the magnitude of the net force on $q_2$ if $q_1=2e$, $q_2=-8e$, and $q_3=4e$?

-a) 8.613E-15 N

-b) 9.474E-15 N

-c) 1.042E-14 N

+d) 1.146E-14 N

-e) 1.261E-14 N

Key: B0

1)

Three small charged objects are placed as shown, where $b=2a$, and $a=4\times 10^{-7}\text{m}$. What is the magnitude of the net force on $q_2$ if $q_1=1e$, $q_2=-7e$, and $q_3=4e$?

-a) 9.750E-15 N

-b) 1.072E-14 N

-c) 1.180E-14 N

-d) 1.298E-14 N

+e) 1.427E-14 N

2)

Three small charged objects are placed as shown, where $b=2a$, and $a=4\times 10^{-7}\text{m}$.what angle does the force on $q_2$ make above the $-x$ axis if $q_1=3e$, $q_2=-9e$, and $q_3=6e$?

-a) 5.767E+01 degrees

+b) 6.343E+01 degrees

-c) 6.978E+01 degrees

-d) 7.676E+01 degrees

-e) 8.443E+01 degrees

3)

 $E_z(x=0,z)=\underset{-a}{\overset{b}{\int }}f(x,z)dx$
is an integral that calculates the z-component of the electric field at point P situated above the x-axis where a charged rod of length (a+b) is located. The distance between point P and the x-axis is z=1.5 m. Evaluate $f(x,y)$ at x=0.79 m if a=0.75 m, b=2.1 m. The total charge on the rod is 6 nC.

+a) 5.825E+00 V/m²

-b) 6.407E+00 V/m²

-c) 7.048E+00 V/m²

-d) 7.753E+00 V/m²

-e) 8.528E+00 V/m²

4)

A ring is uniformly charged with a net charge of 2 nC. The radius of the ring is R=1.8 m, with its center at the origin and oriented normal to the z axis as shown. what is the magnitude of the electric field at a distance z=1.3 m (on axis) away from the loop's center?

-a) 1.764E+09 N/C²

-b) 1.941E+09 N/C²

+c) 2.135E+09 N/C²

-d) 2.348E+09 N/C²

-e) 2.583E+09 N/C²

5)  $E(z)=\underset{0}{\overset{R}{\int }}f(r^{\prime },z)d{r}^{\prime }$
is an integral that calculates the magnitude of the electric field at a distance $z$ fromthe center of a thin circular disk as measured along a line normal to the plane of the disk. The disk's radius is $R=8.3\text{ m}$ and the surface charge density is $\sigma =5{\text{ nC/m}}^3$. Evaluate $f(r^{\prime },z)$ at $r^{\prime }=5.3\text{ m}$.

+a) 1.022E+00 V/m²

-b) 1.125E+00 V/m²

-c) 1.237E+00 V/m²

-d) 1.361E+00 V/m²

-e) 1.497E+00 V/m²

6) A large thin isolated square plate has an area of 9 m². It is uniformly charged with 8 nC of charge. What is the magnitude of the electric field 3 mm from the center of the plate's surface?

-a) 3.428E+01 N/C

-b) 3.771E+01 N/C

-c) 4.148E+01 N/C

-d) 4.563E+01 N/C

+e) 5.020E+01 N/C

Key: B1

1)  $E(z)=\underset{0}{\overset{R}{\int }}f(r^{\prime },z)d{r}^{\prime }$
is an integral that calculates the magnitude of the electric field at a distance $z$ fromthe center of a thin circular disk as measured along a line normal to the plane of the disk. The disk's radius is $R=6.8\text{ m}$ and the surface charge density is $\sigma =6{\text{ nC/m}}^3$. Evaluate $f(r^{\prime },z)$ at $r^{\prime }=3.6\text{ m}$.

-a) 1.258E+00 V/m²

-b) 1.384E+00 V/m²

-c) 1.522E+00 V/m²

+d) 1.674E+00 V/m²

-e) 1.842E+00 V/m²

2)

A ring is uniformly charged with a net charge of 2 nC. The radius of the ring is R=1.6 m, with its center at the origin and oriented normal to the z axis as shown. what is the magnitude of the electric field at a distance z=0.99 m (on axis) away from the loop's center?

-a) 2.429E+09 N/C²

+b) 2.672E+09 N/C²

-c) 2.939E+09 N/C²

-d) 3.233E+09 N/C²

-e) 3.556E+09 N/C²

3)

 $E_z(x=0,z)=\underset{-a}{\overset{b}{\int }}f(x,z)dx$
is an integral that calculates the z-component of the electric field at point P situated above the x-axis where a charged rod of length (a+b) is located. The distance between point P and the x-axis is z=1.3 m. Evaluate $f(x,y)$ at x=0.96 m if a=0.63 m, b=1.4 m. The total charge on the rod is 3 nC.

-a) 3.719E+00 V/m²

+b) 4.091E+00 V/m²

-c) 4.500E+00 V/m²

-d) 4.950E+00 V/m²

-e) 5.445E+00 V/m²

4)

Three small charged objects are placed as shown, where $b=2a$, and $a=2\times 10^{-7}\text{m}$.what angle does the force on $q_2$ make above the $-x$ axis if $q_1=2e$, $q_2=-7e$, and $q_3=5e$?

-a) 4.357E+01 degrees

-b) 4.793E+01 degrees

-c) 5.272E+01 degrees

+d) 5.799E+01 degrees

-e) 6.379E+01 degrees

5)

Three small charged objects are placed as shown, where $b=2a$, and $a=6\times 10^{-7}\text{m}$. What is the magnitude of the net force on $q_2$ if $q_1=1e$, $q_2=-8e$, and $q_3=2e$?

+a) 5.732E-15 N

-b) 6.305E-15 N

-c) 6.936E-15 N

-d) 7.629E-15 N

-e) 8.392E-15 N

6) A large thin isolated square plate has an area of 6 m². It is uniformly charged with 5 nC of charge. What is the magnitude of the electric field 1 mm from the center of the plate's surface?

-a) 3.214E+01 N/C

-b) 3.536E+01 N/C

-c) 3.889E+01 N/C

-d) 4.278E+01 N/C

+e) 4.706E+01 N/C

Key: B2

1)

 $E_z(x=0,z)=\underset{-a}{\overset{b}{\int }}f(x,z)dx$
is an integral that calculates the z-component of the electric field at point P situated above the x-axis where a charged rod of length (a+b) is located. The distance between point P and the x-axis is z=1.3 m. Evaluate $f(x,y)$ at x=0.83 m if a=0.82 m, b=1.3 m. The total charge on the rod is 7 nC.

-a) 8.690E+00 V/m²

-b) 9.559E+00 V/m²

+c) 1.051E+01 V/m²

-d) 1.157E+01 V/m²

-e) 1.272E+01 V/m²

2)  $E(z)=\underset{0}{\overset{R}{\int }}f(r^{\prime },z)d{r}^{\prime }$
is an integral that calculates the magnitude of the electric field at a distance $z$ fromthe center of a thin circular disk as measured along a line normal to the plane of the disk. The disk's radius is $R=4.3\text{ m}$ and the surface charge density is $\sigma =2{\text{ nC/m}}^3$. Evaluate $f(r^{\prime },z)$ at $r^{\prime }=2.4\text{ m}$.

+a) 5.647E+00 V/m²

-b) 6.212E+00 V/m²

-c) 6.833E+00 V/m²

-d) 7.517E+00 V/m²

-e) 8.268E+00 V/m²

3)

Three small charged objects are placed as shown, where $b=2a$, and $a=6\times 10^{-7}\text{m}$.what angle does the force on $q_2$ make above the $-x$ axis if $q_1=2e$, $q_2=-9e$, and $q_3=5e$?

-a) 5.272E+01 degrees

+b) 5.799E+01 degrees

-c) 6.379E+01 degrees

-d) 7.017E+01 degrees

-e) 7.719E+01 degrees

4)

A ring is uniformly charged with a net charge of 9 nC. The radius of the ring is R=1.9 m, with its center at the origin and oriented normal to the z axis as shown. what is the magnitude of the electric field at a distance z=1.4 m (on axis) away from the loop's center?

-a) 7.119E+09 N/C²

-b) 7.831E+09 N/C²

+c) 8.614E+09 N/C²

-d) 9.476E+09 N/C²

-e) 1.042E+10 N/C²

5)

Three small charged objects are placed as shown, where $b=2a$, and $a=2\times 10^{-7}\text{m}$. What is the magnitude of the net force on $q_2$ if $q_1=1e$, $q_2=-8e$, and $q_3=2e$?

-a) 3.876E-14 N

-b) 4.263E-14 N

-c) 4.690E-14 N

+d) 5.159E-14 N

-e) 5.675E-14 N

6) A large thin isolated square plate has an area of 5 m². It is uniformly charged with 8 nC of charge. What is the magnitude of the electric field 3 mm from the center of the plate's surface?

-a) 6.171E+01 N/C

-b) 6.788E+01 N/C

-c) 7.467E+01 N/C

-d) 8.214E+01 N/C

+e) 9.035E+01 N/C

Key: C0

1)

Three small charged objects are placed as shown, where $b=2a$, and $a=2\times 10^{-7}\text{m}$. What is the magnitude of the net force on $q_2$ if $q_1=1e$, $q_2=-9e$, and $q_3=4e$?

-a) 5.014E-14 N

-b) 5.515E-14 N

-c) 6.067E-14 N

-d) 6.674E-14 N

+e) 7.341E-14 N

2)

Three small charged objects are placed as shown, where $b=2a$, and $a=2\times 10^{-7}\text{m}$.what angle does the force on $q_2$ make above the $-x$ axis if $q_1=3e$, $q_2=-9e$, and $q_3=5e$?

-a) 6.125E+01 degrees

+b) 6.738E+01 degrees

-c) 7.412E+01 degrees

-d) 8.153E+01 degrees

-e) 8.968E+01 degrees

3)

 $E_z(x=0,z)=\underset{-a}{\overset{b}{\int }}f(x,z)dx$
is an integral that calculates the z-component of the electric field at point P situated above the x-axis where a charged rod of length (a+b) is located. The distance between point P and the x-axis is z=1.8 m. Evaluate $f(x,y)$ at x=0.65 m if a=0.85 m, b=1.8 m. The total charge on the rod is 5 nC.

-a) 3.959E+00 V/m²

+b) 4.355E+00 V/m²

-c) 4.790E+00 V/m²

-d) 5.269E+00 V/m²

-e) 5.796E+00 V/m²

4)

A ring is uniformly charged with a net charge of 7 nC. The radius of the ring is R=1.7 m, with its center at the origin and oriented normal to the z axis as shown. what is the magnitude of the electric field at a distance z=1.1 m (on axis) away from the loop's center?

+a) 8.336E+09 N/C²

-b) 9.170E+09 N/C²

-c) 1.009E+10 N/C²

-d) 1.110E+10 N/C²

-e) 1.220E+10 N/C²

5)  $E(z)=\underset{0}{\overset{R}{\int }}f(r^{\prime },z)d{r}^{\prime }$
is an integral that calculates the magnitude of the electric field at a distance $z$ fromthe center of a thin circular disk as measured along a line normal to the plane of the disk. The disk's radius is $R=3.0\text{ m}$ and the surface charge density is $\sigma =8{\text{ nC/m}}^3$. Evaluate $f(r^{\prime },z)$ at $r^{\prime }=2.0\text{ m}$.

-a) 9.459E+00 V/m²

+b) 1.040E+01 V/m²

-c) 1.145E+01 V/m²

-d) 1.259E+01 V/m²

-e) 1.385E+01 V/m²

6) A large thin isolated square plate has an area of 6 m². It is uniformly charged with 5 nC of charge. What is the magnitude of the electric field 1 mm from the center of the plate's surface?

-a) 3.214E+01 N/C

-b) 3.536E+01 N/C

-c) 3.889E+01 N/C

-d) 4.278E+01 N/C

+e) 4.706E+01 N/C

Key: C1

1)  $E(z)=\underset{0}{\overset{R}{\int }}f(r^{\prime },z)d{r}^{\prime }$
is an integral that calculates the magnitude of the electric field at a distance $z$ fromthe center of a thin circular disk as measured along a line normal to the plane of the disk. The disk's radius is $R=4.3\text{ m}$ and the surface charge density is $\sigma =2{\text{ nC/m}}^3$. Evaluate $f(r^{\prime },z)$ at $r^{\prime }=2.4\text{ m}$.

+a) 5.647E+00 V/m²

-b) 6.212E+00 V/m²

-c) 6.833E+00 V/m²

-d) 7.517E+00 V/m²

-e) 8.268E+00 V/m²

2) A large thin isolated square plate has an area of 3 m². It is uniformly charged with 5 nC of charge. What is the magnitude of the electric field 3 mm from the center of the plate's surface?

+a) 9.412E+01 N/C

-b) 1.035E+02 N/C

-c) 1.139E+02 N/C

-d) 1.253E+02 N/C

-e) 1.378E+02 N/C

3)

Three small charged objects are placed as shown, where $b=2a$, and $a=2\times 10^{-7}\text{m}$. What is the magnitude of the net force on $q_2$ if $q_1=3e$, $q_2=-9e$, and $q_3=6e$?

-a) 1.308E-13 N

-b) 1.439E-13 N

-c) 1.583E-13 N

+d) 1.741E-13 N

-e) 1.915E-13 N

4)

Three small charged objects are placed as shown, where $b=2a$, and $a=6\times 10^{-7}\text{m}$.what angle does the force on $q_2$ make above the $-x$ axis if $q_1=3e$, $q_2=-7e$, and $q_3=4e$?

-a) 5.914E+01 degrees

-b) 6.506E+01 degrees

+c) 7.157E+01 degrees

-d) 7.872E+01 degrees

-e) 8.659E+01 degrees

5)

 $E_z(x=0,z)=\underset{-a}{\overset{b}{\int }}f(x,z)dx$
is an integral that calculates the z-component of the electric field at point P situated above the x-axis where a charged rod of length (a+b) is located. The distance between point P and the x-axis is z=1.2 m. Evaluate $f(x,y)$ at x=0.73 m if a=0.52 m, b=1.6 m. The total charge on the rod is 7 nC.

-a) 9.655E+00 V/m²

-b) 1.062E+01 V/m²

-c) 1.168E+01 V/m²

+d) 1.285E+01 V/m²

-e) 1.414E+01 V/m²

6)

A ring is uniformly charged with a net charge of 4 nC. The radius of the ring is R=1.6 m, with its center at the origin and oriented normal to the z axis as shown. what is the magnitude of the electric field at a distance z=1.0 m (on axis) away from the loop's center?

+a) 5.352E+09 N/C²

-b) 5.887E+09 N/C²

-c) 6.476E+09 N/C²

-d) 7.124E+09 N/C²

-e) 7.836E+09 N/C²

Key: C2

1)

Three small charged objects are placed as shown, where $b=2a$, and $a=6\times 10^{-7}\text{m}$. What is the magnitude of the net force on $q_2$ if $q_1=1e$, $q_2=-7e$, and $q_3=2e$?

-a) 3.426E-15 N

-b) 3.768E-15 N

-c) 4.145E-15 N

-d) 4.560E-15 N

+e) 5.015E-15 N

2)

 $E_z(x=0,z)=\underset{-a}{\overset{b}{\int }}f(x,z)dx$
is an integral that calculates the z-component of the electric field at point P situated above the x-axis where a charged rod of length (a+b) is located. The distance between point P and the x-axis is z=1.5 m. Evaluate $f(x,y)$ at x=0.79 m if a=0.75 m, b=2.1 m. The total charge on the rod is 6 nC.

+a) 5.825E+00 V/m²

-b) 6.407E+00 V/m²

-c) 7.048E+00 V/m²

-d) 7.753E+00 V/m²

-e) 8.528E+00 V/m²

3)

A ring is uniformly charged with a net charge of 3 nC. The radius of the ring is R=1.7 m, with its center at the origin and oriented normal to the z axis as shown. what is the magnitude of the electric field at a distance z=0.34 m (on axis) away from the loop's center?

-a) 1.202E+09 N/C²

-b) 1.322E+09 N/C²

-c) 1.454E+09 N/C²

-d) 1.599E+09 N/C²

+e) 1.759E+09 N/C²

4)

Three small charged objects are placed as shown, where $b=2a$, and $a=4\times 10^{-7}\text{m}$.what angle does the force on $q_2$ make above the $-x$ axis if $q_1=3e$, $q_2=-7e$, and $q_3=5e$?

-a) 5.569E+01 degrees

-b) 6.125E+01 degrees

+c) 6.738E+01 degrees

-d) 7.412E+01 degrees

-e) 8.153E+01 degrees

5) A large thin isolated square plate has an area of 5 m². It is uniformly charged with 7 nC of charge. What is the magnitude of the electric field 1 mm from the center of the plate's surface?

-a) 6.534E+01 N/C

-b) 7.187E+01 N/C

+c) 7.906E+01 N/C

-d) 8.696E+01 N/C

-e) 9.566E+01 N/C

6)  $E(z)=\underset{0}{\overset{R}{\int }}f(r^{\prime },z)d{r}^{\prime }$
is an integral that calculates the magnitude of the electric field at a distance $z$ fromthe center of a thin circular disk as measured along a line normal to the plane of the disk. The disk's radius is $R=6.8\text{ m}$ and the surface charge density is $\sigma =6{\text{ nC/m}}^3$. Evaluate $f(r^{\prime },z)$ at $r^{\prime }=3.6\text{ m}$.

-a) 1.258E+00 V/m²

-b) 1.384E+00 V/m²

-c) 1.522E+00 V/m²

+d) 1.674E+00 V/m²

-e) 1.842E+00 V/m²

Key: D0

1)

Three small charged objects are placed as shown, where $b=2a$, and $a=6\times 10^{-7}\text{m}$. What is the magnitude of the net force on $q_2$ if $q_1=1e$, $q_2=-7e$, and $q_3=2e$?

-a) 3.426E-15 N

-b) 3.768E-15 N

-c) 4.145E-15 N

-d) 4.560E-15 N

+e) 5.015E-15 N

2)

Three small charged objects are placed as shown, where $b=2a$, and $a=2\times 10^{-7}\text{m}$.what angle does the force on $q_2$ make above the $-x$ axis if $q_1=3e$, $q_2=-9e$, and $q_3=5e$?

-a) 6.125E+01 degrees

+b) 6.738E+01 degrees

-c) 7.412E+01 degrees

-d) 8.153E+01 degrees

-e) 8.968E+01 degrees

3)

 $E_z(x=0,z)=\underset{-a}{\overset{b}{\int }}f(x,z)dx$
is an integral that calculates the z-component of the electric field at point P situated above the x-axis where a charged rod of length (a+b) is located. The distance between point P and the x-axis is z=1.4 m. Evaluate $f(x,y)$ at x=1.1 m if a=0.69 m, b=2.2 m. The total charge on the rod is 6 nC.

-a) 3.161E+00 V/m²

-b) 3.477E+00 V/m²

-c) 3.825E+00 V/m²

-d) 4.208E+00 V/m²

+e) 4.628E+00 V/m²

4)

A ring is uniformly charged with a net charge of 2 nC. The radius of the ring is R=1.8 m, with its center at the origin and oriented normal to the z axis as shown. what is the magnitude of the electric field at a distance z=1.3 m (on axis) away from the loop's center?

-a) 1.764E+09 N/C²

-b) 1.941E+09 N/C²

+c) 2.135E+09 N/C²

-d) 2.348E+09 N/C²

-e) 2.583E+09 N/C²

5)  $E(z)=\underset{0}{\overset{R}{\int }}f(r^{\prime },z)d{r}^{\prime }$
is an integral that calculates the magnitude of the electric field at a distance $z$ fromthe center of a thin circular disk as measured along a line normal to the plane of the disk. The disk's radius is $R=2.0\text{ m}$ and the surface charge density is $\sigma =9{\text{ nC/m}}^3$. Evaluate $f(r^{\prime },z)$ at $r^{\prime }=1.2\text{ m}$.

-a) 8.933E+00 V/m²

-b) 9.826E+00 V/m²

+c) 1.081E+01 V/m²

-d) 1.189E+01 V/m²

-e) 1.308E+01 V/m²

6) A large thin isolated square plate has an area of 9 m². It is uniformly charged with 5 nC of charge. What is the magnitude of the electric field 1 mm from the center of the plate's surface?

-a) 2.357E+01 N/C

-b) 2.593E+01 N/C

-c) 2.852E+01 N/C

+d) 3.137E+01 N/C

-e) 3.451E+01 N/C

Key: D1

1)  $E(z)=\underset{0}{\overset{R}{\int }}f(r^{\prime },z)d{r}^{\prime }$
is an integral that calculates the magnitude of the electric field at a distance $z$ fromthe center of a thin circular disk as measured along a line normal to the plane of the disk. The disk's radius is $R=9.1\text{ m}$ and the surface charge density is $\sigma =2{\text{ nC/m}}^3$. Evaluate $f(r^{\prime },z)$ at $r^{\prime }=6.2\text{ m}$.

-a) 4.961E-01 V/m²

-b) 5.457E-01 V/m²

-c) 6.002E-01 V/m²

-d) 6.603E-01 V/m²

+e) 7.263E-01 V/m²

2)

Three small charged objects are placed as shown, where $b=2a$, and $a=6\times 10^{-7}\text{m}$. What is the magnitude of the net force on $q_2$ if $q_1=3e$, $q_2=-7e$, and $q_3=6e$?

-a) 1.028E-14 N

-b) 1.130E-14 N

-c) 1.244E-14 N

-d) 1.368E-14 N

+e) 1.505E-14 N

3)

 $E_z(x=0,z)=\underset{-a}{\overset{b}{\int }}f(x,z)dx$
is an integral that calculates the z-component of the electric field at point P situated above the x-axis where a charged rod of length (a+b) is located. The distance between point P and the x-axis is z=1.8 m. Evaluate $f(x,y)$ at x=1.0 m if a=1.0 m, b=1.8 m. The total charge on the rod is 6 nC.

-a) 3.610E+00 V/m²

+b) 3.971E+00 V/m²

-c) 4.368E+00 V/m²

-d) 4.804E+00 V/m²

-e) 5.285E+00 V/m²

4) A large thin isolated square plate has an area of 6 m². It is uniformly charged with 9 nC of charge. What is the magnitude of the electric field 1 mm from the center of the plate's surface?

-a) 7.701E+01 N/C

+b) 8.471E+01 N/C

-c) 9.318E+01 N/C

-d) 1.025E+02 N/C

-e) 1.127E+02 N/C

5)

A ring is uniformly charged with a net charge of 3 nC. The radius of the ring is R=1.8 m, with its center at the origin and oriented normal to the z axis as shown. what is the magnitude of the electric field at a distance z=1.1 m (on axis) away from the loop's center?

+a) 3.159E+09 N/C²

-b) 3.475E+09 N/C²

-c) 3.823E+09 N/C²

-d) 4.205E+09 N/C²

-e) 4.626E+09 N/C²

6)

Three small charged objects are placed as shown, where $b=2a$, and $a=2\times 10^{-7}\text{m}$.what angle does the force on $q_2$ make above the $-x$ axis if $q_1=2e$, $q_2=-7e$, and $q_3=3e$?

-a) 4.743E+01 degrees

-b) 5.217E+01 degrees

-c) 5.739E+01 degrees

-d) 6.313E+01 degrees

+e) 6.944E+01 degrees

Key: D2

1)

 $E_z(x=0,z)=\underset{-a}{\overset{b}{\int }}f(x,z)dx$
is an integral that calculates the z-component of the electric field at point P situated above the x-axis where a charged rod of length (a+b) is located. The distance between point P and the x-axis is z=1.8 m. Evaluate $f(x,y)$ at x=0.5 m if a=0.67 m, b=2.4 m. The total charge on the rod is 9 nC.

-a) 5.465E+00 V/m²

-b) 6.012E+00 V/m²

-c) 6.613E+00 V/m²

+d) 7.274E+00 V/m²

-e) 8.002E+00 V/m²

2)  $E(z)=\underset{0}{\overset{R}{\int }}f(r^{\prime },z)d{r}^{\prime }$
is an integral that calculates the magnitude of the electric field at a distance $z$ fromthe center of a thin circular disk as measured along a line normal to the plane of the disk. The disk's radius is $R=6.9\text{ m}$ and the surface charge density is $\sigma =9{\text{ nC/m}}^3$. Evaluate $f(r^{\prime },z)$ at $r^{\prime }=4.3\text{ m}$.

-a) 8.924E-01 V/m²

-b) 9.816E-01 V/m²

+c) 1.080E+00 V/m²

-d) 1.188E+00 V/m²

-e) 1.307E+00 V/m²

3)

Three small charged objects are placed as shown, where $b=2a$, and $a=6\times 10^{-7}\text{m}$.what angle does the force on $q_2$ make above the $-x$ axis if $q_1=3e$, $q_2=-7e$, and $q_3=6e$?

+a) 6.343E+01 degrees

-b) 6.978E+01 degrees

-c) 7.676E+01 degrees

-d) 8.443E+01 degrees

-e) 9.288E+01 degrees

4)

Three small charged objects are placed as shown, where $b=2a$, and $a=2\times 10^{-7}\text{m}$. What is the magnitude of the net force on $q_2$ if $q_1=1e$, $q_2=-8e$, and $q_3=2e$?

-a) 3.876E-14 N

-b) 4.263E-14 N

-c) 4.690E-14 N

+d) 5.159E-14 N

-e) 5.675E-14 N

5)

A ring is uniformly charged with a net charge of 9 nC. The radius of the ring is R=1.9 m, with its center at the origin and oriented normal to the z axis as shown. what is the magnitude of the electric field at a distance z=1.4 m (on axis) away from the loop's center?

-a) 7.119E+09 N/C²

-b) 7.831E+09 N/C²

+c) 8.614E+09 N/C²

-d) 9.476E+09 N/C²

-e) 1.042E+10 N/C²

6) A large thin isolated square plate has an area of 9 m². It is uniformly charged with 5 nC of charge. What is the magnitude of the electric field 1 mm from the center of the plate's surface?

-a) 2.357E+01 N/C

-b) 2.593E+01 N/C

-c) 2.852E+01 N/C

+d) 3.137E+01 N/C

-e) 3.451E+01 N/C

Key: E0

1)

Three small charged objects are placed as shown, where $b=2a$, and $a=2\times 10^{-7}\text{m}$. What is the magnitude of the net force on $q_2$ if $q_1=1e$, $q_2=-8e$, and $q_3=3e$?

-a) 5.243E-14 N

+b) 5.768E-14 N

-c) 6.344E-14 N

-d) 6.979E-14 N

-e) 7.677E-14 N

2)

Three small charged objects are placed as shown, where $b=2a$, and $a=2\times 10^{-7}\text{m}$.what angle does the force on $q_2$ make above the $-x$ axis if $q_1=2e$, $q_2=-9e$, and $q_3=4e$?

-a) 5.243E+01 degrees

-b) 5.767E+01 degrees

+c) 6.343E+01 degrees

-d) 6.978E+01 degrees

-e) 7.676E+01 degrees

3)

 $E_z(x=0,z)=\underset{-a}{\overset{b}{\int }}f(x,z)dx$
is an integral that calculates the z-component of the electric field at point P situated above the x-axis where a charged rod of length (a+b) is located. The distance between point P and the x-axis is z=1.5 m. Evaluate $f(x,y)$ at x=1.1 m if a=0.62 m, b=1.3 m. The total charge on the rod is 7 nC.

-a) 6.311E+00 V/m²

-b) 6.943E+00 V/m²

+c) 7.637E+00 V/m²

-d) 8.401E+00 V/m²

-e) 9.241E+00 V/m²

4)

A ring is uniformly charged with a net charge of 6 nC. The radius of the ring is R=1.9 m, with its center at the origin and oriented normal to the z axis as shown. what is the magnitude of the electric field at a distance z=0.4 m (on axis) away from the loop's center?

-a) 2.013E+09 N/C²

-b) 2.214E+09 N/C²

-c) 2.435E+09 N/C²

-d) 2.679E+09 N/C²

+e) 2.947E+09 N/C²

5)  $E(z)=\underset{0}{\overset{R}{\int }}f(r^{\prime },z)d{r}^{\prime }$
is an integral that calculates the magnitude of the electric field at a distance $z$ fromthe center of a thin circular disk as measured along a line normal to the plane of the disk. The disk's radius is $R=3.2\text{ m}$ and the surface charge density is $\sigma =2{\text{ nC/m}}^3$. Evaluate $f(r^{\prime },z)$ at $r^{\prime }=2.2\text{ m}$.

-a) 3.228E+00 V/m²

-b) 3.551E+00 V/m²

-c) 3.906E+00 V/m²

-d) 4.297E+00 V/m²

+e) 4.727E+00 V/m²

6) A large thin isolated square plate has an area of 9 m². It is uniformly charged with 8 nC of charge. What is the magnitude of the electric field 3 mm from the center of the plate's surface?

-a) 3.428E+01 N/C

-b) 3.771E+01 N/C

-c) 4.148E+01 N/C

-d) 4.563E+01 N/C

+e) 5.020E+01 N/C

Key: E1

1)

 $E_z(x=0,z)=\underset{-a}{\overset{b}{\int }}f(x,z)dx$
is an integral that calculates the z-component of the electric field at point P situated above the x-axis where a charged rod of length (a+b) is located. The distance between point P and the x-axis is z=1.7 m. Evaluate $f(x,y)$ at x=0.76 m if a=1.1 m, b=1.6 m. The total charge on the rod is 8 nC.

-a) 5.267E+00 V/m²

-b) 5.794E+00 V/m²

-c) 6.374E+00 V/m²

+d) 7.011E+00 V/m²

-e) 7.712E+00 V/m²

2)

A ring is uniformly charged with a net charge of 8 nC. The radius of the ring is R=1.7 m, with its center at the origin and oriented normal to the z axis as shown. what is the magnitude of the electric field at a distance z=0.32 m (on axis) away from the loop's center?

-a) 3.339E+09 N/C²

-b) 3.673E+09 N/C²

-c) 4.041E+09 N/C²

+d) 4.445E+09 N/C²

-e) 4.889E+09 N/C²

3)

Three small charged objects are placed as shown, where $b=2a$, and $a=2\times 10^{-7}\text{m}$. What is the magnitude of the net force on $q_2$ if $q_1=1e$, $q_2=-8e$, and $q_3=2e$?

-a) 3.876E-14 N

-b) 4.263E-14 N

-c) 4.690E-14 N

+d) 5.159E-14 N

-e) 5.675E-14 N

4)  $E(z)=\underset{0}{\overset{R}{\int }}f(r^{\prime },z)d{r}^{\prime }$
is an integral that calculates the magnitude of the electric field at a distance $z$ fromthe center of a thin circular disk as measured along a line normal to the plane of the disk. The disk's radius is $R=1.8\text{ m}$ and the surface charge density is $\sigma =9{\text{ nC/m}}^3$. Evaluate $f(r^{\prime },z)$ at $r^{\prime }=0.83\text{ m}$.

+a) 2.898E+01 V/m²

-b) 3.188E+01 V/m²

-c) 3.507E+01 V/m²

-d) 3.857E+01 V/m²

-e) 4.243E+01 V/m²

5)

Three small charged objects are placed as shown, where $b=2a$, and $a=4\times 10^{-7}\text{m}$.what angle does the force on $q_2$ make above the $-x$ axis if $q_1=3e$, $q_2=-7e$, and $q_3=5e$?

-a) 5.569E+01 degrees

-b) 6.125E+01 degrees

+c) 6.738E+01 degrees

-d) 7.412E+01 degrees

-e) 8.153E+01 degrees

6) A large thin isolated square plate has an area of 6 m². It is uniformly charged with 9 nC of charge. What is the magnitude of the electric field 3 mm from the center of the plate's surface?

+a) 8.471E+01 N/C

-b) 9.318E+01 N/C

-c) 1.025E+02 N/C

-d) 1.127E+02 N/C

-e) 1.240E+02 N/C

Key: E2

1)

 $E_z(x=0,z)=\underset{-a}{\overset{b}{\int }}f(x,z)dx$
is an integral that calculates the z-component of the electric field at point P situated above the x-axis where a charged rod of length (a+b) is located. The distance between point P and the x-axis is z=1.7 m. Evaluate $f(x,y)$ at x=0.52 m if a=0.88 m, b=1.3 m. The total charge on the rod is 6 nC.

-a) 6.804E+00 V/m²

+b) 7.485E+00 V/m²

-c) 8.233E+00 V/m²

-d) 9.056E+00 V/m²

-e) 9.962E+00 V/m²

2)

Three small charged objects are placed as shown, where $b=2a$, and $a=4\times 10^{-7}\text{m}$. What is the magnitude of the net force on $q_2$ if $q_1=3e$, $q_2=-7e$, and $q_3=6e$?

-a) 2.544E-14 N

-b) 2.798E-14 N

-c) 3.078E-14 N

+d) 3.385E-14 N

-e) 3.724E-14 N

3) A large thin isolated square plate has an area of 9 m². It is uniformly charged with 6 nC of charge. What is the magnitude of the electric field 1 mm from the center of the plate's surface?

-a) 2.571E+01 N/C

-b) 2.828E+01 N/C

-c) 3.111E+01 N/C

-d) 3.422E+01 N/C

+e) 3.765E+01 N/C

4)

A ring is uniformly charged with a net charge of 3 nC. The radius of the ring is R=1.8 m, with its center at the origin and oriented normal to the z axis as shown. what is the magnitude of the electric field at a distance z=1.1 m (on axis) away from the loop's center?

+a) 3.159E+09 N/C²

-b) 3.475E+09 N/C²

-c) 3.823E+09 N/C²

-d) 4.205E+09 N/C²

-e) 4.626E+09 N/C²

5)  $E(z)=\underset{0}{\overset{R}{\int }}f(r^{\prime },z)d{r}^{\prime }$
is an integral that calculates the magnitude of the electric field at a distance $z$ fromthe center of a thin circular disk as measured along a line normal to the plane of the disk. The disk's radius is $R=1.8\text{ m}$ and the surface charge density is $\sigma =3{\text{ nC/m}}^3$. Evaluate $f(r^{\prime },z)$ at $r^{\prime }=1.1\text{ m}$.

-a) 7.517E+00 V/m²

-b) 8.269E+00 V/m²

-c) 9.096E+00 V/m²

-d) 1.001E+01 V/m²

+e) 1.101E+01 V/m²

6)

Three small charged objects are placed as shown, where $b=2a$, and $a=4\times 10^{-7}\text{m}$.what angle does the force on $q_2$ make above the $-x$ axis if $q_1=3e$, $q_2=-8e$, and $q_3=6e$?

-a) 5.243E+01 degrees

-b) 5.767E+01 degrees

+c) 6.343E+01 degrees

-d) 6.978E+01 degrees

-e) 7.676E+01 degrees

Key: F0

1)

Three small charged objects are placed as shown, where $b=2a$, and $a=6\times 10^{-7}\text{m}$. What is the magnitude of the net force on $q_2$ if $q_1=3e$, $q_2=-7e$, and $q_3=5e$?

-a) 9.958E-15 N

-b) 1.095E-14 N

-c) 1.205E-14 N

-d) 1.325E-14 N

+e) 1.458E-14 N

2)

Three small charged objects are placed as shown, where $b=2a$, and $a=2\times 10^{-7}\text{m}$.what angle does the force on $q_2$ make above the $-x$ axis if $q_1=2e$, $q_2=-9e$, and $q_3=4e$?

-a) 5.243E+01 degrees

-b) 5.767E+01 degrees

+c) 6.343E+01 degrees

-d) 6.978E+01 degrees

-e) 7.676E+01 degrees

3)

 $E_z(x=0,z)=\underset{-a}{\overset{b}{\int }}f(x,z)dx$
is an integral that calculates the z-component of the electric field at point P situated above the x-axis where a charged rod of length (a+b) is located. The distance between point P and the x-axis is z=1.3 m. Evaluate $f(x,y)$ at x=0.83 m if a=0.82 m, b=1.3 m. The total charge on the rod is 7 nC.

-a) 8.690E+00 V/m²

-b) 9.559E+00 V/m²

+c) 1.051E+01 V/m²

-d) 1.157E+01 V/m²

-e) 1.272E+01 V/m²

4)

A ring is uniformly charged with a net charge of 7 nC. The radius of the ring is R=1.6 m, with its center at the origin and oriented normal to the z axis as shown. what is the magnitude of the electric field at a distance z=0.35 m (on axis) away from the loop's center?

-a) 4.142E+09 N/C²

-b) 4.556E+09 N/C²

+c) 5.012E+09 N/C²

-d) 5.513E+09 N/C²

-e) 6.064E+09 N/C²

5)  $E(z)=\underset{0}{\overset{R}{\int }}f(r^{\prime },z)d{r}^{\prime }$
is an integral that calculates the magnitude of the electric field at a distance $z$ fromthe center of a thin circular disk as measured along a line normal to the plane of the disk. The disk's radius is $R=1.4\text{ m}$ and the surface charge density is $\sigma =6{\text{ nC/m}}^3$. Evaluate $f(r^{\prime },z)$ at $r^{\prime }=0.56\text{ m}$.

-a) 2.567E+01 V/m²

-b) 2.824E+01 V/m²

-c) 3.106E+01 V/m²

-d) 3.417E+01 V/m²

+e) 3.759E+01 V/m²

6) A large thin isolated square plate has an area of 8 m². It is uniformly charged with 7 nC of charge. What is the magnitude of the electric field 3 mm from the center of the plate's surface?

-a) 4.492E+01 N/C

+b) 4.941E+01 N/C

-c) 5.435E+01 N/C

-d) 5.979E+01 N/C

-e) 6.577E+01 N/C

Key: F1

1)

Three small charged objects are placed as shown, where $b=2a$, and $a=2\times 10^{-7}\text{m}$. What is the magnitude of the net force on $q_2$ if $q_1=3e$, $q_2=-9e$, and $q_3=6e$?

-a) 1.308E-13 N

-b) 1.439E-13 N

-c) 1.583E-13 N

+d) 1.741E-13 N

-e) 1.915E-13 N

2)  $E(z)=\underset{0}{\overset{R}{\int }}f(r^{\prime },z)d{r}^{\prime }$
is an integral that calculates the magnitude of the electric field at a distance $z$ fromthe center of a thin circular disk as measured along a line normal to the plane of the disk. The disk's radius is $R=7.2\text{ m}$ and the surface charge density is $\sigma =3{\text{ nC/m}}^3$. Evaluate $f(r^{\prime },z)$ at $r^{\prime }=3.6\text{ m}$.

+a) 1.606E+00 V/m²

-b) 1.767E+00 V/m²

-c) 1.943E+00 V/m²

-d) 2.138E+00 V/m²

-e) 2.351E+00 V/m²

3) A large thin isolated square plate has an area of 6 m². It is uniformly charged with 9 nC of charge. What is the magnitude of the electric field 2 mm from the center of the plate's surface?

-a) 7.000E+01 N/C

-b) 7.701E+01 N/C

+c) 8.471E+01 N/C

-d) 9.318E+01 N/C

-e) 1.025E+02 N/C

4)

A ring is uniformly charged with a net charge of 7 nC. The radius of the ring is R=1.6 m, with its center at the origin and oriented normal to the z axis as shown. what is the magnitude of the electric field at a distance z=0.35 m (on axis) away from the loop's center?

-a) 4.142E+09 N/C²

-b) 4.556E+09 N/C²

+c) 5.012E+09 N/C²

-d) 5.513E+09 N/C²

-e) 6.064E+09 N/C²

5)

 $E_z(x=0,z)=\underset{-a}{\overset{b}{\int }}f(x,z)dx$
is an integral that calculates the z-component of the electric field at point P situated above the x-axis where a charged rod of length (a+b) is located. The distance between point P and the x-axis is z=1.8 m. Evaluate $f(x,y)$ at x=1.0 m if a=1.0 m, b=1.8 m. The total charge on the rod is 6 nC.

-a) 3.610E+00 V/m²

+b) 3.971E+00 V/m²

-c) 4.368E+00 V/m²

-d) 4.804E+00 V/m²

-e) 5.285E+00 V/m²

6)

Three small charged objects are placed as shown, where $b=2a$, and $a=6\times 10^{-7}\text{m}$.what angle does the force on $q_2$ make above the $-x$ axis if $q_1=3e$, $q_2=-7e$, and $q_3=4e$?

-a) 5.377E+01 degrees

-b) 5.914E+01 degrees

-c) 6.506E+01 degrees

+d) 7.157E+01 degrees

-e) 7.872E+01 degrees

Key: F2

1)

A ring is uniformly charged with a net charge of 2 nC. The radius of the ring is R=1.5 m, with its center at the origin and oriented normal to the z axis as shown. what is the magnitude of the electric field at a distance z=0.33 m (on axis) away from the loop's center?

-a) 1.353E+09 N/C²

-b) 1.488E+09 N/C²

+c) 1.637E+09 N/C²

-d) 1.801E+09 N/C²

-e) 1.981E+09 N/C²

2)

Three small charged objects are placed as shown, where $b=2a$, and $a=2\times 10^{-7}\text{m}$. What is the magnitude of the net force on $q_2$ if $q_1=1e$, $q_2=-7e$, and $q_3=2e$?

-a) 3.391E-14 N

-b) 3.731E-14 N

-c) 4.104E-14 N

+d) 4.514E-14 N

-e) 4.965E-14 N

3)

 $E_z(x=0,z)=\underset{-a}{\overset{b}{\int }}f(x,z)dx$
is an integral that calculates the z-component of the electric field at point P situated above the x-axis where a charged rod of length (a+b) is located. The distance between point P and the x-axis is z=1.9 m. Evaluate $f(x,y)$ at x=0.96 m if a=0.95 m, b=1.8 m. The total charge on the rod is 7 nC.

-a) 3.385E+00 V/m²

-b) 3.724E+00 V/m²

-c) 4.096E+00 V/m²

+d) 4.506E+00 V/m²

-e) 4.957E+00 V/m²

4)

Three small charged objects are placed as shown, where $b=2a$, and $a=4\times 10^{-7}\text{m}$.what angle does the force on $q_2$ make above the $-x$ axis if $q_1=1e$, $q_2=-8e$, and $q_3=4e$?

-a) 3.719E+01 degrees

-b) 4.091E+01 degrees

+c) 4.500E+01 degrees

-d) 4.950E+01 degrees

-e) 5.445E+01 degrees

5) A large thin isolated square plate has an area of 6 m². It is uniformly charged with 6 nC of charge. What is the magnitude of the electric field 2 mm from the center of the plate's surface?

+a) 5.647E+01 N/C

-b) 6.212E+01 N/C

-c) 6.833E+01 N/C

-d) 7.516E+01 N/C

-e) 8.268E+01 N/C

6)  $E(z)=\underset{0}{\overset{R}{\int }}f(r^{\prime },z)d{r}^{\prime }$
is an integral that calculates the magnitude of the electric field at a distance $z$ fromthe center of a thin circular disk as measured along a line normal to the plane of the disk. The disk's radius is $R=6.9\text{ m}$ and the surface charge density is $\sigma =9{\text{ nC/m}}^3$. Evaluate $f(r^{\prime },z)$ at $r^{\prime }=4.3\text{ m}$.

-a) 8.924E-01 V/m²

-b) 9.816E-01 V/m²

+c) 1.080E+00 V/m²

-d) 1.188E+00 V/m²

-e) 1.307E+00 V/m²

Key: G0

1)

Three small charged objects are placed as shown, where $b=2a$, and $a=2\times 10^{-7}\text{m}$. What is the magnitude of the net force on $q_2$ if $q_1=1e$, $q_2=-7e$, and $q_3=2e$?

-a) 3.391E-14 N

-b) 3.731E-14 N

-c) 4.104E-14 N

+d) 4.514E-14 N

-e) 4.965E-14 N

2)

Three small charged objects are placed as shown, where $b=2a$, and $a=6\times 10^{-7}\text{m}$.what angle does the force on $q_2$ make above the $-x$ axis if $q_1=3e$, $q_2=-7e$, and $q_3=4e$?

-a) 5.914E+01 degrees

-b) 6.506E+01 degrees

+c) 7.157E+01 degrees

-d) 7.872E+01 degrees

-e) 8.659E+01 degrees

3)

 $E_z(x=0,z)=\underset{-a}{\overset{b}{\int }}f(x,z)dx$
is an integral that calculates the z-component of the electric field at point P situated above the x-axis where a charged rod of length (a+b) is located. The distance between point P and the x-axis is z=1.3 m. Evaluate $f(x,y)$ at x=0.83 m if a=0.82 m, b=1.3 m. The total charge on the rod is 7 nC.

-a) 8.690E+00 V/m²

-b) 9.559E+00 V/m²

+c) 1.051E+01 V/m²

-d) 1.157E+01 V/m²

-e) 1.272E+01 V/m²

4)

A ring is uniformly charged with a net charge of 7 nC. The radius of the ring is R=1.7 m, with its center at the origin and oriented normal to the z axis as shown. what is the magnitude of the electric field at a distance z=1.1 m (on axis) away from the loop's center?

+a) 8.336E+09 N/C²

-b) 9.170E+09 N/C²

-c) 1.009E+10 N/C²

-d) 1.110E+10 N/C²

-e) 1.220E+10 N/C²

5)  $E(z)=\underset{0}{\overset{R}{\int }}f(r^{\prime },z)d{r}^{\prime }$
is an integral that calculates the magnitude of the electric field at a distance $z$ fromthe center of a thin circular disk as measured along a line normal to the plane of the disk. The disk's radius is $R=3.0\text{ m}$ and the surface charge density is $\sigma =8{\text{ nC/m}}^3$. Evaluate $f(r^{\prime },z)$ at $r^{\prime }=2.0\text{ m}$.

-a) 9.459E+00 V/m²

+b) 1.040E+01 V/m²

-c) 1.145E+01 V/m²

-d) 1.259E+01 V/m²

-e) 1.385E+01 V/m²

6) A large thin isolated square plate has an area of 6 m². It is uniformly charged with 5 nC of charge. What is the magnitude of the electric field 1 mm from the center of the plate's surface?

-a) 3.214E+01 N/C

-b) 3.536E+01 N/C

-c) 3.889E+01 N/C

-d) 4.278E+01 N/C

+e) 4.706E+01 N/C

Key: G1

1)  $E(z)=\underset{0}{\overset{R}{\int }}f(r^{\prime },z)d{r}^{\prime }$
is an integral that calculates the magnitude of the electric field at a distance $z$ fromthe center of a thin circular disk as measured along a line normal to the plane of the disk. The disk's radius is $R=2.8\text{ m}$ and the surface charge density is $\sigma =3{\text{ nC/m}}^3$. Evaluate $f(r^{\prime },z)$ at $r^{\prime }=1.9\text{ m}$.

-a) 4.295E+00 V/m²

+b) 4.724E+00 V/m²

-c) 5.196E+00 V/m²

-d) 5.716E+00 V/m²

-e) 6.288E+00 V/m²

2)

Three small charged objects are placed as shown, where $b=2a$, and $a=6\times 10^{-7}\text{m}$.what angle does the force on $q_2$ make above the $-x$ axis if $q_1=2e$, $q_2=-9e$, and $q_3=5e$?

-a) 5.272E+01 degrees

+b) 5.799E+01 degrees

-c) 6.379E+01 degrees

-d) 7.017E+01 degrees

-e) 7.719E+01 degrees

3)

Three small charged objects are placed as shown, where $b=2a$, and $a=4\times 10^{-7}\text{m}$. What is the magnitude of the net force on $q_2$ if $q_1=2e$, $q_2=-8e$, and $q_3=3e$?

-a) 2.036E-14 N

-b) 2.240E-14 N

+c) 2.464E-14 N

-d) 2.710E-14 N

-e) 2.981E-14 N

4) A large thin isolated square plate has an area of 9 m². It is uniformly charged with 8 nC of charge. What is the magnitude of the electric field 3 mm from the center of the plate's surface?

-a) 3.428E+01 N/C

-b) 3.771E+01 N/C

-c) 4.148E+01 N/C

-d) 4.563E+01 N/C

+e) 5.020E+01 N/C

5)

 $E_z(x=0,z)=\underset{-a}{\overset{b}{\int }}f(x,z)dx$
is an integral that calculates the z-component of the electric field at point P situated above the x-axis where a charged rod of length (a+b) is located. The distance between point P and the x-axis is z=1.4 m. Evaluate $f(x,y)$ at x=1.1 m if a=0.69 m, b=2.2 m. The total charge on the rod is 6 nC.

-a) 3.161E+00 V/m²

-b) 3.477E+00 V/m²

-c) 3.825E+00 V/m²

-d) 4.208E+00 V/m²

+e) 4.628E+00 V/m²

6)

A ring is uniformly charged with a net charge of 2 nC. The radius of the ring is R=1.5 m, with its center at the origin and oriented normal to the z axis as shown. what is the magnitude of the electric field at a distance z=0.33 m (on axis) away from the loop's center?

-a) 1.353E+09 N/C²

-b) 1.488E+09 N/C²

+c) 1.637E+09 N/C²

-d) 1.801E+09 N/C²

-e) 1.981E+09 N/C²

Key: G2

1)

A ring is uniformly charged with a net charge of 4 nC. The radius of the ring is R=1.6 m, with its center at the origin and oriented normal to the z axis as shown. what is the magnitude of the electric field at a distance z=1.0 m (on axis) away from the loop's center?

+a) 5.352E+09 N/C²

-b) 5.887E+09 N/C²

-c) 6.476E+09 N/C²

-d) 7.124E+09 N/C²

-e) 7.836E+09 N/C²

2) A large thin isolated square plate has an area of 9 m². It is uniformly charged with 8 nC of charge. What is the magnitude of the electric field 3 mm from the center of the plate's surface?

-a) 3.428E+01 N/C

-b) 3.771E+01 N/C

-c) 4.148E+01 N/C

-d) 4.563E+01 N/C

+e) 5.020E+01 N/C

3)

Three small charged objects are placed as shown, where $b=2a$, and $a=2\times 10^{-7}\text{m}$. What is the magnitude of the net force on $q_2$ if $q_1=1e$, $q_2=-8e$, and $q_3=3e$?

-a) 5.243E-14 N

+b) 5.768E-14 N

-c) 6.344E-14 N

-d) 6.979E-14 N

-e) 7.677E-14 N

4)  $E(z)=\underset{0}{\overset{R}{\int }}f(r^{\prime },z)d{r}^{\prime }$
is an integral that calculates the magnitude of the electric field at a distance $z$ fromthe center of a thin circular disk as measured along a line normal to the plane of the disk. The disk's radius is $R=3.0\text{ m}$ and the surface charge density is $\sigma =8{\text{ nC/m}}^3$. Evaluate $f(r^{\prime },z)$ at $r^{\prime }=2.0\text{ m}$.

-a) 9.459E+00 V/m²

+b) 1.040E+01 V/m²

-c) 1.145E+01 V/m²

-d) 1.259E+01 V/m²

-e) 1.385E+01 V/m²

5)

Three small charged objects are placed as shown, where $b=2a$, and $a=4\times 10^{-7}\text{m}$.what angle does the force on $q_2$ make above the $-x$ axis if $q_1=3e$, $q_2=-8e$, and $q_3=6e$?

-a) 5.243E+01 degrees

-b) 5.767E+01 degrees

+c) 6.343E+01 degrees

-d) 6.978E+01 degrees

-e) 7.676E+01 degrees

6)

 $E_z(x=0,z)=\underset{-a}{\overset{b}{\int }}f(x,z)dx$
is an integral that calculates the z-component of the electric field at point P situated above the x-axis where a charged rod of length (a+b) is located. The distance between point P and the x-axis is z=1.8 m. Evaluate $f(x,y)$ at x=0.5 m if a=0.67 m, b=2.4 m. The total charge on the rod is 9 nC.

-a) 5.465E+00 V/m²

-b) 6.012E+00 V/m²

-c) 6.613E+00 V/m²

+d) 7.274E+00 V/m²

-e) 8.002E+00 V/m²

Key: H0

1)

Three small charged objects are placed as shown, where $b=2a$, and $a=6\times 10^{-7}\text{m}$. What is the magnitude of the net force on $q_2$ if $q_1=2e$, $q_2=-8e$, and $q_3=4e$?

-a) 8.613E-15 N

-b) 9.474E-15 N

-c) 1.042E-14 N

+d) 1.146E-14 N

-e) 1.261E-14 N

2)

Three small charged objects are placed as shown, where $b=2a$, and $a=6\times 10^{-7}\text{m}$.what angle does the force on $q_2$ make above the $-x$ axis if $q_1=2e$, $q_2=-9e$, and $q_3=4e$?

-a) 4.766E+01 degrees

-b) 5.243E+01 degrees

-c) 5.767E+01 degrees

+d) 6.343E+01 degrees

-e) 6.978E+01 degrees

3)

 $E_z(x=0,z)=\underset{-a}{\overset{b}{\int }}f(x,z)dx$
is an integral that calculates the z-component of the electric field at point P situated above the x-axis where a charged rod of length (a+b) is located. The distance between point P and the x-axis is z=1.2 m. Evaluate $f(x,y)$ at x=0.73 m if a=0.52 m, b=1.6 m. The total charge on the rod is 7 nC.

-a) 9.655E+00 V/m²

-b) 1.062E+01 V/m²

-c) 1.168E+01 V/m²

+d) 1.285E+01 V/m²

-e) 1.414E+01 V/m²

4)

A ring is uniformly charged with a net charge of 4 nC. The radius of the ring is R=1.6 m, with its center at the origin and oriented normal to the z axis as shown. what is the magnitude of the electric field at a distance z=1.0 m (on axis) away from the loop's center?

+a) 5.352E+09 N/C²

-b) 5.887E+09 N/C²

-c) 6.476E+09 N/C²

-d) 7.124E+09 N/C²

-e) 7.836E+09 N/C²

5)  $E(z)=\underset{0}{\overset{R}{\int }}f(r^{\prime },z)d{r}^{\prime }$
is an integral that calculates the magnitude of the electric field at a distance $z$ fromthe center of a thin circular disk as measured along a line normal to the plane of the disk. The disk's radius is $R=8.7\text{ m}$ and the surface charge density is $\sigma =7{\text{ nC/m}}^3$. Evaluate $f(r^{\prime },z)$ at $r^{\prime }=5.8\text{ m}$.

-a) 3.722E-01 V/m²

-b) 4.094E-01 V/m²

-c) 4.504E-01 V/m²

+d) 4.954E-01 V/m²

-e) 5.450E-01 V/m²

6) A large thin isolated square plate has an area of 9 m². It is uniformly charged with 5 nC of charge. What is the magnitude of the electric field 1 mm from the center of the plate's surface?

-a) 2.357E+01 N/C

-b) 2.593E+01 N/C

-c) 2.852E+01 N/C

+d) 3.137E+01 N/C

-e) 3.451E+01 N/C

Key: H1

1) A large thin isolated square plate has an area of 5 m². It is uniformly charged with 7 nC of charge. What is the magnitude of the electric field 1 mm from the center of the plate's surface?

-a) 6.534E+01 N/C

-b) 7.187E+01 N/C

+c) 7.906E+01 N/C

-d) 8.696E+01 N/C

-e) 9.566E+01 N/C

2)

Three small charged objects are placed as shown, where $b=2a$, and $a=6\times 10^{-7}\text{m}$. What is the magnitude of the net force on $q_2$ if $q_1=3e$, $q_2=-7e$, and $q_3=5e$?

-a) 9.958E-15 N

-b) 1.095E-14 N

-c) 1.205E-14 N

-d) 1.325E-14 N

+e) 1.458E-14 N

3)

 $E_z(x=0,z)=\underset{-a}{\overset{b}{\int }}f(x,z)dx$
is an integral that calculates the z-component of the electric field at point P situated above the x-axis where a charged rod of length (a+b) is located. The distance between point P and the x-axis is z=1.6 m. Evaluate $f(x,y)$ at x=0.73 m if a=0.64 m, b=1.8 m. The total charge on the rod is 3 nC.

-a) 2.955E+00 V/m²

+b) 3.250E+00 V/m²

-c) 3.575E+00 V/m²

-d) 3.933E+00 V/m²

-e) 4.326E+00 V/m²

4)  $E(z)=\underset{0}{\overset{R}{\int }}f(r^{\prime },z)d{r}^{\prime }$
is an integral that calculates the magnitude of the electric field at a distance $z$ fromthe center of a thin circular disk as measured along a line normal to the plane of the disk. The disk's radius is $R=8.7\text{ m}$ and the surface charge density is $\sigma =7{\text{ nC/m}}^3$. Evaluate $f(r^{\prime },z)$ at $r^{\prime }=5.8\text{ m}$.

-a) 3.722E-01 V/m²

-b) 4.094E-01 V/m²

-c) 4.504E-01 V/m²

+d) 4.954E-01 V/m²

-e) 5.450E-01 V/m²

5)

Three small charged objects are placed as shown, where $b=2a$, and $a=4\times 10^{-7}\text{m}$.what angle does the force on $q_2$ make above the $-x$ axis if $q_1=3e$, $q_2=-8e$, and $q_3=6e$?

-a) 5.243E+01 degrees

-b) 5.767E+01 degrees

+c) 6.343E+01 degrees

-d) 6.978E+01 degrees

-e) 7.676E+01 degrees

6)

A ring is uniformly charged with a net charge of 6 nC. The radius of the ring is R=1.9 m, with its center at the origin and oriented normal to the z axis as shown. what is the magnitude of the electric field at a distance z=0.4 m (on axis) away from the loop's center?

-a) 2.013E+09 N/C²

-b) 2.214E+09 N/C²

-c) 2.435E+09 N/C²

-d) 2.679E+09 N/C²

+e) 2.947E+09 N/C²

Key: H2

1)

 $E_z(x=0,z)=\underset{-a}{\overset{b}{\int }}f(x,z)dx$
is an integral that calculates the z-component of the electric field at point P situated above the x-axis where a charged rod of length (a+b) is located. The distance between point P and the x-axis is z=1.2 m. Evaluate $f(x,y)$ at x=0.54 m if a=0.76 m, b=1.7 m. The total charge on the rod is 8 nC.

-a) 1.399E+01 V/m²

+b) 1.539E+01 V/m²

-c) 1.693E+01 V/m²

-d) 1.862E+01 V/m²

-e) 2.049E+01 V/m²

2)

Three small charged objects are placed as shown, where $b=2a$, and $a=2\times 10^{-7}\text{m}$.what angle does the force on $q_2$ make above the $-x$ axis if $q_1=2e$, $q_2=-7e$, and $q_3=3e$?

-a) 4.743E+01 degrees

-b) 5.217E+01 degrees

-c) 5.739E+01 degrees

-d) 6.313E+01 degrees

+e) 6.944E+01 degrees

3)  $E(z)=\underset{0}{\overset{R}{\int }}f(r^{\prime },z)d{r}^{\prime }$
is an integral that calculates the magnitude of the electric field at a distance $z$ fromthe center of a thin circular disk as measured along a line normal to the plane of the disk. The disk's radius is $R=6.9\text{ m}$ and the surface charge density is $\sigma =9{\text{ nC/m}}^3$. Evaluate $f(r^{\prime },z)$ at $r^{\prime }=4.3\text{ m}$.

-a) 8.924E-01 V/m²

-b) 9.816E-01 V/m²

+c) 1.080E+00 V/m²

-d) 1.188E+00 V/m²

-e) 1.307E+00 V/m²

4)

Three small charged objects are placed as shown, where $b=2a$, and $a=6\times 10^{-7}\text{m}$. What is the magnitude of the net force on $q_2$ if $q_1=2e$, $q_2=-8e$, and $q_3=4e$?

-a) 8.613E-15 N

-b) 9.474E-15 N

-c) 1.042E-14 N

+d) 1.146E-14 N

-e) 1.261E-14 N

5) A large thin isolated square plate has an area of 8 m². It is uniformly charged with 6 nC of charge. What is the magnitude of the electric field 1 mm from the center of the plate's surface?

-a) 3.500E+01 N/C

-b) 3.850E+01 N/C

+c) 4.235E+01 N/C

-d) 4.659E+01 N/C

-e) 5.125E+01 N/C

6)

A ring is uniformly charged with a net charge of 3 nC. The radius of the ring is R=1.7 m, with its center at the origin and oriented normal to the z axis as shown. what is the magnitude of the electric field at a distance z=0.34 m (on axis) away from the loop's center?

-a) 1.202E+09 N/C²

-b) 1.322E+09 N/C²

-c) 1.454E+09 N/C²

-d) 1.599E+09 N/C²

+e) 1.759E+09 N/C²

Key: I0

1)

Three small charged objects are placed as shown, where $b=2a$, and $a=2\times 10^{-7}\text{m}$. What is the magnitude of the net force on $q_2$ if $q_1=3e$, $q_2=-9e$, and $q_3=6e$?

-a) 1.308E-13 N

-b) 1.439E-13 N

-c) 1.583E-13 N

+d) 1.741E-13 N

-e) 1.915E-13 N

2)

Three small charged objects are placed as shown, where $b=2a$, and $a=6\times 10^{-7}\text{m}$.what angle does the force on $q_2$ make above the $-x$ axis if $q_1=3e$, $q_2=-8e$, and $q_3=5e$?

-a) 5.062E+01 degrees

-b) 5.569E+01 degrees

-c) 6.125E+01 degrees

+d) 6.738E+01 degrees

-e) 7.412E+01 degrees

3)

 $E_z(x=0,z)=\underset{-a}{\overset{b}{\int }}f(x,z)dx$
is an integral that calculates the z-component of the electric field at point P situated above the x-axis where a charged rod of length (a+b) is located. The distance between point P and the x-axis is z=1.6 m. Evaluate $f(x,y)$ at x=0.73 m if a=0.64 m, b=1.8 m. The total charge on the rod is 3 nC.

-a) 2.955E+00 V/m²

+b) 3.250E+00 V/m²

-c) 3.575E+00 V/m²

-d) 3.933E+00 V/m²

-e) 4.326E+00 V/m²

4)

A ring is uniformly charged with a net charge of 7 nC. The radius of the ring is R=1.7 m, with its center at the origin and oriented normal to the z axis as shown. what is the magnitude of the electric field at a distance z=1.2 m (on axis) away from the loop's center?

-a) 6.925E+09 N/C²

-b) 7.617E+09 N/C²

+c) 8.379E+09 N/C²

-d) 9.217E+09 N/C²

-e) 1.014E+10 N/C²

5)  $E(z)=\underset{0}{\overset{R}{\int }}f(r^{\prime },z)d{r}^{\prime }$
is an integral that calculates the magnitude of the electric field at a distance $z$ fromthe center of a thin circular disk as measured along a line normal to the plane of the disk. The disk's radius is $R=4.3\text{ m}$ and the surface charge density is $\sigma =2{\text{ nC/m}}^3$. Evaluate $f(r^{\prime },z)$ at $r^{\prime }=2.4\text{ m}$.

+a) 5.647E+00 V/m²

-b) 6.212E+00 V/m²

-c) 6.833E+00 V/m²

-d) 7.517E+00 V/m²

-e) 8.268E+00 V/m²

6) A large thin isolated square plate has an area of 5 m². It is uniformly charged with 8 nC of charge. What is the magnitude of the electric field 3 mm from the center of the plate's surface?

-a) 6.171E+01 N/C

-b) 6.788E+01 N/C

-c) 7.467E+01 N/C

-d) 8.214E+01 N/C

+e) 9.035E+01 N/C

Key: I1

1)

 $E_z(x=0,z)=\underset{-a}{\overset{b}{\int }}f(x,z)dx$
is an integral that calculates the z-component of the electric field at point P situated above the x-axis where a charged rod of length (a+b) is located. The distance between point P and the x-axis is z=1.8 m. Evaluate $f(x,y)$ at x=0.5 m if a=0.67 m, b=2.4 m. The total charge on the rod is 9 nC.

-a) 5.465E+00 V/m²

-b) 6.012E+00 V/m²

-c) 6.613E+00 V/m²

+d) 7.274E+00 V/m²

-e) 8.002E+00 V/m²

2)

Three small charged objects are placed as shown, where $b=2a$, and $a=6\times 10^{-7}\text{m}$. What is the magnitude of the net force on $q_2$ if $q_1=2e$, $q_2=-8e$, and $q_3=4e$?

-a) 8.613E-15 N

-b) 9.474E-15 N

-c) 1.042E-14 N

+d) 1.146E-14 N

-e) 1.261E-14 N

3)

Three small charged objects are placed as shown, where $b=2a$, and $a=4\times 10^{-7}\text{m}$.what angle does the force on $q_2$ make above the $-x$ axis if $q_1=2e$, $q_2=-9e$, and $q_3=5e$?

-a) 3.961E+01 degrees

-b) 4.357E+01 degrees

-c) 4.793E+01 degrees

-d) 5.272E+01 degrees

+e) 5.799E+01 degrees

4)

A ring is uniformly charged with a net charge of 7 nC. The radius of the ring is R=1.7 m, with its center at the origin and oriented normal to the z axis as shown. what is the magnitude of the electric field at a distance z=1.2 m (on axis) away from the loop's center?

-a) 6.925E+09 N/C²

-b) 7.617E+09 N/C²

+c) 8.379E+09 N/C²

-d) 9.217E+09 N/C²

-e) 1.014E+10 N/C²

5)  $E(z)=\underset{0}{\overset{R}{\int }}f(r^{\prime },z)d{r}^{\prime }$
is an integral that calculates the magnitude of the electric field at a distance $z$ fromthe center of a thin circular disk as measured along a line normal to the plane of the disk. The disk's radius is $R=9.1\text{ m}$ and the surface charge density is $\sigma =2{\text{ nC/m}}^3$. Evaluate $f(r^{\prime },z)$ at $r^{\prime }=6.2\text{ m}$.

-a) 4.961E-01 V/m²

-b) 5.457E-01 V/m²

-c) 6.002E-01 V/m²

-d) 6.603E-01 V/m²

+e) 7.263E-01 V/m²

6) A large thin isolated square plate has an area of 4 m². It is uniformly charged with 5 nC of charge. What is the magnitude of the electric field 1 mm from the center of the plate's surface?

-a) 4.821E+01 N/C

-b) 5.303E+01 N/C

-c) 5.834E+01 N/C

-d) 6.417E+01 N/C

+e) 7.059E+01 N/C

Key: I2

1)  $E(z)=\underset{0}{\overset{R}{\int }}f(r^{\prime },z)d{r}^{\prime }$
is an integral that calculates the magnitude of the electric field at a distance $z$ fromthe center of a thin circular disk as measured along a line normal to the plane of the disk. The disk's radius is $R=4.3\text{ m}$ and the surface charge density is $\sigma =2{\text{ nC/m}}^3$. Evaluate $f(r^{\prime },z)$ at $r^{\prime }=2.4\text{ m}$.

+a) 5.647E+00 V/m²

-b) 6.212E+00 V/m²

-c) 6.833E+00 V/m²

-d) 7.517E+00 V/m²

-e) 8.268E+00 V/m²

2)

Three small charged objects are placed as shown, where $b=2a$, and $a=6\times 10^{-7}\text{m}$.what angle does the force on $q_2$ make above the $-x$ axis if $q_1=3e$, $q_2=-7e$, and $q_3=4e$?

-a) 5.914E+01 degrees

-b) 6.506E+01 degrees

+c) 7.157E+01 degrees

-d) 7.872E+01 degrees

-e) 8.659E+01 degrees

3)

Three small charged objects are placed as shown, where $b=2a$, and $a=4\times 10^{-7}\text{m}$. What is the magnitude of the net force on $q_2$ if $q_1=2e$, $q_2=-8e$, and $q_3=5e$?

-a) 2.248E-14 N

-b) 2.473E-14 N

+c) 2.721E-14 N

-d) 2.993E-14 N

-e) 3.292E-14 N

4)

A ring is uniformly charged with a net charge of 2 nC. The radius of the ring is R=1.6 m, with its center at the origin and oriented normal to the z axis as shown. what is the magnitude of the electric field at a distance z=0.99 m (on axis) away from the loop's center?

-a) 2.429E+09 N/C²

+b) 2.672E+09 N/C²

-c) 2.939E+09 N/C²

-d) 3.233E+09 N/C²

-e) 3.556E+09 N/C²

5) A large thin isolated square plate has an area of 9 m². It is uniformly charged with 6 nC of charge. What is the magnitude of the electric field 1 mm from the center of the plate's surface?

-a) 2.571E+01 N/C

-b) 2.828E+01 N/C

-c) 3.111E+01 N/C

-d) 3.422E+01 N/C

+e) 3.765E+01 N/C

6)

 $E_z(x=0,z)=\underset{-a}{\overset{b}{\int }}f(x,z)dx$
is an integral that calculates the z-component of the electric field at point P situated above the x-axis where a charged rod of length (a+b) is located. The distance between point P and the x-axis is z=1.9 m. Evaluate $f(x,y)$ at x=0.96 m if a=0.95 m, b=1.8 m. The total charge on the rod is 7 nC.

-a) 3.385E+00 V/m²

-b) 3.724E+00 V/m²

-c) 4.096E+00 V/m²

+d) 4.506E+00 V/m²

-e) 4.957E+00 V/m²

Key: J0

1)

Three small charged objects are placed as shown, where $b=2a$, and $a=4\times 10^{-7}\text{m}$. What is the magnitude of the net force on $q_2$ if $q_1=2e$, $q_2=-8e$, and $q_3=5e$?

-a) 2.248E-14 N

-b) 2.473E-14 N

+c) 2.721E-14 N

-d) 2.993E-14 N

-e) 3.292E-14 N

2)

Three small charged objects are placed as shown, where $b=2a$, and $a=2\times 10^{-7}\text{m}$.what angle does the force on $q_2$ make above the $-x$ axis if $q_1=3e$, $q_2=-9e$, and $q_3=5e$?

-a) 6.125E+01 degrees

+b) 6.738E+01 degrees

-c) 7.412E+01 degrees

-d) 8.153E+01 degrees

-e) 8.968E+01 degrees

3)

 $E_z(x=0,z)=\underset{-a}{\overset{b}{\int }}f(x,z)dx$
is an integral that calculates the z-component of the electric field at point P situated above the x-axis where a charged rod of length (a+b) is located. The distance between point P and the x-axis is z=1.9 m. Evaluate $f(x,y)$ at x=0.54 m if a=1.0 m, b=2.0 m. The total charge on the rod is 3 nC.

-a) 1.665E+00 V/m²

-b) 1.831E+00 V/m²

-c) 2.014E+00 V/m²

+d) 2.216E+00 V/m²

-e) 2.437E+00 V/m²

4)

A ring is uniformly charged with a net charge of 7 nC. The radius of the ring is R=1.6 m, with its center at the origin and oriented normal to the z axis as shown. what is the magnitude of the electric field at a distance z=0.35 m (on axis) away from the loop's center?

-a) 4.142E+09 N/C²

-b) 4.556E+09 N/C²

+c) 5.012E+09 N/C²

-d) 5.513E+09 N/C²

-e) 6.064E+09 N/C²

5)  $E(z)=\underset{0}{\overset{R}{\int }}f(r^{\prime },z)d{r}^{\prime }$
is an integral that calculates the magnitude of the electric field at a distance $z$ fromthe center of a thin circular disk as measured along a line normal to the plane of the disk. The disk's radius is $R=9.1\text{ m}$ and the surface charge density is $\sigma =2{\text{ nC/m}}^3$. Evaluate $f(r^{\prime },z)$ at $r^{\prime }=6.2\text{ m}$.

-a) 4.961E-01 V/m²

-b) 5.457E-01 V/m²

-c) 6.002E-01 V/m²

-d) 6.603E-01 V/m²

+e) 7.263E-01 V/m²

6) A large thin isolated square plate has an area of 4 m². It is uniformly charged with 5 nC of charge. What is the magnitude of the electric field 1 mm from the center of the plate's surface?

-a) 4.821E+01 N/C

-b) 5.303E+01 N/C

-c) 5.834E+01 N/C

-d) 6.417E+01 N/C

+e) 7.059E+01 N/C

Key: J1

1)

 $E_z(x=0,z)=\underset{-a}{\overset{b}{\int }}f(x,z)dx$
is an integral that calculates the z-component of the electric field at point P situated above the x-axis where a charged rod of length (a+b) is located. The distance between point P and the x-axis is z=1.5 m. Evaluate $f(x,y)$ at x=1.1 m if a=0.61 m, b=1.7 m. The total charge on the rod is 8 nC.

-a) 5.995E+00 V/m²

-b) 6.595E+00 V/m²

+c) 7.254E+00 V/m²

-d) 7.980E+00 V/m²

-e) 8.778E+00 V/m²

2) A large thin isolated square plate has an area of 3 m². It is uniformly charged with 5 nC of charge. What is the magnitude of the electric field 3 mm from the center of the plate's surface?

+a) 9.412E+01 N/C

-b) 1.035E+02 N/C

-c) 1.139E+02 N/C

-d) 1.253E+02 N/C

-e) 1.378E+02 N/C

3)  $E(z)=\underset{0}{\overset{R}{\int }}f(r^{\prime },z)d{r}^{\prime }$
is an integral that calculates the magnitude of the electric field at a distance $z$ fromthe center of a thin circular disk as measured along a line normal to the plane of the disk. The disk's radius is $R=7.2\text{ m}$ and the surface charge density is $\sigma =3{\text{ nC/m}}^3$. Evaluate $f(r^{\prime },z)$ at $r^{\prime }=3.6\text{ m}$.

+a) 1.606E+00 V/m²

-b) 1.767E+00 V/m²

-c) 1.943E+00 V/m²

-d) 2.138E+00 V/m²

-e) 2.351E+00 V/m²

4)

Three small charged objects are placed as shown, where $b=2a$, and $a=4\times 10^{-7}\text{m}$. What is the magnitude of the net force on $q_2$ if $q_1=2e$, $q_2=-8e$, and $q_3=3e$?

-a) 2.036E-14 N

-b) 2.240E-14 N

+c) 2.464E-14 N

-d) 2.710E-14 N

-e) 2.981E-14 N

5)

A ring is uniformly charged with a net charge of 2 nC. The radius of the ring is R=1.5 m, with its center at the origin and oriented normal to the z axis as shown. what is the magnitude of the electric field at a distance z=0.33 m (on axis) away from the loop's center?

-a) 1.353E+09 N/C²

-b) 1.488E+09 N/C²

+c) 1.637E+09 N/C²

-d) 1.801E+09 N/C²

-e) 1.981E+09 N/C²

6)

Three small charged objects are placed as shown, where $b=2a$, and $a=4\times 10^{-7}\text{m}$.what angle does the force on $q_2$ make above the $-x$ axis if $q_1=2e$, $q_2=-9e$, and $q_3=5e$?

-a) 3.961E+01 degrees

-b) 4.357E+01 degrees

-c) 4.793E+01 degrees

-d) 5.272E+01 degrees

+e) 5.799E+01 degrees

Key: J2

1)  $E(z)=\underset{0}{\overset{R}{\int }}f(r^{\prime },z)d{r}^{\prime }$
is an integral that calculates the magnitude of the electric field at a distance $z$ fromthe center of a thin circular disk as measured along a line normal to the plane of the disk. The disk's radius is $R=8.3\text{ m}$ and the surface charge density is $\sigma =5{\text{ nC/m}}^3$. Evaluate $f(r^{\prime },z)$ at $r^{\prime }=5.3\text{ m}$.

+a) 1.022E+00 V/m²

-b) 1.125E+00 V/m²

-c) 1.237E+00 V/m²

-d) 1.361E+00 V/m²

-e) 1.497E+00 V/m²

2) A large thin isolated square plate has an area of 3 m². It is uniformly charged with 9 nC of charge. What is the magnitude of the electric field 3 mm from the center of the plate's surface?

+a) 1.694E+02 N/C

-b) 1.864E+02 N/C

-c) 2.050E+02 N/C

-d) 2.255E+02 N/C

-e) 2.480E+02 N/C

3)

Three small charged objects are placed as shown, where $b=2a$, and $a=6\times 10^{-7}\text{m}$. What is the magnitude of the net force on $q_2$ if $q_1=1e$, $q_2=-7e$, and $q_3=2e$?

-a) 3.426E-15 N

-b) 3.768E-15 N

-c) 4.145E-15 N

-d) 4.560E-15 N

+e) 5.015E-15 N

4)

 $E_z(x=0,z)=\underset{-a}{\overset{b}{\int }}f(x,z)dx$
is an integral that calculates the z-component of the electric field at point P situated above the x-axis where a charged rod of length (a+b) is located. The distance between point P and the x-axis is z=1.8 m. Evaluate $f(x,y)$ at x=0.65 m if a=0.85 m, b=1.8 m. The total charge on the rod is 5 nC.

-a) 3.959E+00 V/m²

+b) 4.355E+00 V/m²

-c) 4.790E+00 V/m²

-d) 5.269E+00 V/m²

-e) 5.796E+00 V/m²

5)

Three small charged objects are placed as shown, where $b=2a$, and $a=4\times 10^{-7}\text{m}$.what angle does the force on $q_2$ make above the $-x$ axis if $q_1=3e$, $q_2=-9e$, and $q_3=6e$?

-a) 5.767E+01 degrees

+b) 6.343E+01 degrees

-c) 6.978E+01 degrees

-d) 7.676E+01 degrees

-e) 8.443E+01 degrees

6)

A ring is uniformly charged with a net charge of 8 nC. The radius of the ring is R=1.7 m, with its center at the origin and oriented normal to the z axis as shown. what is the magnitude of the electric field at a distance z=0.32 m (on axis) away from the loop's center?

-a) 3.339E+09 N/C²

-b) 3.673E+09 N/C²

-c) 4.041E+09 N/C²

+d) 4.445E+09 N/C²

-e) 4.889E+09 N/C²

Key: K0

1)

Three small charged objects are placed as shown, where $b=2a$, and $a=4\times 10^{-7}\text{m}$. What is the magnitude of the net force on $q_2$ if $q_1=2e$, $q_2=-8e$, and $q_3=5e$?

-a) 2.248E-14 N

-b) 2.473E-14 N

+c) 2.721E-14 N

-d) 2.993E-14 N

-e) 3.292E-14 N

2)

Three small charged objects are placed as shown, where $b=2a$, and $a=4\times 10^{-7}\text{m}$.what angle does the force on $q_2$ make above the $-x$ axis if $q_1=3e$, $q_2=-7e$, and $q_3=5e$?

-a) 5.569E+01 degrees

-b) 6.125E+01 degrees

+c) 6.738E+01 degrees

-d) 7.412E+01 degrees

-e) 8.153E+01 degrees

3)

 $E_z(x=0,z)=\underset{-a}{\overset{b}{\int }}f(x,z)dx$
is an integral that calculates the z-component of the electric field at point P situated above the x-axis where a charged rod of length (a+b) is located. The distance between point P and the x-axis is z=1.7 m. Evaluate $f(x,y)$ at x=0.52 m if a=0.88 m, b=1.3 m. The total charge on the rod is 6 nC.

-a) 6.804E+00 V/m²

+b) 7.485E+00 V/m²

-c) 8.233E+00 V/m²

-d) 9.056E+00 V/m²

-e) 9.962E+00 V/m²

4)

A ring is uniformly charged with a net charge of 4 nC. The radius of the ring is R=1.6 m, with its center at the origin and oriented normal to the z axis as shown. what is the magnitude of the electric field at a distance z=1.0 m (on axis) away from the loop's center?

+a) 5.352E+09 N/C²

-b) 5.887E+09 N/C²

-c) 6.476E+09 N/C²

-d) 7.124E+09 N/C²

-e) 7.836E+09 N/C²

5)  $E(z)=\underset{0}{\overset{R}{\int }}f(r^{\prime },z)d{r}^{\prime }$
is an integral that calculates the magnitude of the electric field at a distance $z$ fromthe center of a thin circular disk as measured along a line normal to the plane of the disk. The disk's radius is $R=3.3\text{ m}$ and the surface charge density is $\sigma =4{\text{ nC/m}}^3$. Evaluate $f(r^{\prime },z)$ at $r^{\prime }=2.0\text{ m}$.

-a) 6.877E+00 V/m²

-b) 7.565E+00 V/m²

+c) 8.321E+00 V/m²

-d) 9.153E+00 V/m²

-e) 1.007E+01 V/m²

6) A large thin isolated square plate has an area of 4 m². It is uniformly charged with 5 nC of charge. What is the magnitude of the electric field 1 mm from the center of the plate's surface?

-a) 4.821E+01 N/C

-b) 5.303E+01 N/C

-c) 5.834E+01 N/C

-d) 6.417E+01 N/C

+e) 7.059E+01 N/C

Key: K1

1) A large thin isolated square plate has an area of 4 m². It is uniformly charged with 5 nC of charge. What is the magnitude of the electric field 1 mm from the center of the plate's surface?

-a) 4.821E+01 N/C

-b) 5.303E+01 N/C

-c) 5.834E+01 N/C

-d) 6.417E+01 N/C

+e) 7.059E+01 N/C

2)  $E(z)=\underset{0}{\overset{R}{\int }}f(r^{\prime },z)d{r}^{\prime }$
is an integral that calculates the magnitude of the electric field at a distance $z$ fromthe center of a thin circular disk as measured along a line normal to the plane of the disk. The disk's radius is $R=2.8\text{ m}$ and the surface charge density is $\sigma =3{\text{ nC/m}}^3$. Evaluate $f(r^{\prime },z)$ at $r^{\prime }=1.9\text{ m}$.

-a) 4.295E+00 V/m²

+b) 4.724E+00 V/m²

-c) 5.196E+00 V/m²

-d) 5.716E+00 V/m²

-e) 6.288E+00 V/m²

3)

 $E_z(x=0,z)=\underset{-a}{\overset{b}{\int }}f(x,z)dx$
is an integral that calculates the z-component of the electric field at point P situated above the x-axis where a charged rod of length (a+b) is located. The distance between point P and the x-axis is z=1.8 m. Evaluate $f(x,y)$ at x=0.65 m if a=0.85 m, b=1.8 m. The total charge on the rod is 5 nC.

-a) 3.959E+00 V/m²

+b) 4.355E+00 V/m²

-c) 4.790E+00 V/m²

-d) 5.269E+00 V/m²

-e) 5.796E+00 V/m²

4)

A ring is uniformly charged with a net charge of 5 nC. The radius of the ring is R=1.9 m, with its center at the origin and oriented normal to the z axis as shown. what is the magnitude of the electric field at a distance z=1.3 m (on axis) away from the loop's center?

+a) 4.788E+09 N/C²

-b) 5.267E+09 N/C²

-c) 5.793E+09 N/C²

-d) 6.373E+09 N/C²

-e) 7.010E+09 N/C²

5)

Three small charged objects are placed as shown, where $b=2a$, and $a=6\times 10^{-7}\text{m}$. What is the magnitude of the net force on $q_2$ if $q_1=1e$, $q_2=-8e$, and $q_3=2e$?

+a) 5.732E-15 N

-b) 6.305E-15 N

-c) 6.936E-15 N

-d) 7.629E-15 N

-e) 8.392E-15 N

6)

Three small charged objects are placed as shown, where $b=2a$, and $a=2\times 10^{-7}\text{m}$.what angle does the force on $q_2$ make above the $-x$ axis if $q_1=3e$, $q_2=-9e$, and $q_3=5e$?

-a) 6.125E+01 degrees

+b) 6.738E+01 degrees

-c) 7.412E+01 degrees

-d) 8.153E+01 degrees

-e) 8.968E+01 degrees

Key: K2

1) A large thin isolated square plate has an area of 6 m². It is uniformly charged with 9 nC of charge. What is the magnitude of the electric field 3 mm from the center of the plate's surface?

+a) 8.471E+01 N/C

-b) 9.318E+01 N/C

-c) 1.025E+02 N/C

-d) 1.127E+02 N/C

-e) 1.240E+02 N/C

2)

Three small charged objects are placed as shown, where $b=2a$, and $a=2\times 10^{-7}\text{m}$. What is the magnitude of the net force on $q_2$ if $q_1=1e$, $q_2=-8e$, and $q_3=3e$?

-a) 5.243E-14 N

+b) 5.768E-14 N

-c) 6.344E-14 N

-d) 6.979E-14 N

-e) 7.677E-14 N

3)

Three small charged objects are placed as shown, where $b=2a$, and $a=6\times 10^{-7}\text{m}$.what angle does the force on $q_2$ make above the $-x$ axis if $q_1=2e$, $q_2=-9e$, and $q_3=4e$?

-a) 4.766E+01 degrees

-b) 5.243E+01 degrees

-c) 5.767E+01 degrees

+d) 6.343E+01 degrees

-e) 6.978E+01 degrees

4)  $E(z)=\underset{0}{\overset{R}{\int }}f(r^{\prime },z)d{r}^{\prime }$
is an integral that calculates the magnitude of the electric field at a distance $z$ fromthe center of a thin circular disk as measured along a line normal to the plane of the disk. The disk's radius is $R=1.8\text{ m}$ and the surface charge density is $\sigma =3{\text{ nC/m}}^3$. Evaluate $f(r^{\prime },z)$ at $r^{\prime }=1.1\text{ m}$.

-a) 7.517E+00 V/m²

-b) 8.269E+00 V/m²

-c) 9.096E+00 V/m²

-d) 1.001E+01 V/m²

+e) 1.101E+01 V/m²

5)

A ring is uniformly charged with a net charge of 5 nC. The radius of the ring is R=1.9 m, with its center at the origin and oriented normal to the z axis as shown. what is the magnitude of the electric field at a distance z=1.3 m (on axis) away from the loop's center?

+a) 4.788E+09 N/C²

-b) 5.267E+09 N/C²

-c) 5.793E+09 N/C²

-d) 6.373E+09 N/C²

-e) 7.010E+09 N/C²

6)

 $E_z(x=0,z)=\underset{-a}{\overset{b}{\int }}f(x,z)dx$
is an integral that calculates the z-component of the electric field at point P situated above the x-axis where a charged rod of length (a+b) is located. The distance between point P and the x-axis is z=1.8 m. Evaluate $f(x,y)$ at x=1.0 m if a=1.0 m, b=1.8 m. The total charge on the rod is 6 nC.

-a) 3.610E+00 V/m²

+b) 3.971E+00 V/m²

-c) 4.368E+00 V/m²

-d) 4.804E+00 V/m²

-e) 5.285E+00 V/m²

Key: L0

1)

Three small charged objects are placed as shown, where $b=2a$, and $a=4\times 10^{-7}\text{m}$. What is the magnitude of the net force on $q_2$ if $q_1=3e$, $q_2=-7e$, and $q_3=6e$?

-a) 2.544E-14 N

-b) 2.798E-14 N

-c) 3.078E-14 N

+d) 3.385E-14 N

-e) 3.724E-14 N

2)

Three small charged objects are placed as shown, where $b=2a$, and $a=4\times 10^{-7}\text{m}$.what angle does the force on $q_2$ make above the $-x$ axis if $q_1=3e$, $q_2=-8e$, and $q_3=6e$?

-a) 5.243E+01 degrees

-b) 5.767E+01 degrees

+c) 6.343E+01 degrees

-d) 6.978E+01 degrees

-e) 7.676E+01 degrees

3)

 $E_z(x=0,z)=\underset{-a}{\overset{b}{\int }}f(x,z)dx$
is an integral that calculates the z-component of the electric field at point P situated above the x-axis where a charged rod of length (a+b) is located. The distance between point P and the x-axis is z=1.8 m. Evaluate $f(x,y)$ at x=0.65 m if a=0.85 m, b=1.8 m. The total charge on the rod is 5 nC.

-a) 3.959E+00 V/m²

+b) 4.355E+00 V/m²

-c) 4.790E+00 V/m²

-d) 5.269E+00 V/m²

-e) 5.796E+00 V/m²

4)

A ring is uniformly charged with a net charge of 2 nC. The radius of the ring is R=1.5 m, with its center at the origin and oriented normal to the z axis as shown. what is the magnitude of the electric field at a distance z=0.33 m (on axis) away from the loop's center?

-a) 1.353E+09 N/C²

-b) 1.488E+09 N/C²

+c) 1.637E+09 N/C²

-d) 1.801E+09 N/C²

-e) 1.981E+09 N/C²

5)  $E(z)=\underset{0}{\overset{R}{\int }}f(r^{\prime },z)d{r}^{\prime }$
is an integral that calculates the magnitude of the electric field at a distance $z$ fromthe center of a thin circular disk as measured along a line normal to the plane of the disk. The disk's radius is $R=2.8\text{ m}$ and the surface charge density is $\sigma =3{\text{ nC/m}}^3$. Evaluate $f(r^{\prime },z)$ at $r^{\prime }=1.9\text{ m}$.

-a) 4.295E+00 V/m²

+b) 4.724E+00 V/m²

-c) 5.196E+00 V/m²

-d) 5.716E+00 V/m²

-e) 6.288E+00 V/m²

6) A large thin isolated square plate has an area of 6 m². It is uniformly charged with 9 nC of charge. What is the magnitude of the electric field 2 mm from the center of the plate's surface?

-a) 7.000E+01 N/C

-b) 7.701E+01 N/C

+c) 8.471E+01 N/C

-d) 9.318E+01 N/C

-e) 1.025E+02 N/C

Key: L1

1)

Three small charged objects are placed as shown, where $b=2a$, and $a=2\times 10^{-7}\text{m}$.what angle does the force on $q_2$ make above the $-x$ axis if $q_1=2e$, $q_2=-9e$, and $q_3=4e$?

-a) 5.243E+01 degrees

-b) 5.767E+01 degrees

+c) 6.343E+01 degrees

-d) 6.978E+01 degrees

-e) 7.676E+01 degrees

2)

 $E_z(x=0,z)=\underset{-a}{\overset{b}{\int }}f(x,z)dx$
is an integral that calculates the z-component of the electric field at point P situated above the x-axis where a charged rod of length (a+b) is located. The distance between point P and the x-axis is z=1.7 m. Evaluate $f(x,y)$ at x=0.76 m if a=1.1 m, b=1.6 m. The total charge on the rod is 8 nC.

-a) 5.267E+00 V/m²

-b) 5.794E+00 V/m²

-c) 6.374E+00 V/m²

+d) 7.011E+00 V/m²

-e) 7.712E+00 V/m²

3)

A ring is uniformly charged with a net charge of 8 nC. The radius of the ring is R=1.7 m, with its center at the origin and oriented normal to the z axis as shown. what is the magnitude of the electric field at a distance z=0.32 m (on axis) away from the loop's center?

-a) 3.339E+09 N/C²

-b) 3.673E+09 N/C²

-c) 4.041E+09 N/C²

+d) 4.445E+09 N/C²

-e) 4.889E+09 N/C²

4)

Three small charged objects are placed as shown, where $b=2a$, and $a=6\times 10^{-7}\text{m}$. What is the magnitude of the net force on $q_2$ if $q_1=1e$, $q_2=-8e$, and $q_3=2e$?

+a) 5.732E-15 N

-b) 6.305E-15 N

-c) 6.936E-15 N

-d) 7.629E-15 N

-e) 8.392E-15 N

5)  $E(z)=\underset{0}{\overset{R}{\int }}f(r^{\prime },z)d{r}^{\prime }$
is an integral that calculates the magnitude of the electric field at a distance $z$ fromthe center of a thin circular disk as measured along a line normal to the plane of the disk. The disk's radius is $R=7.9\text{ m}$ and the surface charge density is $\sigma =2{\text{ nC/m}}^3$. Evaluate $f(r^{\prime },z)$ at $r^{\prime }=5.1\text{ m}$.

-a) 8.253E-01 V/m²

-b) 9.079E-01 V/m²

+c) 9.987E-01 V/m²

-d) 1.099E+00 V/m²

-e) 1.208E+00 V/m²

6) A large thin isolated square plate has an area of 4 m². It is uniformly charged with 5 nC of charge. What is the magnitude of the electric field 1 mm from the center of the plate's surface?

-a) 4.821E+01 N/C

-b) 5.303E+01 N/C

-c) 5.834E+01 N/C

-d) 6.417E+01 N/C

+e) 7.059E+01 N/C

Key: L2

1)

 $E_z(x=0,z)=\underset{-a}{\overset{b}{\int }}f(x,z)dx$
is an integral that calculates the z-component of the electric field at point P situated above the x-axis where a charged rod of length (a+b) is located. The distance between point P and the x-axis is z=1.9 m. Evaluate $f(x,y)$ at x=0.83 m if a=0.7 m, b=1.8 m. The total charge on the rod is 9 nC.

+a) 6.897E+00 V/m²

-b) 7.587E+00 V/m²

-c) 8.345E+00 V/m²

-d) 9.180E+00 V/m²

-e) 1.010E+01 V/m²

2)

Three small charged objects are placed as shown, where $b=2a$, and $a=2\times 10^{-7}\text{m}$.what angle does the force on $q_2$ make above the $-x$ axis if $q_1=1e$, $q_2=-7e$, and $q_3=4e$?

-a) 4.091E+01 degrees

+b) 4.500E+01 degrees

-c) 4.950E+01 degrees

-d) 5.445E+01 degrees

-e) 5.990E+01 degrees

3) A large thin isolated square plate has an area of 6 m². It is uniformly charged with 5 nC of charge. What is the magnitude of the electric field 1 mm from the center of the plate's surface?

-a) 3.214E+01 N/C

-b) 3.536E+01 N/C

-c) 3.889E+01 N/C

-d) 4.278E+01 N/C

+e) 4.706E+01 N/C

4)

Three small charged objects are placed as shown, where $b=2a$, and $a=6\times 10^{-7}\text{m}$. What is the magnitude of the net force on $q_2$ if $q_1=1e$, $q_2=-8e$, and $q_3=2e$?

+a) 5.732E-15 N

-b) 6.305E-15 N

-c) 6.936E-15 N

-d) 7.629E-15 N

-e) 8.392E-15 N

5)  $E(z)=\underset{0}{\overset{R}{\int }}f(r^{\prime },z)d{r}^{\prime }$
is an integral that calculates the magnitude of the electric field at a distance $z$ fromthe center of a thin circular disk as measured along a line normal to the plane of the disk. The disk's radius is $R=8.7\text{ m}$ and the surface charge density is $\sigma =7{\text{ nC/m}}^3$. Evaluate $f(r^{\prime },z)$ at $r^{\prime }=5.8\text{ m}$.

-a) 3.722E-01 V/m²

-b) 4.094E-01 V/m²

-c) 4.504E-01 V/m²

+d) 4.954E-01 V/m²

-e) 5.450E-01 V/m²

6)

A ring is uniformly charged with a net charge of 6 nC. The radius of the ring is R=1.9 m, with its center at the origin and oriented normal to the z axis as shown. what is the magnitude of the electric field at a distance z=0.4 m (on axis) away from the loop's center?

-a) 2.013E+09 N/C²

-b) 2.214E+09 N/C²

-c) 2.435E+09 N/C²

-d) 2.679E+09 N/C²

+e) 2.947E+09 N/C²

Key: M0

1)

Three small charged objects are placed as shown, where $b=2a$, and $a=2\times 10^{-7}\text{m}$. What is the magnitude of the net force on $q_2$ if $q_1=1e$, $q_2=-7e$, and $q_3=2e$?

-a) 3.391E-14 N

-b) 3.731E-14 N

-c) 4.104E-14 N

+d) 4.514E-14 N

-e) 4.965E-14 N

2)

Three small charged objects are placed as shown, where $b=2a$, and $a=2\times 10^{-7}\text{m}$.what angle does the force on $q_2$ make above the $-x$ axis if $q_1=2e$, $q_2=-7e$, and $q_3=3e$?

-a) 4.743E+01 degrees

-b) 5.217E+01 degrees

-c) 5.739E+01 degrees

-d) 6.313E+01 degrees

+e) 6.944E+01 degrees

3)

 $E_z(x=0,z)=\underset{-a}{\overset{b}{\int }}f(x,z)dx$
is an integral that calculates the z-component of the electric field at point P situated above the x-axis where a charged rod of length (a+b) is located. The distance between point P and the x-axis is z=1.5 m. Evaluate $f(x,y)$ at x=1.1 m if a=0.62 m, b=1.3 m. The total charge on the rod is 7 nC.

-a) 6.311E+00 V/m²

-b) 6.943E+00 V/m²

+c) 7.637E+00 V/m²

-d) 8.401E+00 V/m²

-e) 9.241E+00 V/m²

4)

A ring is uniformly charged with a net charge of 4 nC. The radius of the ring is R=1.6 m, with its center at the origin and oriented normal to the z axis as shown. what is the magnitude of the electric field at a distance z=1.0 m (on axis) away from the loop's center?

+a) 5.352E+09 N/C²

-b) 5.887E+09 N/C²

-c) 6.476E+09 N/C²

-d) 7.124E+09 N/C²

-e) 7.836E+09 N/C²

5)  $E(z)=\underset{0}{\overset{R}{\int }}f(r^{\prime },z)d{r}^{\prime }$
is an integral that calculates the magnitude of the electric field at a distance $z$ fromthe center of a thin circular disk as measured along a line normal to the plane of the disk. The disk's radius is $R=2.0\text{ m}$ and the surface charge density is $\sigma =9{\text{ nC/m}}^3$. Evaluate $f(r^{\prime },z)$ at $r^{\prime }=1.2\text{ m}$.

-a) 8.933E+00 V/m²

-b) 9.826E+00 V/m²

+c) 1.081E+01 V/m²

-d) 1.189E+01 V/m²

-e) 1.308E+01 V/m²

6) A large thin isolated square plate has an area of 3 m². It is uniformly charged with 9 nC of charge. What is the magnitude of the electric field 3 mm from the center of the plate's surface?

+a) 1.694E+02 N/C

-b) 1.864E+02 N/C

-c) 2.050E+02 N/C

-d) 2.255E+02 N/C

-e) 2.480E+02 N/C

Key: M1

1)

A ring is uniformly charged with a net charge of 3 nC. The radius of the ring is R=1.8 m, with its center at the origin and oriented normal to the z axis as shown. what is the magnitude of the electric field at a distance z=1.1 m (on axis) away from the loop's center?

+a) 3.159E+09 N/C²

-b) 3.475E+09 N/C²

-c) 3.823E+09 N/C²

-d) 4.205E+09 N/C²

-e) 4.626E+09 N/C²

2)  $E(z)=\underset{0}{\overset{R}{\int }}f(r^{\prime },z)d{r}^{\prime }$
is an integral that calculates the magnitude of the electric field at a distance $z$ fromthe center of a thin circular disk as measured along a line normal to the plane of the disk. The disk's radius is $R=7.5\text{ m}$ and the surface charge density is $\sigma =3{\text{ nC/m}}^3$. Evaluate $f(r^{\prime },z)$ at $r^{\prime }=2.6\text{ m}$.

-a) 7.820E-01 V/m²

+b) 8.602E-01 V/m²

-c) 9.462E-01 V/m²

-d) 1.041E+00 V/m²

-e) 1.145E+00 V/m²

3)

Three small charged objects are placed as shown, where $b=2a$, and $a=6\times 10^{-7}\text{m}$. What is the magnitude of the net force on $q_2$ if $q_1=2e$, $q_2=-8e$, and $q_3=4e$?

-a) 8.613E-15 N

-b) 9.474E-15 N

-c) 1.042E-14 N

+d) 1.146E-14 N

-e) 1.261E-14 N

4)

 $E_z(x=0,z)=\underset{-a}{\overset{b}{\int }}f(x,z)dx$
is an integral that calculates the z-component of the electric field at point P situated above the x-axis where a charged rod of length (a+b) is located. The distance between point P and the x-axis is z=1.8 m. Evaluate $f(x,y)$ at x=1.0 m if a=1.0 m, b=1.8 m. The total charge on the rod is 6 nC.

-a) 3.610E+00 V/m²

+b) 3.971E+00 V/m²

-c) 4.368E+00 V/m²

-d) 4.804E+00 V/m²

-e) 5.285E+00 V/m²

5)

Three small charged objects are placed as shown, where $b=2a$, and $a=4\times 10^{-7}\text{m}$.what angle does the force on $q_2$ make above the $-x$ axis if $q_1=1e$, $q_2=-8e$, and $q_3=4e$?

-a) 3.719E+01 degrees

-b) 4.091E+01 degrees

+c) 4.500E+01 degrees

-d) 4.950E+01 degrees

-e) 5.445E+01 degrees

6) A large thin isolated square plate has an area of 6 m². It is uniformly charged with 9 nC of charge. What is the magnitude of the electric field 2 mm from the center of the plate's surface?

-a) 7.000E+01 N/C

-b) 7.701E+01 N/C

+c) 8.471E+01 N/C

-d) 9.318E+01 N/C

-e) 1.025E+02 N/C

Key: M2

1)  $E(z)=\underset{0}{\overset{R}{\int }}f(r^{\prime },z)d{r}^{\prime }$
is an integral that calculates the magnitude of the electric field at a distance $z$ fromthe center of a thin circular disk as measured along a line normal to the plane of the disk. The disk's radius is $R=6.9\text{ m}$ and the surface charge density is $\sigma =9{\text{ nC/m}}^3$. Evaluate $f(r^{\prime },z)$ at $r^{\prime }=4.3\text{ m}$.

-a) 8.924E-01 V/m²

-b) 9.816E-01 V/m²

+c) 1.080E+00 V/m²

-d) 1.188E+00 V/m²

-e) 1.307E+00 V/m²

2)

 $E_z(x=0,z)=\underset{-a}{\overset{b}{\int }}f(x,z)dx$
is an integral that calculates the z-component of the electric field at point P situated above the x-axis where a charged rod of length (a+b) is located. The distance between point P and the x-axis is z=1.5 m. Evaluate $f(x,y)$ at x=0.79 m if a=0.75 m, b=2.1 m. The total charge on the rod is 6 nC.

+a) 5.825E+00 V/m²

-b) 6.407E+00 V/m²

-c) 7.048E+00 V/m²

-d) 7.753E+00 V/m²

-e) 8.528E+00 V/m²

3)

Three small charged objects are placed as shown, where $b=2a$, and $a=2\times 10^{-7}\text{m}$.what angle does the force on $q_2$ make above the $-x$ axis if $q_1=2e$, $q_2=-9e$, and $q_3=4e$?

-a) 5.243E+01 degrees

-b) 5.767E+01 degrees

+c) 6.343E+01 degrees

-d) 6.978E+01 degrees

-e) 7.676E+01 degrees

4) A large thin isolated square plate has an area of 8 m². It is uniformly charged with 7 nC of charge. What is the magnitude of the electric field 3 mm from the center of the plate's surface?

-a) 4.492E+01 N/C

+b) 4.941E+01 N/C

-c) 5.435E+01 N/C

-d) 5.979E+01 N/C

-e) 6.577E+01 N/C

5)

Three small charged objects are placed as shown, where $b=2a$, and $a=4\times 10^{-7}\text{m}$. What is the magnitude of the net force on $q_2$ if $q_1=3e$, $q_2=-7e$, and $q_3=6e$?

-a) 2.544E-14 N

-b) 2.798E-14 N

-c) 3.078E-14 N

+d) 3.385E-14 N

-e) 3.724E-14 N

6)

A ring is uniformly charged with a net charge of 2 nC. The radius of the ring is R=1.5 m, with its center at the origin and oriented normal to the z axis as shown. what is the magnitude of the electric field at a distance z=0.33 m (on axis) away from the loop's center?

-a) 1.353E+09 N/C²

-b) 1.488E+09 N/C²

+c) 1.637E+09 N/C²

-d) 1.801E+09 N/C²

-e) 1.981E+09 N/C²

Key: N0

1)

Three small charged objects are placed as shown, where $b=2a$, and $a=4\times 10^{-7}\text{m}$. What is the magnitude of the net force on $q_2$ if $q_1=2e$, $q_2=-7e$, and $q_3=3e$?

-a) 1.473E-14 N

-b) 1.620E-14 N

-c) 1.782E-14 N

-d) 1.960E-14 N

+e) 2.156E-14 N

2)

Three small charged objects are placed as shown, where $b=2a$, and $a=2\times 10^{-7}\text{m}$.what angle does the force on $q_2$ make above the $-x$ axis if $q_1=2e$, $q_2=-7e$, and $q_3=5e$?

-a) 4.357E+01 degrees

-b) 4.793E+01 degrees

-c) 5.272E+01 degrees

+d) 5.799E+01 degrees

-e) 6.379E+01 degrees

3)

 $E_z(x=0,z)=\underset{-a}{\overset{b}{\int }}f(x,z)dx$
is an integral that calculates the z-component of the electric field at point P situated above the x-axis where a charged rod of length (a+b) is located. The distance between point P and the x-axis is z=1.5 m. Evaluate $f(x,y)$ at x=0.79 m if a=0.75 m, b=2.1 m. The total charge on the rod is 6 nC.

+a) 5.825E+00 V/m²

-b) 6.407E+00 V/m²

-c) 7.048E+00 V/m²

-d) 7.753E+00 V/m²

-e) 8.528E+00 V/m²

4)

A ring is uniformly charged with a net charge of 3 nC. The radius of the ring is R=1.8 m, with its center at the origin and oriented normal to the z axis as shown. what is the magnitude of the electric field at a distance z=1.1 m (on axis) away from the loop's center?

+a) 3.159E+09 N/C²

-b) 3.475E+09 N/C²

-c) 3.823E+09 N/C²

-d) 4.205E+09 N/C²

-e) 4.626E+09 N/C²

5)  $E(z)=\underset{0}{\overset{R}{\int }}f(r^{\prime },z)d{r}^{\prime }$
is an integral that calculates the magnitude of the electric field at a distance $z$ fromthe center of a thin circular disk as measured along a line normal to the plane of the disk. The disk's radius is $R=7.5\text{ m}$ and the surface charge density is $\sigma =3{\text{ nC/m}}^3$. Evaluate $f(r^{\prime },z)$ at $r^{\prime }=2.6\text{ m}$.

-a) 7.820E-01 V/m²

+b) 8.602E-01 V/m²

-c) 9.462E-01 V/m²

-d) 1.041E+00 V/m²

-e) 1.145E+00 V/m²

6) A large thin isolated square plate has an area of 4 m². It is uniformly charged with 5 nC of charge. What is the magnitude of the electric field 1 mm from the center of the plate's surface?

-a) 4.821E+01 N/C

-b) 5.303E+01 N/C

-c) 5.834E+01 N/C

-d) 6.417E+01 N/C

+e) 7.059E+01 N/C

Key: N1

1)

A ring is uniformly charged with a net charge of 7 nC. The radius of the ring is R=1.7 m, with its center at the origin and oriented normal to the z axis as shown. what is the magnitude of the electric field at a distance z=1.1 m (on axis) away from the loop's center?

+a) 8.336E+09 N/C²

-b) 9.170E+09 N/C²

-c) 1.009E+10 N/C²

-d) 1.110E+10 N/C²

-e) 1.220E+10 N/C²

2)

Three small charged objects are placed as shown, where $b=2a$, and $a=2\times 10^{-7}\text{m}$. What is the magnitude of the net force on $q_2$ if $q_1=1e$, $q_2=-9e$, and $q_3=4e$?

-a) 5.014E-14 N

-b) 5.515E-14 N

-c) 6.067E-14 N

-d) 6.674E-14 N

+e) 7.341E-14 N

3)  $E(z)=\underset{0}{\overset{R}{\int }}f(r^{\prime },z)d{r}^{\prime }$
is an integral that calculates the magnitude of the electric field at a distance $z$ fromthe center of a thin circular disk as measured along a line normal to the plane of the disk. The disk's radius is $R=9.1\text{ m}$ and the surface charge density is $\sigma =2{\text{ nC/m}}^3$. Evaluate $f(r^{\prime },z)$ at $r^{\prime }=6.2\text{ m}$.

-a) 4.961E-01 V/m²

-b) 5.457E-01 V/m²

-c) 6.002E-01 V/m²

-d) 6.603E-01 V/m²

+e) 7.263E-01 V/m²

4) A large thin isolated square plate has an area of 9 m². It is uniformly charged with 6 nC of charge. What is the magnitude of the electric field 1 mm from the center of the plate's surface?

-a) 2.571E+01 N/C

-b) 2.828E+01 N/C

-c) 3.111E+01 N/C

-d) 3.422E+01 N/C

+e) 3.765E+01 N/C

5)

Three small charged objects are placed as shown, where $b=2a$, and $a=2\times 10^{-7}\text{m}$.what angle does the force on $q_2$ make above the $-x$ axis if $q_1=2e$, $q_2=-7e$, and $q_3=5e$?

-a) 4.357E+01 degrees

-b) 4.793E+01 degrees

-c) 5.272E+01 degrees

+d) 5.799E+01 degrees

-e) 6.379E+01 degrees

6)

 $E_z(x=0,z)=\underset{-a}{\overset{b}{\int }}f(x,z)dx$
is an integral that calculates the z-component of the electric field at point P situated above the x-axis where a charged rod of length (a+b) is located. The distance between point P and the x-axis is z=1.9 m. Evaluate $f(x,y)$ at x=0.96 m if a=0.95 m, b=1.8 m. The total charge on the rod is 7 nC.

-a) 3.385E+00 V/m²

-b) 3.724E+00 V/m²

-c) 4.096E+00 V/m²

+d) 4.506E+00 V/m²

-e) 4.957E+00 V/m²

Key: N2

1) A large thin isolated square plate has an area of 3 m². It is uniformly charged with 5 nC of charge. What is the magnitude of the electric field 3 mm from the center of the plate's surface?

+a) 9.412E+01 N/C

-b) 1.035E+02 N/C

-c) 1.139E+02 N/C

-d) 1.253E+02 N/C

-e) 1.378E+02 N/C

2)  $E(z)=\underset{0}{\overset{R}{\int }}f(r^{\prime },z)d{r}^{\prime }$
is an integral that calculates the magnitude of the electric field at a distance $z$ fromthe center of a thin circular disk as measured along a line normal to the plane of the disk. The disk's radius is $R=3.3\text{ m}$ and the surface charge density is $\sigma =4{\text{ nC/m}}^3$. Evaluate $f(r^{\prime },z)$ at $r^{\prime }=2.0\text{ m}$.

-a) 6.877E+00 V/m²

-b) 7.565E+00 V/m²

+c) 8.321E+00 V/m²

-d) 9.153E+00 V/m²

-e) 1.007E+01 V/m²

3)

A ring is uniformly charged with a net charge of 5 nC. The radius of the ring is R=1.6 m, with its center at the origin and oriented normal to the z axis as shown. what is the magnitude of the electric field at a distance z=1.1 m (on axis) away from the loop's center?

-a) 5.581E+09 N/C²

-b) 6.139E+09 N/C²

+c) 6.753E+09 N/C²

-d) 7.428E+09 N/C²

-e) 8.171E+09 N/C²

4)

Three small charged objects are placed as shown, where $b=2a$, and $a=4\times 10^{-7}\text{m}$. What is the magnitude of the net force on $q_2$ if $q_1=2e$, $q_2=-7e$, and $q_3=3e$?

-a) 1.473E-14 N

-b) 1.620E-14 N

-c) 1.782E-14 N

-d) 1.960E-14 N

+e) 2.156E-14 N

5)

Three small charged objects are placed as shown, where $b=2a$, and $a=6\times 10^{-7}\text{m}$.what angle does the force on $q_2$ make above the $-x$ axis if $q_1=3e$, $q_2=-7e$, and $q_3=4e$?

-a) 5.914E+01 degrees

-b) 6.506E+01 degrees

+c) 7.157E+01 degrees

-d) 7.872E+01 degrees

-e) 8.659E+01 degrees

6)

 $E_z(x=0,z)=\underset{-a}{\overset{b}{\int }}f(x,z)dx$
is an integral that calculates the z-component of the electric field at point P situated above the x-axis where a charged rod of length (a+b) is located. The distance between point P and the x-axis is z=1.2 m. Evaluate $f(x,y)$ at x=0.54 m if a=0.76 m, b=1.7 m. The total charge on the rod is 8 nC.

-a) 1.399E+01 V/m²

+b) 1.539E+01 V/m²

-c) 1.693E+01 V/m²

-d) 1.862E+01 V/m²

-e) 2.049E+01 V/m²

Key: O0

1)

Three small charged objects are placed as shown, where $b=2a$, and $a=2\times 10^{-7}\text{m}$. What is the magnitude of the net force on $q_2$ if $q_1=1e$, $q_2=-7e$, and $q_3=2e$?

-a) 3.391E-14 N

-b) 3.731E-14 N

-c) 4.104E-14 N

+d) 4.514E-14 N

-e) 4.965E-14 N

2)

Three small charged objects are placed as shown, where $b=2a$, and $a=6\times 10^{-7}\text{m}$.what angle does the force on $q_2$ make above the $-x$ axis if $q_1=2e$, $q_2=-9e$, and $q_3=4e$?

-a) 4.766E+01 degrees

-b) 5.243E+01 degrees

-c) 5.767E+01 degrees

+d) 6.343E+01 degrees

-e) 6.978E+01 degrees

3)

 $E_z(x=0,z)=\underset{-a}{\overset{b}{\int }}f(x,z)dx$
is an integral that calculates the z-component of the electric field at point P situated above the x-axis where a charged rod of length (a+b) is located. The distance between point P and the x-axis is z=1.8 m. Evaluate $f(x,y)$ at x=1.0 m if a=1.0 m, b=1.8 m. The total charge on the rod is 6 nC.

-a) 3.610E+00 V/m²

+b) 3.971E+00 V/m²

-c) 4.368E+00 V/m²

-d) 4.804E+00 V/m²

-e) 5.285E+00 V/m²

4)

A ring is uniformly charged with a net charge of 7 nC. The radius of the ring is R=1.6 m, with its center at the origin and oriented normal to the z axis as shown. what is the magnitude of the electric field at a distance z=0.35 m (on axis) away from the loop's center?

-a) 4.142E+09 N/C²

-b) 4.556E+09 N/C²

+c) 5.012E+09 N/C²

-d) 5.513E+09 N/C²

-e) 6.064E+09 N/C²

5)  $E(z)=\underset{0}{\overset{R}{\int }}f(r^{\prime },z)d{r}^{\prime }$
is an integral that calculates the magnitude of the electric field at a distance $z$ fromthe center of a thin circular disk as measured along a line normal to the plane of the disk. The disk's radius is $R=1.4\text{ m}$ and the surface charge density is $\sigma =6{\text{ nC/m}}^3$. Evaluate $f(r^{\prime },z)$ at $r^{\prime }=0.56\text{ m}$.

-a) 2.567E+01 V/m²

-b) 2.824E+01 V/m²

-c) 3.106E+01 V/m²

-d) 3.417E+01 V/m²

+e) 3.759E+01 V/m²

6) A large thin isolated square plate has an area of 6 m². It is uniformly charged with 9 nC of charge. What is the magnitude of the electric field 3 mm from the center of the plate's surface?

+a) 8.471E+01 N/C

-b) 9.318E+01 N/C

-c) 1.025E+02 N/C

-d) 1.127E+02 N/C

-e) 1.240E+02 N/C

Key: O1

1)

Three small charged objects are placed as shown, where $b=2a$, and $a=2\times 10^{-7}\text{m}$. What is the magnitude of the net force on $q_2$ if $q_1=1e$, $q_2=-7e$, and $q_3=2e$?

-a) 3.391E-14 N

-b) 3.731E-14 N

-c) 4.104E-14 N

+d) 4.514E-14 N

-e) 4.965E-14 N

2)

A ring is uniformly charged with a net charge of 6 nC. The radius of the ring is R=1.9 m, with its center at the origin and oriented normal to the z axis as shown. what is the magnitude of the electric field at a distance z=0.4 m (on axis) away from the loop's center?

-a) 2.013E+09 N/C²

-b) 2.214E+09 N/C²

-c) 2.435E+09 N/C²

-d) 2.679E+09 N/C²

+e) 2.947E+09 N/C²

3)

Three small charged objects are placed as shown, where $b=2a$, and $a=4\times 10^{-7}\text{m}$.what angle does the force on $q_2$ make above the $-x$ axis if $q_1=2e$, $q_2=-9e$, and $q_3=5e$?

-a) 3.961E+01 degrees

-b) 4.357E+01 degrees

-c) 4.793E+01 degrees

-d) 5.272E+01 degrees

+e) 5.799E+01 degrees

4)

 $E_z(x=0,z)=\underset{-a}{\overset{b}{\int }}f(x,z)dx$
is an integral that calculates the z-component of the electric field at point P situated above the x-axis where a charged rod of length (a+b) is located. The distance between point P and the x-axis is z=1.7 m. Evaluate $f(x,y)$ at x=0.52 m if a=0.88 m, b=1.3 m. The total charge on the rod is 6 nC.

-a) 6.804E+00 V/m²

+b) 7.485E+00 V/m²

-c) 8.233E+00 V/m²

-d) 9.056E+00 V/m²

-e) 9.962E+00 V/m²

5) A large thin isolated square plate has an area of 6 m². It is uniformly charged with 6 nC of charge. What is the magnitude of the electric field 2 mm from the center of the plate's surface?

+a) 5.647E+01 N/C

-b) 6.212E+01 N/C

-c) 6.833E+01 N/C

-d) 7.516E+01 N/C

-e) 8.268E+01 N/C

6)  $E(z)=\underset{0}{\overset{R}{\int }}f(r^{\prime },z)d{r}^{\prime }$
is an integral that calculates the magnitude of the electric field at a distance $z$ fromthe center of a thin circular disk as measured along a line normal to the plane of the disk. The disk's radius is $R=8.1\text{ m}$ and the surface charge density is $\sigma =3{\text{ nC/m}}^3$. Evaluate $f(r^{\prime },z)$ at $r^{\prime }=4.2\text{ m}$.

-a) 5.134E-01 V/m²

+b) 5.648E-01 V/m²

-c) 6.212E-01 V/m²

-d) 6.834E-01 V/m²

-e) 7.517E-01 V/m²

Key: O2

1)

Three small charged objects are placed as shown, where $b=2a$, and $a=4\times 10^{-7}\text{m}$.what angle does the force on $q_2$ make above the $-x$ axis if $q_1=3e$, $q_2=-7e$, and $q_3=5e$?

-a) 5.569E+01 degrees

-b) 6.125E+01 degrees

+c) 6.738E+01 degrees

-d) 7.412E+01 degrees

-e) 8.153E+01 degrees

2) A large thin isolated square plate has an area of 9 m². It is uniformly charged with 8 nC of charge. What is the magnitude of the electric field 3 mm from the center of the plate's surface?

-a) 3.428E+01 N/C

-b) 3.771E+01 N/C

-c) 4.148E+01 N/C

-d) 4.563E+01 N/C

+e) 5.020E+01 N/C

3)

 $E_z(x=0,z)=\underset{-a}{\overset{b}{\int }}f(x,z)dx$
is an integral that calculates the z-component of the electric field at point P situated above the x-axis where a charged rod of length (a+b) is located. The distance between point P and the x-axis is z=1.9 m. Evaluate $f(x,y)$ at x=0.54 m if a=1.0 m, b=2.0 m. The total charge on the rod is 3 nC.

-a) 1.665E+00 V/m²

-b) 1.831E+00 V/m²

-c) 2.014E+00 V/m²

+d) 2.216E+00 V/m²

-e) 2.437E+00 V/m²

4)  $E(z)=\underset{0}{\overset{R}{\int }}f(r^{\prime },z)d{r}^{\prime }$
is an integral that calculates the magnitude of the electric field at a distance $z$ fromthe center of a thin circular disk as measured along a line normal to the plane of the disk. The disk's radius is $R=6.8\text{ m}$ and the surface charge density is $\sigma =6{\text{ nC/m}}^3$. Evaluate $f(r^{\prime },z)$ at $r^{\prime }=3.6\text{ m}$.

-a) 1.258E+00 V/m²

-b) 1.384E+00 V/m²

-c) 1.522E+00 V/m²

+d) 1.674E+00 V/m²

-e) 1.842E+00 V/m²

5)

Three small charged objects are placed as shown, where $b=2a$, and $a=6\times 10^{-7}\text{m}$. What is the magnitude of the net force on $q_2$ if $q_1=3e$, $q_2=-7e$, and $q_3=5e$?

-a) 9.958E-15 N

-b) 1.095E-14 N

-c) 1.205E-14 N

-d) 1.325E-14 N

+e) 1.458E-14 N

6)

A ring is uniformly charged with a net charge of 7 nC. The radius of the ring is R=1.7 m, with its center at the origin and oriented normal to the z axis as shown. what is the magnitude of the electric field at a distance z=1.2 m (on axis) away from the loop's center?

-a) 6.925E+09 N/C²

-b) 7.617E+09 N/C²

+c) 8.379E+09 N/C²

-d) 9.217E+09 N/C²

-e) 1.014E+10 N/C²

Key: P0

1)

Three small charged objects are placed as shown, where $b=2a$, and $a=2\times 10^{-7}\text{m}$. What is the magnitude of the net force on $q_2$ if $q_1=1e$, $q_2=-8e$, and $q_3=3e$?

-a) 5.243E-14 N

+b) 5.768E-14 N

-c) 6.344E-14 N

-d) 6.979E-14 N

-e) 7.677E-14 N

2)

Three small charged objects are placed as shown, where $b=2a$, and $a=2\times 10^{-7}\text{m}$.what angle does the force on $q_2$ make above the $-x$ axis if $q_1=1e$, $q_2=-8e$, and $q_3=3e$?

-a) 3.629E+01 degrees

-b) 3.992E+01 degrees

-c) 4.391E+01 degrees

-d) 4.830E+01 degrees

+e) 5.313E+01 degrees

3)

 $E_z(x=0,z)=\underset{-a}{\overset{b}{\int }}f(x,z)dx$
is an integral that calculates the z-component of the electric field at point P situated above the x-axis where a charged rod of length (a+b) is located. The distance between point P and the x-axis is z=1.6 m. Evaluate $f(x,y)$ at x=0.73 m if a=0.64 m, b=1.8 m. The total charge on the rod is 3 nC.

-a) 2.955E+00 V/m²

+b) 3.250E+00 V/m²

-c) 3.575E+00 V/m²

-d) 3.933E+00 V/m²

-e) 4.326E+00 V/m²

4)

A ring is uniformly charged with a net charge of 3 nC. The radius of the ring is R=1.8 m, with its center at the origin and oriented normal to the z axis as shown. what is the magnitude of the electric field at a distance z=1.1 m (on axis) away from the loop's center?

+a) 3.159E+09 N/C²

-b) 3.475E+09 N/C²

-c) 3.823E+09 N/C²

-d) 4.205E+09 N/C²

-e) 4.626E+09 N/C²

5)  $E(z)=\underset{0}{\overset{R}{\int }}f(r^{\prime },z)d{r}^{\prime }$
is an integral that calculates the magnitude of the electric field at a distance $z$ fromthe center of a thin circular disk as measured along a line normal to the plane of the disk. The disk's radius is $R=1.8\text{ m}$ and the surface charge density is $\sigma =3{\text{ nC/m}}^3$. Evaluate $f(r^{\prime },z)$ at $r^{\prime }=1.1\text{ m}$.

-a) 7.517E+00 V/m²

-b) 8.269E+00 V/m²

-c) 9.096E+00 V/m²

-d) 1.001E+01 V/m²

+e) 1.101E+01 V/m²

6) A large thin isolated square plate has an area of 6 m². It is uniformly charged with 9 nC of charge. What is the magnitude of the electric field 2 mm from the center of the plate's surface?

-a) 7.000E+01 N/C

-b) 7.701E+01 N/C

+c) 8.471E+01 N/C

-d) 9.318E+01 N/C

-e) 1.025E+02 N/C

Key: P1

1)

 $E_z(x=0,z)=\underset{-a}{\overset{b}{\int }}f(x,z)dx$
is an integral that calculates the z-component of the electric field at point P situated above the x-axis where a charged rod of length (a+b) is located. The distance between point P and the x-axis is z=1.8 m. Evaluate $f(x,y)$ at x=0.65 m if a=0.85 m, b=1.8 m. The total charge on the rod is 5 nC.

-a) 3.959E+00 V/m²

+b) 4.355E+00 V/m²

-c) 4.790E+00 V/m²

-d) 5.269E+00 V/m²

-e) 5.796E+00 V/m²

2) A large thin isolated square plate has an area of 8 m². It is uniformly charged with 5 nC of charge. What is the magnitude of the electric field 1 mm from the center of the plate's surface?

-a) 2.652E+01 N/C

-b) 2.917E+01 N/C

-c) 3.209E+01 N/C

+d) 3.529E+01 N/C

-e) 3.882E+01 N/C

3)

A ring is uniformly charged with a net charge of 5 nC. The radius of the ring is R=1.6 m, with its center at the origin and oriented normal to the z axis as shown. what is the magnitude of the electric field at a distance z=1.1 m (on axis) away from the loop's center?

-a) 5.581E+09 N/C²

-b) 6.139E+09 N/C²

+c) 6.753E+09 N/C²

-d) 7.428E+09 N/C²

-e) 8.171E+09 N/C²

4)

Three small charged objects are placed as shown, where $b=2a$, and $a=4\times 10^{-7}\text{m}$. What is the magnitude of the net force on $q_2$ if $q_1=3e$, $q_2=-7e$, and $q_3=6e$?

-a) 2.544E-14 N

-b) 2.798E-14 N

-c) 3.078E-14 N

+d) 3.385E-14 N

-e) 3.724E-14 N

5)

Three small charged objects are placed as shown, where $b=2a$, and $a=6\times 10^{-7}\text{m}$.what angle does the force on $q_2$ make above the $-x$ axis if $q_1=2e$, $q_2=-9e$, and $q_3=5e$?

-a) 5.272E+01 degrees

+b) 5.799E+01 degrees

-c) 6.379E+01 degrees

-d) 7.017E+01 degrees

-e) 7.719E+01 degrees

6)  $E(z)=\underset{0}{\overset{R}{\int }}f(r^{\prime },z)d{r}^{\prime }$
is an integral that calculates the magnitude of the electric field at a distance $z$ fromthe center of a thin circular disk as measured along a line normal to the plane of the disk. The disk's radius is $R=8.7\text{ m}$ and the surface charge density is $\sigma =7{\text{ nC/m}}^3$. Evaluate $f(r^{\prime },z)$ at $r^{\prime }=5.8\text{ m}$.

-a) 3.722E-01 V/m²

-b) 4.094E-01 V/m²

-c) 4.504E-01 V/m²

+d) 4.954E-01 V/m²

-e) 5.450E-01 V/m²

Key: P2

1)

A ring is uniformly charged with a net charge of 7 nC. The radius of the ring is R=1.7 m, with its center at the origin and oriented normal to the z axis as shown. what is the magnitude of the electric field at a distance z=1.1 m (on axis) away from the loop's center?

+a) 8.336E+09 N/C²

-b) 9.170E+09 N/C²

-c) 1.009E+10 N/C²

-d) 1.110E+10 N/C²

-e) 1.220E+10 N/C²

2)  $E(z)=\underset{0}{\overset{R}{\int }}f(r^{\prime },z)d{r}^{\prime }$
is an integral that calculates the magnitude of the electric field at a distance $z$ fromthe center of a thin circular disk as measured along a line normal to the plane of the disk. The disk's radius is $R=7.9\text{ m}$ and the surface charge density is $\sigma =2{\text{ nC/m}}^3$. Evaluate $f(r^{\prime },z)$ at $r^{\prime }=5.1\text{ m}$.

-a) 8.253E-01 V/m²

-b) 9.079E-01 V/m²

+c) 9.987E-01 V/m²

-d) 1.099E+00 V/m²

-e) 1.208E+00 V/m²

3)

Three small charged objects are placed as shown, where $b=2a$, and $a=2\times 10^{-7}\text{m}$. What is the magnitude of the net force on $q_2$ if $q_1=1e$, $q_2=-8e$, and $q_3=2e$?

-a) 3.876E-14 N

-b) 4.263E-14 N

-c) 4.690E-14 N

+d) 5.159E-14 N

-e) 5.675E-14 N

4) A large thin isolated square plate has an area of 6 m². It is uniformly charged with 5 nC of charge. What is the magnitude of the electric field 2 mm from the center of the plate's surface?

-a) 3.214E+01 N/C

-b) 3.536E+01 N/C

-c) 3.889E+01 N/C

-d) 4.278E+01 N/C

+e) 4.706E+01 N/C

5)

Three small charged objects are placed as shown, where $b=2a$, and $a=4\times 10^{-7}\text{m}$.what angle does the force on $q_2$ make above the $-x$ axis if $q_1=1e$, $q_2=-8e$, and $q_3=4e$?

-a) 3.719E+01 degrees

-b) 4.091E+01 degrees

+c) 4.500E+01 degrees

-d) 4.950E+01 degrees

-e) 5.445E+01 degrees

6)

 $E_z(x=0,z)=\underset{-a}{\overset{b}{\int }}f(x,z)dx$
is an integral that calculates the z-component of the electric field at point P situated above the x-axis where a charged rod of length (a+b) is located. The distance between point P and the x-axis is z=1.5 m. Evaluate $f(x,y)$ at x=0.79 m if a=0.75 m, b=2.1 m. The total charge on the rod is 6 nC.

+a) 5.825E+00 V/m²

-b) 6.407E+00 V/m²

-c) 7.048E+00 V/m²

-d) 7.753E+00 V/m²

-e) 8.528E+00 V/m²

Key: Q0

1)

Three small charged objects are placed as shown, where $b=2a$, and $a=2\times 10^{-7}\text{m}$. What is the magnitude of the net force on $q_2$ if $q_1=3e$, $q_2=-9e$, and $q_3=6e$?

-a) 1.308E-13 N

-b) 1.439E-13 N

-c) 1.583E-13 N

+d) 1.741E-13 N

-e) 1.915E-13 N

2)

Three small charged objects are placed as shown, where $b=2a$, and $a=6\times 10^{-7}\text{m}$.what angle does the force on $q_2$ make above the $-x$ axis if $q_1=3e$, $q_2=-7e$, and $q_3=6e$?

+a) 6.343E+01 degrees

-b) 6.978E+01 degrees

-c) 7.676E+01 degrees

-d) 8.443E+01 degrees

-e) 9.288E+01 degrees

3)

 $E_z(x=0,z)=\underset{-a}{\overset{b}{\int }}f(x,z)dx$
is an integral that calculates the z-component of the electric field at point P situated above the x-axis where a charged rod of length (a+b) is located. The distance between point P and the x-axis is z=1.7 m. Evaluate $f(x,y)$ at x=0.76 m if a=1.1 m, b=1.6 m. The total charge on the rod is 8 nC.

-a) 5.267E+00 V/m²

-b) 5.794E+00 V/m²

-c) 6.374E+00 V/m²

+d) 7.011E+00 V/m²

-e) 7.712E+00 V/m²

4)

A ring is uniformly charged with a net charge of 8 nC. The radius of the ring is R=1.7 m, with its center at the origin and oriented normal to the z axis as shown. what is the magnitude of the electric field at a distance z=0.32 m (on axis) away from the loop's center?

-a) 3.339E+09 N/C²

-b) 3.673E+09 N/C²

-c) 4.041E+09 N/C²

+d) 4.445E+09 N/C²

-e) 4.889E+09 N/C²

5)  $E(z)=\underset{0}{\overset{R}{\int }}f(r^{\prime },z)d{r}^{\prime }$
is an integral that calculates the magnitude of the electric field at a distance $z$ fromthe center of a thin circular disk as measured along a line normal to the plane of the disk. The disk's radius is $R=7.5\text{ m}$ and the surface charge density is $\sigma =3{\text{ nC/m}}^3$. Evaluate $f(r^{\prime },z)$ at $r^{\prime }=2.6\text{ m}$.

-a) 7.820E-01 V/m²

+b) 8.602E-01 V/m²

-c) 9.462E-01 V/m²

-d) 1.041E+00 V/m²

-e) 1.145E+00 V/m²

6) A large thin isolated square plate has an area of 5 m². It is uniformly charged with 8 nC of charge. What is the magnitude of the electric field 3 mm from the center of the plate's surface?

-a) 6.171E+01 N/C

-b) 6.788E+01 N/C

-c) 7.467E+01 N/C

-d) 8.214E+01 N/C

+e) 9.035E+01 N/C

Key: Q1

1)  $E(z)=\underset{0}{\overset{R}{\int }}f(r^{\prime },z)d{r}^{\prime }$
is an integral that calculates the magnitude of the electric field at a distance $z$ fromthe center of a thin circular disk as measured along a line normal to the plane of the disk. The disk's radius is $R=2.8\text{ m}$ and the surface charge density is $\sigma =3{\text{ nC/m}}^3$. Evaluate $f(r^{\prime },z)$ at $r^{\prime }=1.9\text{ m}$.

-a) 4.295E+00 V/m²

+b) 4.724E+00 V/m²

-c) 5.196E+00 V/m²

-d) 5.716E+00 V/m²

-e) 6.288E+00 V/m²

2)

A ring is uniformly charged with a net charge of 6 nC. The radius of the ring is R=1.9 m, with its center at the origin and oriented normal to the z axis as shown. what is the magnitude of the electric field at a distance z=0.4 m (on axis) away from the loop's center?

-a) 2.013E+09 N/C²

-b) 2.214E+09 N/C²

-c) 2.435E+09 N/C²

-d) 2.679E+09 N/C²

+e) 2.947E+09 N/C²

3)

Three small charged objects are placed as shown, where $b=2a$, and $a=2\times 10^{-7}\text{m}$. What is the magnitude of the net force on $q_2$ if $q_1=1e$, $q_2=-8e$, and $q_3=3e$?

-a) 5.243E-14 N

+b) 5.768E-14 N

-c) 6.344E-14 N

-d) 6.979E-14 N

-e) 7.677E-14 N

4)

Three small charged objects are placed as shown, where $b=2a$, and $a=2\times 10^{-7}\text{m}$.what angle does the force on $q_2$ make above the $-x$ axis if $q_1=1e$, $q_2=-8e$, and $q_3=3e$?

-a) 3.629E+01 degrees

-b) 3.992E+01 degrees

-c) 4.391E+01 degrees

-d) 4.830E+01 degrees

+e) 5.313E+01 degrees

5)

 $E_z(x=0,z)=\underset{-a}{\overset{b}{\int }}f(x,z)dx$
is an integral that calculates the z-component of the electric field at point P situated above the x-axis where a charged rod of length (a+b) is located. The distance between point P and the x-axis is z=1.9 m. Evaluate $f(x,y)$ at x=0.54 m if a=1.0 m, b=2.0 m. The total charge on the rod is 3 nC.

-a) 1.665E+00 V/m²

-b) 1.831E+00 V/m²

-c) 2.014E+00 V/m²

+d) 2.216E+00 V/m²

-e) 2.437E+00 V/m²

6) A large thin isolated square plate has an area of 8 m². It is uniformly charged with 5 nC of charge. What is the magnitude of the electric field 1 mm from the center of the plate's surface?

-a) 2.652E+01 N/C

-b) 2.917E+01 N/C

-c) 3.209E+01 N/C

+d) 3.529E+01 N/C

-e) 3.882E+01 N/C

Key: Q2

1)

Three small charged objects are placed as shown, where $b=2a$, and $a=4\times 10^{-7}\text{m}$. What is the magnitude of the net force on $q_2$ if $q_1=2e$, $q_2=-7e$, and $q_3=3e$?

-a) 1.473E-14 N

-b) 1.620E-14 N

-c) 1.782E-14 N

-d) 1.960E-14 N

+e) 2.156E-14 N

2)

 $E_z(x=0,z)=\underset{-a}{\overset{b}{\int }}f(x,z)dx$
is an integral that calculates the z-component of the electric field at point P situated above the x-axis where a charged rod of length (a+b) is located. The distance between point P and the x-axis is z=1.6 m. Evaluate $f(x,y)$ at x=0.73 m if a=0.64 m, b=1.8 m. The total charge on the rod is 3 nC.

-a) 2.955E+00 V/m²

+b) 3.250E+00 V/m²

-c) 3.575E+00 V/m²

-d) 3.933E+00 V/m²

-e) 4.326E+00 V/m²

3)

Three small charged objects are placed as shown, where $b=2a$, and $a=4\times 10^{-7}\text{m}$.what angle does the force on $q_2$ make above the $-x$ axis if $q_1=1e$, $q_2=-8e$, and $q_3=4e$?

-a) 3.719E+01 degrees

-b) 4.091E+01 degrees

+c) 4.500E+01 degrees

-d) 4.950E+01 degrees

-e) 5.445E+01 degrees

4) A large thin isolated square plate has an area of 6 m². It is uniformly charged with 5 nC of charge. What is the magnitude of the electric field 1 mm from the center of the plate's surface?

-a) 3.214E+01 N/C

-b) 3.536E+01 N/C

-c) 3.889E+01 N/C

-d) 4.278E+01 N/C

+e) 4.706E+01 N/C

5)  $E(z)=\underset{0}{\overset{R}{\int }}f(r^{\prime },z)d{r}^{\prime }$
is an integral that calculates the magnitude of the electric field at a distance $z$ fromthe center of a thin circular disk as measured along a line normal to the plane of the disk. The disk's radius is $R=9.1\text{ m}$ and the surface charge density is $\sigma =2{\text{ nC/m}}^3$. Evaluate $f(r^{\prime },z)$ at $r^{\prime }=6.2\text{ m}$.

-a) 4.961E-01 V/m²

-b) 5.457E-01 V/m²

-c) 6.002E-01 V/m²

-d) 6.603E-01 V/m²

+e) 7.263E-01 V/m²

6)

A ring is uniformly charged with a net charge of 9 nC. The radius of the ring is R=1.9 m, with its center at the origin and oriented normal to the z axis as shown. what is the magnitude of the electric field at a distance z=1.4 m (on axis) away from the loop's center?

-a) 7.119E+09 N/C²

-b) 7.831E+09 N/C²

+c) 8.614E+09 N/C²

-d) 9.476E+09 N/C²

-e) 1.042E+10 N/C²

Key: R0

1)

Three small charged objects are placed as shown, where $b=2a$, and $a=4\times 10^{-7}\text{m}$. What is the magnitude of the net force on $q_2$ if $q_1=2e$, $q_2=-8e$, and $q_3=3e$?

-a) 2.036E-14 N

-b) 2.240E-14 N

+c) 2.464E-14 N

-d) 2.710E-14 N

-e) 2.981E-14 N

2)

Three small charged objects are placed as shown, where $b=2a$, and $a=6\times 10^{-7}\text{m}$.what angle does the force on $q_2$ make above the $-x$ axis if $q_1=2e$, $q_2=-9e$, and $q_3=4e$?

-a) 4.766E+01 degrees

-b) 5.243E+01 degrees

-c) 5.767E+01 degrees

+d) 6.343E+01 degrees

-e) 6.978E+01 degrees

3)

 $E_z(x=0,z)=\underset{-a}{\overset{b}{\int }}f(x,z)dx$
is an integral that calculates the z-component of the electric field at point P situated above the x-axis where a charged rod of length (a+b) is located. The distance between point P and the x-axis is z=1.2 m. Evaluate $f(x,y)$ at x=0.54 m if a=0.76 m, b=1.7 m. The total charge on the rod is 8 nC.

-a) 1.399E+01 V/m²

+b) 1.539E+01 V/m²

-c) 1.693E+01 V/m²

-d) 1.862E+01 V/m²

-e) 2.049E+01 V/m²

4)

A ring is uniformly charged with a net charge of 3 nC. The radius of the ring is R=1.8 m, with its center at the origin and oriented normal to the z axis as shown. what is the magnitude of the electric field at a distance z=1.1 m (on axis) away from the loop's center?

+a) 3.159E+09 N/C²

-b) 3.475E+09 N/C²

-c) 3.823E+09 N/C²

-d) 4.205E+09 N/C²

-e) 4.626E+09 N/C²

5)  $E(z)=\underset{0}{\overset{R}{\int }}f(r^{\prime },z)d{r}^{\prime }$
is an integral that calculates the magnitude of the electric field at a distance $z$ fromthe center of a thin circular disk as measured along a line normal to the plane of the disk. The disk's radius is $R=2.8\text{ m}$ and the surface charge density is $\sigma =3{\text{ nC/m}}^3$. Evaluate $f(r^{\prime },z)$ at $r^{\prime }=1.9\text{ m}$.

-a) 4.295E+00 V/m²

+b) 4.724E+00 V/m²

-c) 5.196E+00 V/m²

-d) 5.716E+00 V/m²

-e) 6.288E+00 V/m²

6) A large thin isolated square plate has an area of 9 m². It is uniformly charged with 6 nC of charge. What is the magnitude of the electric field 1 mm from the center of the plate's surface?

-a) 2.571E+01 N/C

-b) 2.828E+01 N/C

-c) 3.111E+01 N/C

-d) 3.422E+01 N/C

+e) 3.765E+01 N/C

Key: R1

1)  $E(z)=\underset{0}{\overset{R}{\int }}f(r^{\prime },z)d{r}^{\prime }$
is an integral that calculates the magnitude of the electric field at a distance $z$ fromthe center of a thin circular disk as measured along a line normal to the plane of the disk. The disk's radius is $R=3.3\text{ m}$ and the surface charge density is $\sigma =4{\text{ nC/m}}^3$. Evaluate $f(r^{\prime },z)$ at $r^{\prime }=2.0\text{ m}$.

-a) 6.877E+00 V/m²

-b) 7.565E+00 V/m²

+c) 8.321E+00 V/m²

-d) 9.153E+00 V/m²

-e) 1.007E+01 V/m²

2)

Three small charged objects are placed as shown, where $b=2a$, and $a=2\times 10^{-7}\text{m}$.what angle does the force on $q_2$ make above the $-x$ axis if $q_1=2e$, $q_2=-7e$, and $q_3=5e$?

-a) 4.357E+01 degrees

-b) 4.793E+01 degrees

-c) 5.272E+01 degrees

+d) 5.799E+01 degrees

-e) 6.379E+01 degrees

3) A large thin isolated square plate has an area of 5 m². It is uniformly charged with 8 nC of charge. What is the magnitude of the electric field 3 mm from the center of the plate's surface?

-a) 6.171E+01 N/C

-b) 6.788E+01 N/C

-c) 7.467E+01 N/C

-d) 8.214E+01 N/C

+e) 9.035E+01 N/C

4)

 $E_z(x=0,z)=\underset{-a}{\overset{b}{\int }}f(x,z)dx$
is an integral that calculates the z-component of the electric field at point P situated above the x-axis where a charged rod of length (a+b) is located. The distance between point P and the x-axis is z=1.7 m. Evaluate $f(x,y)$ at x=0.76 m if a=1.1 m, b=1.6 m. The total charge on the rod is 8 nC.

-a) 5.267E+00 V/m²

-b) 5.794E+00 V/m²

-c) 6.374E+00 V/m²

+d) 7.011E+00 V/m²

-e) 7.712E+00 V/m²

5)

Three small charged objects are placed as shown, where $b=2a$, and $a=6\times 10^{-7}\text{m}$. What is the magnitude of the net force on $q_2$ if $q_1=2e$, $q_2=-8e$, and $q_3=4e$?

-a) 8.613E-15 N

-b) 9.474E-15 N

-c) 1.042E-14 N

+d) 1.146E-14 N

-e) 1.261E-14 N

6)

A ring is uniformly charged with a net charge of 5 nC. The radius of the ring is R=1.6 m, with its center at the origin and oriented normal to the z axis as shown. what is the magnitude of the electric field at a distance z=1.1 m (on axis) away from the loop's center?

-a) 5.581E+09 N/C²

-b) 6.139E+09 N/C²

+c) 6.753E+09 N/C²

-d) 7.428E+09 N/C²

-e) 8.171E+09 N/C²

Key: R2

1)

A ring is uniformly charged with a net charge of 7 nC. The radius of the ring is R=1.7 m, with its center at the origin and oriented normal to the z axis as shown. what is the magnitude of the electric field at a distance z=1.1 m (on axis) away from the loop's center?

+a) 8.336E+09 N/C²

-b) 9.170E+09 N/C²

-c) 1.009E+10 N/C²

-d) 1.110E+10 N/C²

-e) 1.220E+10 N/C²

2)

 $E_z(x=0,z)=\underset{-a}{\overset{b}{\int }}f(x,z)dx$
is an integral that calculates the z-component of the electric field at point P situated above the x-axis where a charged rod of length (a+b) is located. The distance between point P and the x-axis is z=1.9 m. Evaluate $f(x,y)$ at x=0.54 m if a=1.0 m, b=2.0 m. The total charge on the rod is 3 nC.

-a) 1.665E+00 V/m²

-b) 1.831E+00 V/m²

-c) 2.014E+00 V/m²

+d) 2.216E+00 V/m²

-e) 2.437E+00 V/m²

3)

Three small charged objects are placed as shown, where $b=2a$, and $a=4\times 10^{-7}\text{m}$. What is the magnitude of the net force on $q_2$ if $q_1=1e$, $q_2=-8e$, and $q_3=2e$?

-a) 1.172E-14 N

+b) 1.290E-14 N

-c) 1.419E-14 N

-d) 1.561E-14 N

-e) 1.717E-14 N

4) A large thin isolated square plate has an area of 6 m². It is uniformly charged with 5 nC of charge. What is the magnitude of the electric field 2 mm from the center of the plate's surface?

-a) 3.214E+01 N/C

-b) 3.536E+01 N/C

-c) 3.889E+01 N/C

-d) 4.278E+01 N/C

+e) 4.706E+01 N/C

5)

Three small charged objects are placed as shown, where $b=2a$, and $a=2\times 10^{-7}\text{m}$.what angle does the force on $q_2$ make above the $-x$ axis if $q_1=2e$, $q_2=-7e$, and $q_3=3e$?

-a) 4.743E+01 degrees

-b) 5.217E+01 degrees

-c) 5.739E+01 degrees

-d) 6.313E+01 degrees

+e) 6.944E+01 degrees

6)  $E(z)=\underset{0}{\overset{R}{\int }}f(r^{\prime },z)d{r}^{\prime }$
is an integral that calculates the magnitude of the electric field at a distance $z$ fromthe center of a thin circular disk as measured along a line normal to the plane of the disk. The disk's radius is $R=6.9\text{ m}$ and the surface charge density is $\sigma =9{\text{ nC/m}}^3$. Evaluate $f(r^{\prime },z)$ at $r^{\prime }=4.3\text{ m}$.

-a) 8.924E-01 V/m²

-b) 9.816E-01 V/m²

+c) 1.080E+00 V/m²

-d) 1.188E+00 V/m²

-e) 1.307E+00 V/m²

Key: S0

1)

Three small charged objects are placed as shown, where $b=2a$, and $a=6\times 10^{-7}\text{m}$. What is the magnitude of the net force on $q_2$ if $q_1=3e$, $q_2=-7e$, and $q_3=5e$?

-a) 9.958E-15 N

-b) 1.095E-14 N

-c) 1.205E-14 N

-d) 1.325E-14 N

+e) 1.458E-14 N

2)

Three small charged objects are placed as shown, where $b=2a$, and $a=6\times 10^{-7}\text{m}$.what angle does the force on $q_2$ make above the $-x$ axis if $q_1=2e$, $q_2=-9e$, and $q_3=4e$?

-a) 4.766E+01 degrees

-b) 5.243E+01 degrees

-c) 5.767E+01 degrees

+d) 6.343E+01 degrees

-e) 6.978E+01 degrees

3)

 $E_z(x=0,z)=\underset{-a}{\overset{b}{\int }}f(x,z)dx$
is an integral that calculates the z-component of the electric field at point P situated above the x-axis where a charged rod of length (a+b) is located. The distance between point P and the x-axis is z=1.6 m. Evaluate $f(x,y)$ at x=0.73 m if a=0.64 m, b=1.8 m. The total charge on the rod is 3 nC.

-a) 2.955E+00 V/m²

+b) 3.250E+00 V/m²

-c) 3.575E+00 V/m²

-d) 3.933E+00 V/m²

-e) 4.326E+00 V/m²

4)

A ring is uniformly charged with a net charge of 5 nC. The radius of the ring is R=1.9 m, with its center at the origin and oriented normal to the z axis as shown. what is the magnitude of the electric field at a distance z=1.3 m (on axis) away from the loop's center?

+a) 4.788E+09 N/C²

-b) 5.267E+09 N/C²

-c) 5.793E+09 N/C²

-d) 6.373E+09 N/C²

-e) 7.010E+09 N/C²

5)  $E(z)=\underset{0}{\overset{R}{\int }}f(r^{\prime },z)d{r}^{\prime }$
is an integral that calculates the magnitude of the electric field at a distance $z$ fromthe center of a thin circular disk as measured along a line normal to the plane of the disk. The disk's radius is $R=2.8\text{ m}$ and the surface charge density is $\sigma =3{\text{ nC/m}}^3$. Evaluate $f(r^{\prime },z)$ at $r^{\prime }=1.9\text{ m}$.

-a) 4.295E+00 V/m²

+b) 4.724E+00 V/m²

-c) 5.196E+00 V/m²

-d) 5.716E+00 V/m²

-e) 6.288E+00 V/m²

6) A large thin isolated square plate has an area of 5 m². It is uniformly charged with 8 nC of charge. What is the magnitude of the electric field 3 mm from the center of the plate's surface?

-a) 6.171E+01 N/C

-b) 6.788E+01 N/C

-c) 7.467E+01 N/C

-d) 8.214E+01 N/C

+e) 9.035E+01 N/C

Key: S1

1)

A ring is uniformly charged with a net charge of 3 nC. The radius of the ring is R=1.8 m, with its center at the origin and oriented normal to the z axis as shown. what is the magnitude of the electric field at a distance z=1.1 m (on axis) away from the loop's center?

+a) 3.159E+09 N/C²

-b) 3.475E+09 N/C²

-c) 3.823E+09 N/C²

-d) 4.205E+09 N/C²

-e) 4.626E+09 N/C²

2)  $E(z)=\underset{0}{\overset{R}{\int }}f(r^{\prime },z)d{r}^{\prime }$
is an integral that calculates the magnitude of the electric field at a distance $z$ fromthe center of a thin circular disk as measured along a line normal to the plane of the disk. The disk's radius is $R=9.1\text{ m}$ and the surface charge density is $\sigma =2{\text{ nC/m}}^3$. Evaluate $f(r^{\prime },z)$ at $r^{\prime }=6.2\text{ m}$.

-a) 4.961E-01 V/m²

-b) 5.457E-01 V/m²

-c) 6.002E-01 V/m²

-d) 6.603E-01 V/m²

+e) 7.263E-01 V/m²

3)

Three small charged objects are placed as shown, where $b=2a$, and $a=2\times 10^{-7}\text{m}$.what angle does the force on $q_2$ make above the $-x$ axis if $q_1=2e$, $q_2=-7e$, and $q_3=5e$?

-a) 4.357E+01 degrees

-b) 4.793E+01 degrees

-c) 5.272E+01 degrees

+d) 5.799E+01 degrees

-e) 6.379E+01 degrees

4) A large thin isolated square plate has an area of 3 m². It is uniformly charged with 9 nC of charge. What is the magnitude of the electric field 3 mm from the center of the plate's surface?

+a) 1.694E+02 N/C

-b) 1.864E+02 N/C

-c) 2.050E+02 N/C

-d) 2.255E+02 N/C

-e) 2.480E+02 N/C

5)

Three small charged objects are placed as shown, where $b=2a$, and $a=6\times 10^{-7}\text{m}$. What is the magnitude of the net force on $q_2$ if $q_1=3e$, $q_2=-7e$, and $q_3=6e$?

-a) 1.028E-14 N

-b) 1.130E-14 N

-c) 1.244E-14 N

-d) 1.368E-14 N

+e) 1.505E-14 N

6)

 $E_z(x=0,z)=\underset{-a}{\overset{b}{\int }}f(x,z)dx$
is an integral that calculates the z-component of the electric field at point P situated above the x-axis where a charged rod of length (a+b) is located. The distance between point P and the x-axis is z=1.2 m. Evaluate $f(x,y)$ at x=0.54 m if a=0.76 m, b=1.7 m. The total charge on the rod is 8 nC.

-a) 1.399E+01 V/m²

+b) 1.539E+01 V/m²

-c) 1.693E+01 V/m²

-d) 1.862E+01 V/m²

-e) 2.049E+01 V/m²

Key: S2

1)

Three small charged objects are placed as shown, where $b=2a$, and $a=2\times 10^{-7}\text{m}$. What is the magnitude of the net force on $q_2$ if $q_1=1e$, $q_2=-9e$, and $q_3=4e$?

-a) 5.014E-14 N

-b) 5.515E-14 N

-c) 6.067E-14 N

-d) 6.674E-14 N

+e) 7.341E-14 N

2)  $E(z)=\underset{0}{\overset{R}{\int }}f(r^{\prime },z)d{r}^{\prime }$
is an integral that calculates the magnitude of the electric field at a distance $z$ fromthe center of a thin circular disk as measured along a line normal to the plane of the disk. The disk's radius is $R=1.4\text{ m}$ and the surface charge density is $\sigma =6{\text{ nC/m}}^3$. Evaluate $f(r^{\prime },z)$ at $r^{\prime }=0.56\text{ m}$.

-a) 2.567E+01 V/m²

-b) 2.824E+01 V/m²

-c) 3.106E+01 V/m²

-d) 3.417E+01 V/m²

+e) 3.759E+01 V/m²

3)

 $E_z(x=0,z)=\underset{-a}{\overset{b}{\int }}f(x,z)dx$
is an integral that calculates the z-component of the electric field at point P situated above the x-axis where a charged rod of length (a+b) is located. The distance between point P and the x-axis is z=1.8 m. Evaluate $f(x,y)$ at x=0.65 m if a=0.85 m, b=1.8 m. The total charge on the rod is 5 nC.

-a) 3.959E+00 V/m²

+b) 4.355E+00 V/m²

-c) 4.790E+00 V/m²

-d) 5.269E+00 V/m²

-e) 5.796E+00 V/m²

4)

A ring is uniformly charged with a net charge of 6 nC. The radius of the ring is R=1.9 m, with its center at the origin and oriented normal to the z axis as shown. what is the magnitude of the electric field at a distance z=0.4 m (on axis) away from the loop's center?

-a) 2.013E+09 N/C²

-b) 2.214E+09 N/C²

-c) 2.435E+09 N/C²

-d) 2.679E+09 N/C²

+e) 2.947E+09 N/C²

5) A large thin isolated square plate has an area of 6 m². It is uniformly charged with 9 nC of charge. What is the magnitude of the electric field 3 mm from the center of the plate's surface?

+a) 8.471E+01 N/C

-b) 9.318E+01 N/C

-c) 1.025E+02 N/C

-d) 1.127E+02 N/C

-e) 1.240E+02 N/C

6)

Three small charged objects are placed as shown, where $b=2a$, and $a=6\times 10^{-7}\text{m}$.what angle does the force on $q_2$ make above the $-x$ axis if $q_1=3e$, $q_2=-7e$, and $q_3=6e$?

+a) 6.343E+01 degrees

-b) 6.978E+01 degrees

-c) 7.676E+01 degrees

-d) 8.443E+01 degrees

-e) 9.288E+01 degrees

Key: T0

1)

Three small charged objects are placed as shown, where $b=2a$, and $a=4\times 10^{-7}\text{m}$. What is the magnitude of the net force on $q_2$ if $q_1=2e$, $q_2=-8e$, and $q_3=5e$?

-a) 2.248E-14 N

-b) 2.473E-14 N

+c) 2.721E-14 N

-d) 2.993E-14 N

-e) 3.292E-14 N

2)

Three small charged objects are placed as shown, where $b=2a$, and $a=4\times 10^{-7}\text{m}$.what angle does the force on $q_2$ make above the $-x$ axis if $q_1=1e$, $q_2=-8e$, and $q_3=4e$?

-a) 3.719E+01 degrees

-b) 4.091E+01 degrees

+c) 4.500E+01 degrees

-d) 4.950E+01 degrees

-e) 5.445E+01 degrees

3)

 $E_z(x=0,z)=\underset{-a}{\overset{b}{\int }}f(x,z)dx$
is an integral that calculates the z-component of the electric field at point P situated above the x-axis where a charged rod of length (a+b) is located. The distance between point P and the x-axis is z=1.3 m. Evaluate $f(x,y)$ at x=0.83 m if a=0.82 m, b=1.3 m. The total charge on the rod is 7 nC.

-a) 8.690E+00 V/m²

-b) 9.559E+00 V/m²

+c) 1.051E+01 V/m²

-d) 1.157E+01 V/m²

-e) 1.272E+01 V/m²

4)

A ring is uniformly charged with a net charge of 2 nC. The radius of the ring is R=1.5 m, with its center at the origin and oriented normal to the z axis as shown. what is the magnitude of the electric field at a distance z=0.33 m (on axis) away from the loop's center?

-a) 1.353E+09 N/C²

-b) 1.488E+09 N/C²

+c) 1.637E+09 N/C²

-d) 1.801E+09 N/C²

-e) 1.981E+09 N/C²

5)  $E(z)=\underset{0}{\overset{R}{\int }}f(r^{\prime },z)d{r}^{\prime }$
is an integral that calculates the magnitude of the electric field at a distance $z$ fromthe center of a thin circular disk as measured along a line normal to the plane of the disk. The disk's radius is $R=8.1\text{ m}$ and the surface charge density is $\sigma =3{\text{ nC/m}}^3$. Evaluate $f(r^{\prime },z)$ at $r^{\prime }=4.2\text{ m}$.

-a) 5.134E-01 V/m²

+b) 5.648E-01 V/m²

-c) 6.212E-01 V/m²

-d) 6.834E-01 V/m²

-e) 7.517E-01 V/m²

6) A large thin isolated square plate has an area of 3 m². It is uniformly charged with 9 nC of charge. What is the magnitude of the electric field 3 mm from the center of the plate's surface?

+a) 1.694E+02 N/C

-b) 1.864E+02 N/C

-c) 2.050E+02 N/C

-d) 2.255E+02 N/C

-e) 2.480E+02 N/C

Key: T1

1)

A ring is uniformly charged with a net charge of 7 nC. The radius of the ring is R=1.6 m, with its center at the origin and oriented normal to the z axis as shown. what is the magnitude of the electric field at a distance z=0.34 m (on axis) away from the loop's center?

-a) 3.672E+09 N/C²

-b) 4.039E+09 N/C²

-c) 4.443E+09 N/C²

+d) 4.887E+09 N/C²

-e) 5.376E+09 N/C²

2) A large thin isolated square plate has an area of 4 m². It is uniformly charged with 5 nC of charge. What is the magnitude of the electric field 1 mm from the center of the plate's surface?

-a) 4.821E+01 N/C

-b) 5.303E+01 N/C

-c) 5.834E+01 N/C

-d) 6.417E+01 N/C

+e) 7.059E+01 N/C

3)

Three small charged objects are placed as shown, where $b=2a$, and $a=6\times 10^{-7}\text{m}$. What is the magnitude of the net force on $q_2$ if $q_1=3e$, $q_2=-7e$, and $q_3=5e$?

-a) 9.958E-15 N

-b) 1.095E-14 N

-c) 1.205E-14 N

-d) 1.325E-14 N

+e) 1.458E-14 N

4)

Three small charged objects are placed as shown, where $b=2a$, and $a=2\times 10^{-7}\text{m}$.what angle does the force on $q_2$ make above the $-x$ axis if $q_1=1e$, $q_2=-7e$, and $q_3=4e$?

-a) 4.091E+01 degrees

+b) 4.500E+01 degrees

-c) 4.950E+01 degrees

-d) 5.445E+01 degrees

-e) 5.990E+01 degrees

5)

 $E_z(x=0,z)=\underset{-a}{\overset{b}{\int }}f(x,z)dx$
is an integral that calculates the z-component of the electric field at point P situated above the x-axis where a charged rod of length (a+b) is located. The distance between point P and the x-axis is z=1.2 m. Evaluate $f(x,y)$ at x=0.73 m if a=0.52 m, b=1.6 m. The total charge on the rod is 7 nC.

-a) 9.655E+00 V/m²

-b) 1.062E+01 V/m²

-c) 1.168E+01 V/m²

+d) 1.285E+01 V/m²

-e) 1.414E+01 V/m²

6)  $E(z)=\underset{0}{\overset{R}{\int }}f(r^{\prime },z)d{r}^{\prime }$
is an integral that calculates the magnitude of the electric field at a distance $z$ fromthe center of a thin circular disk as measured along a line normal to the plane of the disk. The disk's radius is $R=8.7\text{ m}$ and the surface charge density is $\sigma =7{\text{ nC/m}}^3$. Evaluate $f(r^{\prime },z)$ at $r^{\prime }=5.8\text{ m}$.

-a) 3.722E-01 V/m²

-b) 4.094E-01 V/m²

-c) 4.504E-01 V/m²

+d) 4.954E-01 V/m²

-e) 5.450E-01 V/m²

Key: T2

1) A large thin isolated square plate has an area of 6 m². It is uniformly charged with 9 nC of charge. What is the magnitude of the electric field 2 mm from the center of the plate's surface?

-a) 7.000E+01 N/C

-b) 7.701E+01 N/C

+c) 8.471E+01 N/C

-d) 9.318E+01 N/C

-e) 1.025E+02 N/C

2)  $E(z)=\underset{0}{\overset{R}{\int }}f(r^{\prime },z)d{r}^{\prime }$
is an integral that calculates the magnitude of the electric field at a distance $z$ fromthe center of a thin circular disk as measured along a line normal to the plane of the disk. The disk's radius is $R=1.8\text{ m}$ and the surface charge density is $\sigma =3{\text{ nC/m}}^3$. Evaluate $f(r^{\prime },z)$ at $r^{\prime }=1.1\text{ m}$.

-a) 7.517E+00 V/m²

-b) 8.269E+00 V/m²

-c) 9.096E+00 V/m²

-d) 1.001E+01 V/m²

+e) 1.101E+01 V/m²

3)

A ring is uniformly charged with a net charge of 9 nC. The radius of the ring is R=1.6 m, with its center at the origin and oriented normal to the z axis as shown. what is the magnitude of the electric field at a distance z=0.73 m (on axis) away from the loop's center?

-a) 7.415E+09 N/C²

-b) 8.156E+09 N/C²

-c) 8.972E+09 N/C²

-d) 9.869E+09 N/C²

+e) 1.086E+10 N/C²

4)

Three small charged objects are placed as shown, where $b=2a$, and $a=4\times 10^{-7}\text{m}$. What is the magnitude of the net force on $q_2$ if $q_1=1e$, $q_2=-8e$, and $q_3=2e$?

-a) 1.172E-14 N

+b) 1.290E-14 N

-c) 1.419E-14 N

-d) 1.561E-14 N

-e) 1.717E-14 N

5)

Three small charged objects are placed as shown, where $b=2a$, and $a=2\times 10^{-7}\text{m}$.what angle does the force on $q_2$ make above the $-x$ axis if $q_1=2e$, $q_2=-7e$, and $q_3=3e$?

-a) 4.743E+01 degrees

-b) 5.217E+01 degrees

-c) 5.739E+01 degrees

-d) 6.313E+01 degrees

+e) 6.944E+01 degrees

6)

 $E_z(x=0,z)=\underset{-a}{\overset{b}{\int }}f(x,z)dx$
is an integral that calculates the z-component of the electric field at point P situated above the x-axis where a charged rod of length (a+b) is located. The distance between point P and the x-axis is z=1.8 m. Evaluate $f(x,y)$ at x=0.65 m if a=0.85 m, b=1.8 m. The total charge on the rod is 5 nC.

-a) 3.959E+00 V/m²

+b) 4.355E+00 V/m²

-c) 4.790E+00 V/m²

-d) 5.269E+00 V/m²

-e) 5.796E+00 V/m²

Key: U0

1)

Three small charged objects are placed as shown, where $b=2a$, and $a=6\times 10^{-7}\text{m}$. What is the magnitude of the net force on $q_2$ if $q_1=1e$, $q_2=-7e$, and $q_3=2e$?

-a) 3.426E-15 N

-b) 3.768E-15 N

-c) 4.145E-15 N

-d) 4.560E-15 N

+e) 5.015E-15 N

2)

Three small charged objects are placed as shown, where $b=2a$, and $a=4\times 10^{-7}\text{m}$.what angle does the force on $q_2$ make above the $-x$ axis if $q_1=1e$, $q_2=-8e$, and $q_3=4e$?

-a) 3.719E+01 degrees

-b) 4.091E+01 degrees

+c) 4.500E+01 degrees

-d) 4.950E+01 degrees

-e) 5.445E+01 degrees

3)

 $E_z(x=0,z)=\underset{-a}{\overset{b}{\int }}f(x,z)dx$
is an integral that calculates the z-component of the electric field at point P situated above the x-axis where a charged rod of length (a+b) is located. The distance between point P and the x-axis is z=1.3 m. Evaluate $f(x,y)$ at x=0.83 m if a=0.82 m, b=1.3 m. The total charge on the rod is 7 nC.

-a) 8.690E+00 V/m²

-b) 9.559E+00 V/m²

+c) 1.051E+01 V/m²

-d) 1.157E+01 V/m²

-e) 1.272E+01 V/m²

4)

A ring is uniformly charged with a net charge of 8 nC. The radius of the ring is R=1.7 m, with its center at the origin and oriented normal to the z axis as shown. what is the magnitude of the electric field at a distance z=0.32 m (on axis) away from the loop's center?

-a) 3.339E+09 N/C²

-b) 3.673E+09 N/C²

-c) 4.041E+09 N/C²

+d) 4.445E+09 N/C²

-e) 4.889E+09 N/C²

5)  $E(z)=\underset{0}{\overset{R}{\int }}f(r^{\prime },z)d{r}^{\prime }$
is an integral that calculates the magnitude of the electric field at a distance $z$ fromthe center of a thin circular disk as measured along a line normal to the plane of the disk. The disk's radius is $R=3.0\text{ m}$ and the surface charge density is $\sigma =8{\text{ nC/m}}^3$. Evaluate $f(r^{\prime },z)$ at $r^{\prime }=2.0\text{ m}$.

-a) 9.459E+00 V/m²

+b) 1.040E+01 V/m²

-c) 1.145E+01 V/m²

-d) 1.259E+01 V/m²

-e) 1.385E+01 V/m²

6) A large thin isolated square plate has an area of 6 m². It is uniformly charged with 9 nC of charge. What is the magnitude of the electric field 1 mm from the center of the plate's surface?

-a) 7.701E+01 N/C

+b) 8.471E+01 N/C

-c) 9.318E+01 N/C

-d) 1.025E+02 N/C

-e) 1.127E+02 N/C

Key: U1

1) A large thin isolated square plate has an area of 9 m². It is uniformly charged with 5 nC of charge. What is the magnitude of the electric field 1 mm from the center of the plate's surface?

-a) 2.357E+01 N/C

-b) 2.593E+01 N/C

-c) 2.852E+01 N/C

+d) 3.137E+01 N/C

-e) 3.451E+01 N/C

2)

A ring is uniformly charged with a net charge of 6 nC. The radius of the ring is R=1.9 m, with its center at the origin and oriented normal to the z axis as shown. what is the magnitude of the electric field at a distance z=0.4 m (on axis) away from the loop's center?

-a) 2.013E+09 N/C²

-b) 2.214E+09 N/C²

-c) 2.435E+09 N/C²

-d) 2.679E+09 N/C²

+e) 2.947E+09 N/C²

3)

Three small charged objects are placed as shown, where $b=2a$, and $a=6\times 10^{-7}\text{m}$.what angle does the force on $q_2$ make above the $-x$ axis if $q_1=2e$, $q_2=-9e$, and $q_3=5e$?

-a) 5.272E+01 degrees

+b) 5.799E+01 degrees

-c) 6.379E+01 degrees

-d) 7.017E+01 degrees

-e) 7.719E+01 degrees

4)

Three small charged objects are placed as shown, where $b=2a$, and $a=2\times 10^{-7}\text{m}$. What is the magnitude of the net force on $q_2$ if $q_1=3e$, $q_2=-9e$, and $q_3=6e$?

-a) 1.308E-13 N

-b) 1.439E-13 N

-c) 1.583E-13 N

+d) 1.741E-13 N

-e) 1.915E-13 N

5)

 $E_z(x=0,z)=\underset{-a}{\overset{b}{\int }}f(x,z)dx$
is an integral that calculates the z-component of the electric field at point P situated above the x-axis where a charged rod of length (a+b) is located. The distance between point P and the x-axis is z=1.5 m. Evaluate $f(x,y)$ at x=1.1 m if a=0.61 m, b=1.7 m. The total charge on the rod is 8 nC.

-a) 5.995E+00 V/m²

-b) 6.595E+00 V/m²

+c) 7.254E+00 V/m²

-d) 7.980E+00 V/m²

-e) 8.778E+00 V/m²

6)  $E(z)=\underset{0}{\overset{R}{\int }}f(r^{\prime },z)d{r}^{\prime }$
is an integral that calculates the magnitude of the electric field at a distance $z$ fromthe center of a thin circular disk as measured along a line normal to the plane of the disk. The disk's radius is $R=9.1\text{ m}$ and the surface charge density is $\sigma =2{\text{ nC/m}}^3$. Evaluate $f(r^{\prime },z)$ at $r^{\prime }=6.2\text{ m}$.

-a) 4.961E-01 V/m²

-b) 5.457E-01 V/m²

-c) 6.002E-01 V/m²

-d) 6.603E-01 V/m²

+e) 7.263E-01 V/m²

Key: U2

1) A large thin isolated square plate has an area of 9 m². It is uniformly charged with 6 nC of charge. What is the magnitude of the electric field 1 mm from the center of the plate's surface?

-a) 2.571E+01 N/C

-b) 2.828E+01 N/C

-c) 3.111E+01 N/C

-d) 3.422E+01 N/C

+e) 3.765E+01 N/C

2)

A ring is uniformly charged with a net charge of 8 nC. The radius of the ring is R=1.7 m, with its center at the origin and oriented normal to the z axis as shown. what is the magnitude of the electric field at a distance z=0.32 m (on axis) away from the loop's center?

-a) 3.339E+09 N/C²

-b) 3.673E+09 N/C²

-c) 4.041E+09 N/C²

+d) 4.445E+09 N/C²

-e) 4.889E+09 N/C²

3)

Three small charged objects are placed as shown, where $b=2a$, and $a=6\times 10^{-7}\text{m}$.what angle does the force on $q_2$ make above the $-x$ axis if $q_1=3e$, $q_2=-7e$, and $q_3=6e$?

+a) 6.343E+01 degrees

-b) 6.978E+01 degrees

-c) 7.676E+01 degrees

-d) 8.443E+01 degrees

-e) 9.288E+01 degrees

4)  $E(z)=\underset{0}{\overset{R}{\int }}f(r^{\prime },z)d{r}^{\prime }$
is an integral that calculates the magnitude of the electric field at a distance $z$ fromthe center of a thin circular disk as measured along a line normal to the plane of the disk. The disk's radius is $R=7.2\text{ m}$ and the surface charge density is $\sigma =3{\text{ nC/m}}^3$. Evaluate $f(r^{\prime },z)$ at $r^{\prime }=3.6\text{ m}$.

+a) 1.606E+00 V/m²

-b) 1.767E+00 V/m²

-c) 1.943E+00 V/m²

-d) 2.138E+00 V/m²

-e) 2.351E+00 V/m²

5)

Three small charged objects are placed as shown, where $b=2a$, and $a=6\times 10^{-7}\text{m}$. What is the magnitude of the net force on $q_2$ if $q_1=3e$, $q_2=-7e$, and $q_3=5e$?

-a) 9.958E-15 N

-b) 1.095E-14 N

-c) 1.205E-14 N

-d) 1.325E-14 N

+e) 1.458E-14 N

6)

 $E_z(x=0,z)=\underset{-a}{\overset{b}{\int }}f(x,z)dx$
is an integral that calculates the z-component of the electric field at point P situated above the x-axis where a charged rod of length (a+b) is located. The distance between point P and the x-axis is z=1.8 m. Evaluate $f(x,y)$ at x=1.0 m if a=1.0 m, b=1.8 m. The total charge on the rod is 6 nC.

-a) 3.610E+00 V/m²

+b) 3.971E+00 V/m²

-c) 4.368E+00 V/m²

-d) 4.804E+00 V/m²

-e) 5.285E+00 V/m²

Key: V0

1)

Three small charged objects are placed as shown, where $b=2a$, and $a=2\times 10^{-7}\text{m}$. What is the magnitude of the net force on $q_2$ if $q_1=1e$, $q_2=-8e$, and $q_3=2e$?

-a) 3.876E-14 N

-b) 4.263E-14 N

-c) 4.690E-14 N

+d) 5.159E-14 N

-e) 5.675E-14 N

2)

Three small charged objects are placed as shown, where $b=2a$, and $a=4\times 10^{-7}\text{m}$.what angle does the force on $q_2$ make above the $-x$ axis if $q_1=3e$, $q_2=-7e$, and $q_3=5e$?

-a) 5.569E+01 degrees

-b) 6.125E+01 degrees

+c) 6.738E+01 degrees

-d) 7.412E+01 degrees

-e) 8.153E+01 degrees

3)

 $E_z(x=0,z)=\underset{-a}{\overset{b}{\int }}f(x,z)dx$
is an integral that calculates the z-component of the electric field at point P situated above the x-axis where a charged rod of length (a+b) is located. The distance between point P and the x-axis is z=1.5 m. Evaluate $f(x,y)$ at x=0.79 m if a=0.75 m, b=2.1 m. The total charge on the rod is 6 nC.

+a) 5.825E+00 V/m²

-b) 6.407E+00 V/m²

-c) 7.048E+00 V/m²

-d) 7.753E+00 V/m²

-e) 8.528E+00 V/m²

4)

A ring is uniformly charged with a net charge of 4 nC. The radius of the ring is R=1.6 m, with its center at the origin and oriented normal to the z axis as shown. what is the magnitude of the electric field at a distance z=1.1 m (on axis) away from the loop's center?

+a) 5.402E+09 N/C²

-b) 5.943E+09 N/C²

-c) 6.537E+09 N/C²

-d) 7.191E+09 N/C²

-e) 7.910E+09 N/C²

5)  $E(z)=\underset{0}{\overset{R}{\int }}f(r^{\prime },z)d{r}^{\prime }$
is an integral that calculates the magnitude of the electric field at a distance $z$ fromthe center of a thin circular disk as measured along a line normal to the plane of the disk. The disk's radius is $R=4.3\text{ m}$ and the surface charge density is $\sigma =2{\text{ nC/m}}^3$. Evaluate $f(r^{\prime },z)$ at $r^{\prime }=2.4\text{ m}$.

+a) 5.647E+00 V/m²

-b) 6.212E+00 V/m²

-c) 6.833E+00 V/m²

-d) 7.517E+00 V/m²

-e) 8.268E+00 V/m²

6) A large thin isolated square plate has an area of 6 m². It is uniformly charged with 5 nC of charge. What is the magnitude of the electric field 1 mm from the center of the plate's surface?

-a) 3.214E+01 N/C

-b) 3.536E+01 N/C

-c) 3.889E+01 N/C

-d) 4.278E+01 N/C

+e) 4.706E+01 N/C

Key: V1

1)

A ring is uniformly charged with a net charge of 5 nC. The radius of the ring is R=1.6 m, with its center at the origin and oriented normal to the z axis as shown. what is the magnitude of the electric field at a distance z=1.1 m (on axis) away from the loop's center?

-a) 5.581E+09 N/C²

-b) 6.139E+09 N/C²

+c) 6.753E+09 N/C²

-d) 7.428E+09 N/C²

-e) 8.171E+09 N/C²

2)  $E(z)=\underset{0}{\overset{R}{\int }}f(r^{\prime },z)d{r}^{\prime }$
is an integral that calculates the magnitude of the electric field at a distance $z$ fromthe center of a thin circular disk as measured along a line normal to the plane of the disk. The disk's radius is $R=3.2\text{ m}$ and the surface charge density is $\sigma =2{\text{ nC/m}}^3$. Evaluate $f(r^{\prime },z)$ at $r^{\prime }=2.2\text{ m}$.

-a) 3.228E+00 V/m²

-b) 3.551E+00 V/m²

-c) 3.906E+00 V/m²

-d) 4.297E+00 V/m²

+e) 4.727E+00 V/m²

3)

 $E_z(x=0,z)=\underset{-a}{\overset{b}{\int }}f(x,z)dx$
is an integral that calculates the z-component of the electric field at point P situated above the x-axis where a charged rod of length (a+b) is located. The distance between point P and the x-axis is z=1.9 m. Evaluate $f(x,y)$ at x=0.96 m if a=0.95 m, b=1.8 m. The total charge on the rod is 7 nC.

-a) 3.385E+00 V/m²

-b) 3.724E+00 V/m²

-c) 4.096E+00 V/m²

+d) 4.506E+00 V/m²

-e) 4.957E+00 V/m²

4) A large thin isolated square plate has an area of 8 m². It is uniformly charged with 7 nC of charge. What is the magnitude of the electric field 3 mm from the center of the plate's surface?

-a) 4.492E+01 N/C

+b) 4.941E+01 N/C

-c) 5.435E+01 N/C

-d) 5.979E+01 N/C

-e) 6.577E+01 N/C

5)

Three small charged objects are placed as shown, where $b=2a$, and $a=2\times 10^{-7}\text{m}$.what angle does the force on $q_2$ make above the $-x$ axis if $q_1=1e$, $q_2=-8e$, and $q_3=3e$?

-a) 3.629E+01 degrees

-b) 3.992E+01 degrees

-c) 4.391E+01 degrees

-d) 4.830E+01 degrees

+e) 5.313E+01 degrees

6)

Three small charged objects are placed as shown, where $b=2a$, and $a=2\times 10^{-7}\text{m}$. What is the magnitude of the net force on $q_2$ if $q_1=1e$, $q_2=-8e$, and $q_3=3e$?

-a) 5.243E-14 N

+b) 5.768E-14 N

-c) 6.344E-14 N

-d) 6.979E-14 N

-e) 7.677E-14 N

Key: V2

1)

 $E_z(x=0,z)=\underset{-a}{\overset{b}{\int }}f(x,z)dx$
is an integral that calculates the z-component of the electric field at point P situated above the x-axis where a charged rod of length (a+b) is located. The distance between point P and the x-axis is z=1.8 m. Evaluate $f(x,y)$ at x=0.5 m if a=0.67 m, b=2.4 m. The total charge on the rod is 9 nC.

-a) 5.465E+00 V/m²

-b) 6.012E+00 V/m²

-c) 6.613E+00 V/m²

+d) 7.274E+00 V/m²

-e) 8.002E+00 V/m²

2)

A ring is uniformly charged with a net charge of 2 nC. The radius of the ring is R=1.6 m, with its center at the origin and oriented normal to the z axis as shown. what is the magnitude of the electric field at a distance z=0.99 m (on axis) away from the loop's center?

-a) 2.429E+09 N/C²

+b) 2.672E+09 N/C²

-c) 2.939E+09 N/C²

-d) 3.233E+09 N/C²

-e) 3.556E+09 N/C²

3)

Three small charged objects are placed as shown, where $b=2a$, and $a=6\times 10^{-7}\text{m}$.what angle does the force on $q_2$ make above the $-x$ axis if $q_1=3e$, $q_2=-7e$, and $q_3=6e$?

+a) 6.343E+01 degrees

-b) 6.978E+01 degrees

-c) 7.676E+01 degrees

-d) 8.443E+01 degrees

-e) 9.288E+01 degrees

4) A large thin isolated square plate has an area of 6 m². It is uniformly charged with 5 nC of charge. What is the magnitude of the electric field 2 mm from the center of the plate's surface?

-a) 3.214E+01 N/C

-b) 3.536E+01 N/C

-c) 3.889E+01 N/C

-d) 4.278E+01 N/C

+e) 4.706E+01 N/C

5)

Three small charged objects are placed as shown, where $b=2a$, and $a=6\times 10^{-7}\text{m}$. What is the magnitude of the net force on $q_2$ if $q_1=3e$, $q_2=-7e$, and $q_3=6e$?

-a) 1.028E-14 N

-b) 1.130E-14 N

-c) 1.244E-14 N

-d) 1.368E-14 N

+e) 1.505E-14 N

6)  $E(z)=\underset{0}{\overset{R}{\int }}f(r^{\prime },z)d{r}^{\prime }$
is an integral that calculates the magnitude of the electric field at a distance $z$ fromthe center of a thin circular disk as measured along a line normal to the plane of the disk. The disk's radius is $R=7.2\text{ m}$ and the surface charge density is $\sigma =3{\text{ nC/m}}^3$. Evaluate $f(r^{\prime },z)$ at $r^{\prime }=3.6\text{ m}$.

+a) 1.606E+00 V/m²

-b) 1.767E+00 V/m²

-c) 1.943E+00 V/m²

-d) 2.138E+00 V/m²

-e) 2.351E+00 V/m²

Key: W0

1)

Three small charged objects are placed as shown, where $b=2a$, and $a=2\times 10^{-7}\text{m}$. What is the magnitude of the net force on $q_2$ if $q_1=1e$, $q_2=-9e$, and $q_3=4e$?

-a) 5.014E-14 N

-b) 5.515E-14 N

-c) 6.067E-14 N

-d) 6.674E-14 N

+e) 7.341E-14 N

2)

Three small charged objects are placed as shown, where $b=2a$, and $a=2\times 10^{-7}\text{m}$.what angle does the force on $q_2$ make above the $-x$ axis if $q_1=2e$, $q_2=-7e$, and $q_3=3e$?

-a) 4.743E+01 degrees

-b) 5.217E+01 degrees

-c) 5.739E+01 degrees

-d) 6.313E+01 degrees

+e) 6.944E+01 degrees

3)

 $E_z(x=0,z)=\underset{-a}{\overset{b}{\int }}f(x,z)dx$
is an integral that calculates the z-component of the electric field at point P situated above the x-axis where a charged rod of length (a+b) is located. The distance between point P and the x-axis is z=1.5 m. Evaluate $f(x,y)$ at x=1.1 m if a=0.62 m, b=1.3 m. The total charge on the rod is 7 nC.

-a) 6.311E+00 V/m²

-b) 6.943E+00 V/m²

+c) 7.637E+00 V/m²

-d) 8.401E+00 V/m²

-e) 9.241E+00 V/m²

4)

A ring is uniformly charged with a net charge of 6 nC. The radius of the ring is R=1.9 m, with its center at the origin and oriented normal to the z axis as shown. what is the magnitude of the electric field at a distance z=0.4 m (on axis) away from the loop's center?

-a) 2.013E+09 N/C²

-b) 2.214E+09 N/C²

-c) 2.435E+09 N/C²

-d) 2.679E+09 N/C²

+e) 2.947E+09 N/C²

5)  $E(z)=\underset{0}{\overset{R}{\int }}f(r^{\prime },z)d{r}^{\prime }$
is an integral that calculates the magnitude of the electric field at a distance $z$ fromthe center of a thin circular disk as measured along a line normal to the plane of the disk. The disk's radius is $R=2.8\text{ m}$ and the surface charge density is $\sigma =3{\text{ nC/m}}^3$. Evaluate $f(r^{\prime },z)$ at $r^{\prime }=1.9\text{ m}$.

-a) 4.295E+00 V/m²

+b) 4.724E+00 V/m²

-c) 5.196E+00 V/m²

-d) 5.716E+00 V/m²

-e) 6.288E+00 V/m²

6) A large thin isolated square plate has an area of 5 m². It is uniformly charged with 8 nC of charge. What is the magnitude of the electric field 3 mm from the center of the plate's surface?

-a) 6.171E+01 N/C

-b) 6.788E+01 N/C

-c) 7.467E+01 N/C

-d) 8.214E+01 N/C

+e) 9.035E+01 N/C

Key: W1

1)  $E(z)=\underset{0}{\overset{R}{\int }}f(r^{\prime },z)d{r}^{\prime }$
is an integral that calculates the magnitude of the electric field at a distance $z$ fromthe center of a thin circular disk as measured along a line normal to the plane of the disk. The disk's radius is $R=6.9\text{ m}$ and the surface charge density is $\sigma =9{\text{ nC/m}}^3$. Evaluate $f(r^{\prime },z)$ at $r^{\prime }=4.3\text{ m}$.

-a) 8.924E-01 V/m²

-b) 9.816E-01 V/m²

+c) 1.080E+00 V/m²

-d) 1.188E+00 V/m²

-e) 1.307E+00 V/m²

2) A large thin isolated square plate has an area of 8 m². It is uniformly charged with 7 nC of charge. What is the magnitude of the electric field 3 mm from the center of the plate's surface?

-a) 4.492E+01 N/C

+b) 4.941E+01 N/C

-c) 5.435E+01 N/C

-d) 5.979E+01 N/C

-e) 6.577E+01 N/C

3)

Three small charged objects are placed as shown, where $b=2a$, and $a=6\times 10^{-7}\text{m}$. What is the magnitude of the net force on $q_2$ if $q_1=3e$, $q_2=-7e$, and $q_3=5e$?

-a) 9.958E-15 N

-b) 1.095E-14 N

-c) 1.205E-14 N

-d) 1.325E-14 N

+e) 1.458E-14 N

4)

 $E_z(x=0,z)=\underset{-a}{\overset{b}{\int }}f(x,z)dx$
is an integral that calculates the z-component of the electric field at point P situated above the x-axis where a charged rod of length (a+b) is located. The distance between point P and the x-axis is z=1.5 m. Evaluate $f(x,y)$ at x=1.1 m if a=0.62 m, b=1.3 m. The total charge on the rod is 7 nC.

-a) 6.311E+00 V/m²

-b) 6.943E+00 V/m²

+c) 7.637E+00 V/m²

-d) 8.401E+00 V/m²

-e) 9.241E+00 V/m²

5)

Three small charged objects are placed as shown, where $b=2a$, and $a=6\times 10^{-7}\text{m}$.what angle does the force on $q_2$ make above the $-x$ axis if $q_1=3e$, $q_2=-7e$, and $q_3=4e$?

-a) 5.377E+01 degrees

-b) 5.914E+01 degrees

-c) 6.506E+01 degrees

+d) 7.157E+01 degrees

-e) 7.872E+01 degrees

6)

A ring is uniformly charged with a net charge of 5 nC. The radius of the ring is R=1.6 m, with its center at the origin and oriented normal to the z axis as shown. what is the magnitude of the electric field at a distance z=1.1 m (on axis) away from the loop's center?

-a) 5.581E+09 N/C²

-b) 6.139E+09 N/C²

+c) 6.753E+09 N/C²

-d) 7.428E+09 N/C²

-e) 8.171E+09 N/C²

Key: W2

1)

A ring is uniformly charged with a net charge of 8 nC. The radius of the ring is R=1.7 m, with its center at the origin and oriented normal to the z axis as shown. what is the magnitude of the electric field at a distance z=0.32 m (on axis) away from the loop's center?

-a) 3.339E+09 N/C²

-b) 3.673E+09 N/C²

-c) 4.041E+09 N/C²

+d) 4.445E+09 N/C²

-e) 4.889E+09 N/C²

2) A large thin isolated square plate has an area of 9 m². It is uniformly charged with 6 nC of charge. What is the magnitude of the electric field 1 mm from the center of the plate's surface?

-a) 2.571E+01 N/C

-b) 2.828E+01 N/C

-c) 3.111E+01 N/C

-d) 3.422E+01 N/C

+e) 3.765E+01 N/C

3)

Three small charged objects are placed as shown, where $b=2a$, and $a=2\times 10^{-7}\text{m}$.what angle does the force on $q_2$ make above the $-x$ axis if $q_1=2e$, $q_2=-9e$, and $q_3=4e$?

-a) 5.243E+01 degrees

-b) 5.767E+01 degrees

+c) 6.343E+01 degrees

-d) 6.978E+01 degrees

-e) 7.676E+01 degrees

4)  $E(z)=\underset{0}{\overset{R}{\int }}f(r^{\prime },z)d{r}^{\prime }$
is an integral that calculates the magnitude of the electric field at a distance $z$ fromthe center of a thin circular disk as measured along a line normal to the plane of the disk. The disk's radius is $R=2.0\text{ m}$ and the surface charge density is $\sigma =9{\text{ nC/m}}^3$. Evaluate $f(r^{\prime },z)$ at $r^{\prime }=1.2\text{ m}$.

-a) 8.933E+00 V/m²

-b) 9.826E+00 V/m²

+c) 1.081E+01 V/m²

-d) 1.189E+01 V/m²

-e) 1.308E+01 V/m²

5)

 $E_z(x=0,z)=\underset{-a}{\overset{b}{\int }}f(x,z)dx$
is an integral that calculates the z-component of the electric field at point P situated above the x-axis where a charged rod of length (a+b) is located. The distance between point P and the x-axis is z=1.9 m. Evaluate $f(x,y)$ at x=0.54 m if a=1.0 m, b=2.0 m. The total charge on the rod is 3 nC.

-a) 1.665E+00 V/m²

-b) 1.831E+00 V/m²

-c) 2.014E+00 V/m²

+d) 2.216E+00 V/m²

-e) 2.437E+00 V/m²

6)

Three small charged objects are placed as shown, where $b=2a$, and $a=4\times 10^{-7}\text{m}$. What is the magnitude of the net force on $q_2$ if $q_1=2e$, $q_2=-8e$, and $q_3=3e$?

-a) 2.036E-14 N

-b) 2.240E-14 N

+c) 2.464E-14 N

-d) 2.710E-14 N

-e) 2.981E-14 N

Key: X0

1)

Three small charged objects are placed as shown, where $b=2a$, and $a=4\times 10^{-7}\text{m}$. What is the magnitude of the net force on $q_2$ if $q_1=1e$, $q_2=-7e$, and $q_3=4e$?

-a) 9.750E-15 N

-b) 1.072E-14 N

-c) 1.180E-14 N

-d) 1.298E-14 N

+e) 1.427E-14 N

2)

Three small charged objects are placed as shown, where $b=2a$, and $a=6\times 10^{-7}\text{m}$.what angle does the force on $q_2$ make above the $-x$ axis if $q_1=2e$, $q_2=-9e$, and $q_3=5e$?

-a) 5.272E+01 degrees

+b) 5.799E+01 degrees

-c) 6.379E+01 degrees

-d) 7.017E+01 degrees

-e) 7.719E+01 degrees

3)

 $E_z(x=0,z)=\underset{-a}{\overset{b}{\int }}f(x,z)dx$
is an integral that calculates the z-component of the electric field at point P situated above the x-axis where a charged rod of length (a+b) is located. The distance between point P and the x-axis is z=1.5 m. Evaluate $f(x,y)$ at x=1.1 m if a=0.61 m, b=1.7 m. The total charge on the rod is 8 nC.

-a) 5.995E+00 V/m²

-b) 6.595E+00 V/m²

+c) 7.254E+00 V/m²

-d) 7.980E+00 V/m²

-e) 8.778E+00 V/m²

4)

A ring is uniformly charged with a net charge of 5 nC. The radius of the ring is R=1.6 m, with its center at the origin and oriented normal to the z axis as shown. what is the magnitude of the electric field at a distance z=1.1 m (on axis) away from the loop's center?

-a) 5.581E+09 N/C²

-b) 6.139E+09 N/C²

+c) 6.753E+09 N/C²

-d) 7.428E+09 N/C²

-e) 8.171E+09 N/C²

5)  $E(z)=\underset{0}{\overset{R}{\int }}f(r^{\prime },z)d{r}^{\prime }$
is an integral that calculates the magnitude of the electric field at a distance $z$ fromthe center of a thin circular disk as measured along a line normal to the plane of the disk. The disk's radius is $R=3.3\text{ m}$ and the surface charge density is $\sigma =4{\text{ nC/m}}^3$. Evaluate $f(r^{\prime },z)$ at $r^{\prime }=2.0\text{ m}$.

-a) 6.877E+00 V/m²

-b) 7.565E+00 V/m²

+c) 8.321E+00 V/m²

-d) 9.153E+00 V/m²

-e) 1.007E+01 V/m²

6) A large thin isolated square plate has an area of 5 m². It is uniformly charged with 8 nC of charge. What is the magnitude of the electric field 3 mm from the center of the plate's surface?

-a) 6.171E+01 N/C

-b) 6.788E+01 N/C

-c) 7.467E+01 N/C

-d) 8.214E+01 N/C

+e) 9.035E+01 N/C

Key: X1

1)  $E(z)=\underset{0}{\overset{R}{\int }}f(r^{\prime },z)d{r}^{\prime }$
is an integral that calculates the magnitude of the electric field at a distance $z$ fromthe center of a thin circular disk as measured along a line normal to the plane of the disk. The disk's radius is $R=7.5\text{ m}$ and the surface charge density is $\sigma =3{\text{ nC/m}}^3$. Evaluate $f(r^{\prime },z)$ at $r^{\prime }=2.6\text{ m}$.

-a) 7.820E-01 V/m²

+b) 8.602E-01 V/m²

-c) 9.462E-01 V/m²

-d) 1.041E+00 V/m²

-e) 1.145E+00 V/m²

2)

Three small charged objects are placed as shown, where $b=2a$, and $a=6\times 10^{-7}\text{m}$. What is the magnitude of the net force on $q_2$ if $q_1=2e$, $q_2=-8e$, and $q_3=5e$?

-a) 8.259E-15 N

-b) 9.085E-15 N

-c) 9.993E-15 N

-d) 1.099E-14 N

+e) 1.209E-14 N

3)

A ring is uniformly charged with a net charge of 3 nC. The radius of the ring is R=1.7 m, with its center at the origin and oriented normal to the z axis as shown. what is the magnitude of the electric field at a distance z=0.34 m (on axis) away from the loop's center?

-a) 1.202E+09 N/C²

-b) 1.322E+09 N/C²

-c) 1.454E+09 N/C²

-d) 1.599E+09 N/C²

+e) 1.759E+09 N/C²

4)

Three small charged objects are placed as shown, where $b=2a$, and $a=6\times 10^{-7}\text{m}$.what angle does the force on $q_2$ make above the $-x$ axis if $q_1=3e$, $q_2=-7e$, and $q_3=6e$?

+a) 6.343E+01 degrees

-b) 6.978E+01 degrees

-c) 7.676E+01 degrees

-d) 8.443E+01 degrees

-e) 9.288E+01 degrees

5)

 $E_z(x=0,z)=\underset{-a}{\overset{b}{\int }}f(x,z)dx$
is an integral that calculates the z-component of the electric field at point P situated above the x-axis where a charged rod of length (a+b) is located. The distance between point P and the x-axis is z=1.6 m. Evaluate $f(x,y)$ at x=0.73 m if a=0.64 m, b=1.8 m. The total charge on the rod is 3 nC.

-a) 2.955E+00 V/m²

+b) 3.250E+00 V/m²

-c) 3.575E+00 V/m²

-d) 3.933E+00 V/m²

-e) 4.326E+00 V/m²

6) A large thin isolated square plate has an area of 6 m². It is uniformly charged with 9 nC of charge. What is the magnitude of the electric field 3 mm from the center of the plate's surface?

+a) 8.471E+01 N/C

-b) 9.318E+01 N/C

-c) 1.025E+02 N/C

-d) 1.127E+02 N/C

-e) 1.240E+02 N/C

Key: X2

1)

A ring is uniformly charged with a net charge of 4 nC. The radius of the ring is R=1.6 m, with its center at the origin and oriented normal to the z axis as shown. what is the magnitude of the electric field at a distance z=1.0 m (on axis) away from the loop's center?

+a) 5.352E+09 N/C²

-b) 5.887E+09 N/C²

-c) 6.476E+09 N/C²

-d) 7.124E+09 N/C²

-e) 7.836E+09 N/C²

2)

Three small charged objects are placed as shown, where $b=2a$, and $a=4\times 10^{-7}\text{m}$. What is the magnitude of the net force on $q_2$ if $q_1=2e$, $q_2=-8e$, and $q_3=5e$?

-a) 2.248E-14 N

-b) 2.473E-14 N

+c) 2.721E-14 N

-d) 2.993E-14 N

-e) 3.292E-14 N

3)

Three small charged objects are placed as shown, where $b=2a$, and $a=4\times 10^{-7}\text{m}$.what angle does the force on $q_2$ make above the $-x$ axis if $q_1=2e$, $q_2=-9e$, and $q_3=5e$?

-a) 3.961E+01 degrees

-b) 4.357E+01 degrees

-c) 4.793E+01 degrees

-d) 5.272E+01 degrees

+e) 5.799E+01 degrees

4)  $E(z)=\underset{0}{\overset{R}{\int }}f(r^{\prime },z)d{r}^{\prime }$
is an integral that calculates the magnitude of the electric field at a distance $z$ fromthe center of a thin circular disk as measured along a line normal to the plane of the disk. The disk's radius is $R=1.8\text{ m}$ and the surface charge density is $\sigma =3{\text{ nC/m}}^3$. Evaluate $f(r^{\prime },z)$ at $r^{\prime }=1.1\text{ m}$.

-a) 7.517E+00 V/m²

-b) 8.269E+00 V/m²

-c) 9.096E+00 V/m²

-d) 1.001E+01 V/m²

+e) 1.101E+01 V/m²

5) A large thin isolated square plate has an area of 3 m². It is uniformly charged with 9 nC of charge. What is the magnitude of the electric field 3 mm from the center of the plate's surface?

+a) 1.694E+02 N/C

-b) 1.864E+02 N/C

-c) 2.050E+02 N/C

-d) 2.255E+02 N/C

-e) 2.480E+02 N/C

6)

 $E_z(x=0,z)=\underset{-a}{\overset{b}{\int }}f(x,z)dx$
is an integral that calculates the z-component of the electric field at point P situated above the x-axis where a charged rod of length (a+b) is located. The distance between point P and the x-axis is z=1.5 m. Evaluate $f(x,y)$ at x=1.1 m if a=0.62 m, b=1.3 m. The total charge on the rod is 7 nC.

-a) 6.311E+00 V/m²

-b) 6.943E+00 V/m²

+c) 7.637E+00 V/m²

-d) 8.401E+00 V/m²

-e) 9.241E+00 V/m²

Key: Y0

1)

Three small charged objects are placed as shown, where $b=2a$, and $a=6\times 10^{-7}\text{m}$. What is the magnitude of the net force on $q_2$ if $q_1=2e$, $q_2=-8e$, and $q_3=4e$?

-a) 8.613E-15 N

-b) 9.474E-15 N

-c) 1.042E-14 N

+d) 1.146E-14 N

-e) 1.261E-14 N

2)

Three small charged objects are placed as shown, where $b=2a$, and $a=4\times 10^{-7}\text{m}$.what angle does the force on $q_2$ make above the $-x$ axis if $q_1=3e$, $q_2=-7e$, and $q_3=5e$?

-a) 5.569E+01 degrees

-b) 6.125E+01 degrees

+c) 6.738E+01 degrees

-d) 7.412E+01 degrees

-e) 8.153E+01 degrees

3)

 $E_z(x=0,z)=\underset{-a}{\overset{b}{\int }}f(x,z)dx$
is an integral that calculates the z-component of the electric field at point P situated above the x-axis where a charged rod of length (a+b) is located. The distance between point P and the x-axis is z=1.5 m. Evaluate $f(x,y)$ at x=0.79 m if a=0.75 m, b=2.1 m. The total charge on the rod is 6 nC.

+a) 5.825E+00 V/m²

-b) 6.407E+00 V/m²

-c) 7.048E+00 V/m²

-d) 7.753E+00 V/m²

-e) 8.528E+00 V/m²

4)

A ring is uniformly charged with a net charge of 7 nC. The radius of the ring is R=1.6 m, with its center at the origin and oriented normal to the z axis as shown. what is the magnitude of the electric field at a distance z=0.35 m (on axis) away from the loop's center?

-a) 4.142E+09 N/C²

-b) 4.556E+09 N/C²

+c) 5.012E+09 N/C²

-d) 5.513E+09 N/C²

-e) 6.064E+09 N/C²

5)  $E(z)=\underset{0}{\overset{R}{\int }}f(r^{\prime },z)d{r}^{\prime }$
is an integral that calculates the magnitude of the electric field at a distance $z$ fromthe center of a thin circular disk as measured along a line normal to the plane of the disk. The disk's radius is $R=3.2\text{ m}$ and the surface charge density is $\sigma =2{\text{ nC/m}}^3$. Evaluate $f(r^{\prime },z)$ at $r^{\prime }=2.2\text{ m}$.

-a) 3.228E+00 V/m²

-b) 3.551E+00 V/m²

-c) 3.906E+00 V/m²

-d) 4.297E+00 V/m²

+e) 4.727E+00 V/m²

6) A large thin isolated square plate has an area of 8 m². It is uniformly charged with 7 nC of charge. What is the magnitude of the electric field 3 mm from the center of the plate's surface?

-a) 4.492E+01 N/C

+b) 4.941E+01 N/C

-c) 5.435E+01 N/C

-d) 5.979E+01 N/C

-e) 6.577E+01 N/C

Key: Y1

1) A large thin isolated square plate has an area of 8 m². It is uniformly charged with 7 nC of charge. What is the magnitude of the electric field 3 mm from the center of the plate's surface?

-a) 4.492E+01 N/C

+b) 4.941E+01 N/C

-c) 5.435E+01 N/C

-d) 5.979E+01 N/C

-e) 6.577E+01 N/C

2)

A ring is uniformly charged with a net charge of 4 nC. The radius of the ring is R=1.6 m, with its center at the origin and oriented normal to the z axis as shown. what is the magnitude of the electric field at a distance z=1.1 m (on axis) away from the loop's center?

+a) 5.402E+09 N/C²

-b) 5.943E+09 N/C²

-c) 6.537E+09 N/C²

-d) 7.191E+09 N/C²

-e) 7.910E+09 N/C²

3)

Three small charged objects are placed as shown, where $b=2a$, and $a=2\times 10^{-7}\text{m}$. What is the magnitude of the net force on $q_2$ if $q_1=1e$, $q_2=-7e$, and $q_3=2e$?

-a) 3.391E-14 N

-b) 3.731E-14 N

-c) 4.104E-14 N

+d) 4.514E-14 N

-e) 4.965E-14 N

4)  $E(z)=\underset{0}{\overset{R}{\int }}f(r^{\prime },z)d{r}^{\prime }$
is an integral that calculates the magnitude of the electric field at a distance $z$ fromthe center of a thin circular disk as measured along a line normal to the plane of the disk. The disk's radius is $R=6.9\text{ m}$ and the surface charge density is $\sigma =9{\text{ nC/m}}^3$. Evaluate $f(r^{\prime },z)$ at $r^{\prime }=4.3\text{ m}$.

-a) 8.924E-01 V/m²

-b) 9.816E-01 V/m²

+c) 1.080E+00 V/m²

-d) 1.188E+00 V/m²

-e) 1.307E+00 V/m²

5)

 $E_z(x=0,z)=\underset{-a}{\overset{b}{\int }}f(x,z)dx$
is an integral that calculates the z-component of the electric field at point P situated above the x-axis where a charged rod of length (a+b) is located. The distance between point P and the x-axis is z=1.5 m. Evaluate $f(x,y)$ at x=1.0 m if a=1.1 m, b=1.4 m. The total charge on the rod is 5 nC.

+a) 4.602E+00 V/m²

-b) 5.062E+00 V/m²

-c) 5.568E+00 V/m²

-d) 6.125E+00 V/m²

-e) 6.738E+00 V/m²

6)

Three small charged objects are placed as shown, where $b=2a$, and $a=4\times 10^{-7}\text{m}$.what angle does the force on $q_2$ make above the $-x$ axis if $q_1=1e$, $q_2=-8e$, and $q_3=4e$?

-a) 3.719E+01 degrees

-b) 4.091E+01 degrees

+c) 4.500E+01 degrees

-d) 4.950E+01 degrees

-e) 5.445E+01 degrees

Key: Y2

1)

 $E_z(x=0,z)=\underset{-a}{\overset{b}{\int }}f(x,z)dx$
is an integral that calculates the z-component of the electric field at point P situated above the x-axis where a charged rod of length (a+b) is located. The distance between point P and the x-axis is z=1.8 m. Evaluate $f(x,y)$ at x=0.5 m if a=0.67 m, b=2.4 m. The total charge on the rod is 9 nC.

-a) 5.465E+00 V/m²

-b) 6.012E+00 V/m²

-c) 6.613E+00 V/m²

+d) 7.274E+00 V/m²

-e) 8.002E+00 V/m²

2)

A ring is uniformly charged with a net charge of 2 nC. The radius of the ring is R=1.6 m, with its center at the origin and oriented normal to the z axis as shown. what is the magnitude of the electric field at a distance z=0.99 m (on axis) away from the loop's center?

-a) 2.429E+09 N/C²

+b) 2.672E+09 N/C²

-c) 2.939E+09 N/C²

-d) 3.233E+09 N/C²

-e) 3.556E+09 N/C²

3)

Three small charged objects are placed as shown, where $b=2a$, and $a=6\times 10^{-7}\text{m}$.what angle does the force on $q_2$ make above the $-x$ axis if $q_1=3e$, $q_2=-7e$, and $q_3=6e$?

+a) 6.343E+01 degrees

-b) 6.978E+01 degrees

-c) 7.676E+01 degrees

-d) 8.443E+01 degrees

-e) 9.288E+01 degrees

4)

Three small charged objects are placed as shown, where $b=2a$, and $a=4\times 10^{-7}\text{m}$. What is the magnitude of the net force on $q_2$ if $q_1=2e$, $q_2=-8e$, and $q_3=5e$?

-a) 2.248E-14 N

-b) 2.473E-14 N

+c) 2.721E-14 N

-d) 2.993E-14 N

-e) 3.292E-14 N

5)  $E(z)=\underset{0}{\overset{R}{\int }}f(r^{\prime },z)d{r}^{\prime }$
is an integral that calculates the magnitude of the electric field at a distance $z$ fromthe center of a thin circular disk as measured along a line normal to the plane of the disk. The disk's radius is $R=7.5\text{ m}$ and the surface charge density is $\sigma =3{\text{ nC/m}}^3$. Evaluate $f(r^{\prime },z)$ at $r^{\prime }=2.6\text{ m}$.

-a) 7.820E-01 V/m²

+b) 8.602E-01 V/m²

-c) 9.462E-01 V/m²

-d) 1.041E+00 V/m²

-e) 1.145E+00 V/m²

6) A large thin isolated square plate has an area of 4 m². It is uniformly charged with 5 nC of charge. What is the magnitude of the electric field 1 mm from the center of the plate's surface?

-a) 4.821E+01 N/C

-b) 5.303E+01 N/C

-c) 5.834E+01 N/C

-d) 6.417E+01 N/C

+e) 7.059E+01 N/C

Key: Z0

1)

Three small charged objects are placed as shown, where $b=2a$, and $a=6\times 10^{-7}\text{m}$. What is the magnitude of the net force on $q_2$ if $q_1=1e$, $q_2=-7e$, and $q_3=2e$?

-a) 3.426E-15 N

-b) 3.768E-15 N

-c) 4.145E-15 N

-d) 4.560E-15 N

+e) 5.015E-15 N

2)

Three small charged objects are placed as shown, where $b=2a$, and $a=2\times 10^{-7}\text{m}$.what angle does the force on $q_2$ make above the $-x$ axis if $q_1=1e$, $q_2=-8e$, and $q_3=3e$?

-a) 3.629E+01 degrees

-b) 3.992E+01 degrees

-c) 4.391E+01 degrees

-d) 4.830E+01 degrees

+e) 5.313E+01 degrees

3)

 $E_z(x=0,z)=\underset{-a}{\overset{b}{\int }}f(x,z)dx$
is an integral that calculates the z-component of the electric field at point P situated above the x-axis where a charged rod of length (a+b) is located. The distance between point P and the x-axis is z=1.3 m. Evaluate $f(x,y)$ at x=0.96 m if a=0.63 m, b=1.4 m. The total charge on the rod is 3 nC.

-a) 3.719E+00 V/m²

+b) 4.091E+00 V/m²

-c) 4.500E+00 V/m²

-d) 4.950E+00 V/m²

-e) 5.445E+00 V/m²

4)

A ring is uniformly charged with a net charge of 3 nC. The radius of the ring is R=1.7 m, with its center at the origin and oriented normal to the z axis as shown. what is the magnitude of the electric field at a distance z=0.34 m (on axis) away from the loop's center?

-a) 1.202E+09 N/C²

-b) 1.322E+09 N/C²

-c) 1.454E+09 N/C²

-d) 1.599E+09 N/C²

+e) 1.759E+09 N/C²

5)  $E(z)=\underset{0}{\overset{R}{\int }}f(r^{\prime },z)d{r}^{\prime }$
is an integral that calculates the magnitude of the electric field at a distance $z$ fromthe center of a thin circular disk as measured along a line normal to the plane of the disk. The disk's radius is $R=2.8\text{ m}$ and the surface charge density is $\sigma =3{\text{ nC/m}}^3$. Evaluate $f(r^{\prime },z)$ at $r^{\prime }=1.9\text{ m}$.

-a) 4.295E+00 V/m²

+b) 4.724E+00 V/m²

-c) 5.196E+00 V/m²

-d) 5.716E+00 V/m²

-e) 6.288E+00 V/m²

6) A large thin isolated square plate has an area of 8 m². It is uniformly charged with 5 nC of charge. What is the magnitude of the electric field 1 mm from the center of the plate's surface?

-a) 2.652E+01 N/C

-b) 2.917E+01 N/C

-c) 3.209E+01 N/C

+d) 3.529E+01 N/C

-e) 3.882E+01 N/C

Key: Z1

1)

Three small charged objects are placed as shown, where $b=2a$, and $a=4\times 10^{-7}\text{m}$. What is the magnitude of the net force on $q_2$ if $q_1=2e$, $q_2=-8e$, and $q_3=3e$?

-a) 2.036E-14 N

-b) 2.240E-14 N

+c) 2.464E-14 N

-d) 2.710E-14 N

-e) 2.981E-14 N

2)

Three small charged objects are placed as shown, where $b=2a$, and $a=4\times 10^{-7}\text{m}$.what angle does the force on $q_2$ make above the $-x$ axis if $q_1=2e$, $q_2=-9e$, and $q_3=5e$?

-a) 3.961E+01 degrees

-b) 4.357E+01 degrees

-c) 4.793E+01 degrees

-d) 5.272E+01 degrees

+e) 5.799E+01 degrees

3)

A ring is uniformly charged with a net charge of 2 nC. The radius of the ring is R=1.8 m, with its center at the origin and oriented normal to the z axis as shown. what is the magnitude of the electric field at a distance z=1.3 m (on axis) away from the loop's center?

-a) 1.764E+09 N/C²

-b) 1.941E+09 N/C²

+c) 2.135E+09 N/C²

-d) 2.348E+09 N/C²

-e) 2.583E+09 N/C²

4)  $E(z)=\underset{0}{\overset{R}{\int }}f(r^{\prime },z)d{r}^{\prime }$
is an integral that calculates the magnitude of the electric field at a distance $z$ fromthe center of a thin circular disk as measured along a line normal to the plane of the disk. The disk's radius is $R=8.1\text{ m}$ and the surface charge density is $\sigma =3{\text{ nC/m}}^3$. Evaluate $f(r^{\prime },z)$ at $r^{\prime }=4.2\text{ m}$.

-a) 5.134E-01 V/m²

+b) 5.648E-01 V/m²

-c) 6.212E-01 V/m²

-d) 6.834E-01 V/m²

-e) 7.517E-01 V/m²

5)

 $E_z(x=0,z)=\underset{-a}{\overset{b}{\int }}f(x,z)dx$
is an integral that calculates the z-component of the electric field at point P situated above the x-axis where a charged rod of length (a+b) is located. The distance between point P and the x-axis is z=1.9 m. Evaluate $f(x,y)$ at x=0.54 m if a=1.0 m, b=2.0 m. The total charge on the rod is 3 nC.

-a) 1.665E+00 V/m²

-b) 1.831E+00 V/m²

-c) 2.014E+00 V/m²

+d) 2.216E+00 V/m²

-e) 2.437E+00 V/m²

6) A large thin isolated square plate has an area of 5 m². It is uniformly charged with 7 nC of charge. What is the magnitude of the electric field 1 mm from the center of the plate's surface?

-a) 6.534E+01 N/C

-b) 7.187E+01 N/C

+c) 7.906E+01 N/C

-d) 8.696E+01 N/C

-e) 9.566E+01 N/C

Key: Z2

1)

Three small charged objects are placed as shown, where $b=2a$, and $a=6\times 10^{-7}\text{m}$. What is the magnitude of the net force on $q_2$ if $q_1=3e$, $q_2=-7e$, and $q_3=6e$?

-a) 1.028E-14 N

-b) 1.130E-14 N

-c) 1.244E-14 N

-d) 1.368E-14 N

+e) 1.505E-14 N

2)

 $E_z(x=0,z)=\underset{-a}{\overset{b}{\int }}f(x,z)dx$
is an integral that calculates the z-component of the electric field at point P situated above the x-axis where a charged rod of length (a+b) is located. The distance between point P and the x-axis is z=1.9 m. Evaluate $f(x,y)$ at x=0.54 m if a=1.0 m, b=2.0 m. The total charge on the rod is 3 nC.

-a) 1.665E+00 V/m²

-b) 1.831E+00 V/m²

-c) 2.014E+00 V/m²

+d) 2.216E+00 V/m²

-e) 2.437E+00 V/m²

3)

A ring is uniformly charged with a net charge of 3 nC. The radius of the ring is R=1.8 m, with its center at the origin and oriented normal to the z axis as shown. what is the magnitude of the electric field at a distance z=1.1 m (on axis) away from the loop's center?

+a) 3.159E+09 N/C²

-b) 3.475E+09 N/C²

-c) 3.823E+09 N/C²

-d) 4.205E+09 N/C²

-e) 4.626E+09 N/C²

4)

Three small charged objects are placed as shown, where $b=2a$, and $a=6\times 10^{-7}\text{m}$.what angle does the force on $q_2$ make above the $-x$ axis if $q_1=3e$, $q_2=-7e$, and $q_3=4e$?

-a) 5.377E+01 degrees

-b) 5.914E+01 degrees

-c) 6.506E+01 degrees

+d) 7.157E+01 degrees

-e) 7.872E+01 degrees

5) A large thin isolated square plate has an area of 6 m². It is uniformly charged with 5 nC of charge. What is the magnitude of the electric field 2 mm from the center of the plate's surface?

-a) 3.214E+01 N/C

-b) 3.536E+01 N/C

-c) 3.889E+01 N/C

-d) 4.278E+01 N/C

+e) 4.706E+01 N/C

6)  $E(z)=\underset{0}{\overset{R}{\int }}f(r^{\prime },z)d{r}^{\prime }$
is an integral that calculates the magnitude of the electric field at a distance $z$ fromthe center of a thin circular disk as measured along a line normal to the plane of the disk. The disk's radius is $R=3.0\text{ m}$ and the surface charge density is $\sigma =8{\text{ nC/m}}^3$. Evaluate $f(r^{\prime },z)$ at $r^{\prime }=2.0\text{ m}$.

-a) 9.459E+00 V/m²

+b) 1.040E+01 V/m²

-c) 1.145E+01 V/m²

-d) 1.259E+01 V/m²

-e) 1.385E+01 V/m²