Physics equations/18-Electric charge and field/Q:lineChargesCALCULUS

These questions have not been tested.

• Solutions to many wikiquiz questions (pdf)
• /Quizbank/ (or "testbank" if you prefer)

A

A line charge on the y axis extends from y = -3 to y = 2. What is the y component of the electric field at the point (3, 7)?
Answer: $\frac{1}{4\pi {ϵ}_0}\underset{𝒜}{\overset{ℬ}{\int }}\frac{𝒞\lambda ds}{{[{𝒟}^2+{ℰ}^2]}^{ℱ}}$, where: <quiz display=simple> { |type="{}"} $𝒜=${ -3 }

{ |type="{}"} $ℬ=${ 2 }

{ |type="{}"} $𝒞=${ 7-s }

{ |type="{}"} $𝒟=${ 3 }

{ |type="{}"} $ℰ=${ 7-s }

{ |type="{}"} $ℱ=${ 3/2 }

</quiz>

B

A line charge on the y axis extends from y = 2 to y = 7. What is the y component of the electric field at the point (2, 9)?
Answer: $\frac{1}{4\pi {ϵ}_0}\underset{𝒜}{\overset{ℬ}{\int }}\frac{𝒞\lambda ds}{{[{𝒟}^2+{ℰ}^2]}^{ℱ}}$, where: <quiz display=simple> { |type="{}"} $𝒜=${ 2 }

{ |type="{}"} $ℬ=${ 7 }

{ |type="{}"} $𝒞=${ 9-s }

{ |type="{}"} $𝒟=${ 2 }

{ |type="{}"} $ℰ=${ 9-s }

{ |type="{}"} $ℱ=${ 3/2 }

</quiz>

C

A line charge on the x axis extends from x = 4 to x = 8. What is the y component of the electric field at the point (8, 4)?
Answer: $\frac{1}{4\pi {ϵ}_0}\underset{𝒜}{\overset{ℬ}{\int }}\frac{𝒞\lambda ds}{{[{𝒟}^2+{ℰ}^2]}^{ℱ}}$, where: <quiz display=simple> { |type="{}"} $𝒜=${ 4 }

{ |type="{}"} $ℬ=${ 8 }

{ |type="{}"} $𝒞=${ 4 }

{ |type="{}"} $𝒟=${ 8-s }

{ |type="{}"} $ℰ=${ 4 }

{ |type="{}"} $ℱ=${ 3/2 }

</quiz>

D

A line charge on the y axis extends from y = 4 to y = 6. What is the y component of the electric field at the point (5, 1)?
Answer: $\frac{1}{4\pi {ϵ}_0}\underset{𝒜}{\overset{ℬ}{\int }}\frac{𝒞\lambda ds}{{[{𝒟}^2+{ℰ}^2]}^{ℱ}}$, where: <quiz display=simple> { |type="{}"} $𝒜=${ 4 }

{ |type="{}"} $ℬ=${ 6 }

{ |type="{}"} $𝒞=${ 1-s }

{ |type="{}"} $𝒟=${ 5 }

{ |type="{}"} $ℰ=${ 1-s }

{ |type="{}"} $ℱ=${ 3/2 }

</quiz>

E

A line charge on the x axis extends from x = 3 to x = 7. What is the x component of the electric field at the point (7, 8)?
Answer: $\frac{1}{4\pi {ϵ}_0}\underset{𝒜}{\overset{ℬ}{\int }}\frac{𝒞\lambda ds}{{[{𝒟}^2+{ℰ}^2]}^{ℱ}}$, where: <quiz display=simple> { |type="{}"} $𝒜=${ 3 }

{ |type="{}"} $ℬ=${ 7 }

{ |type="{}"} $𝒞=${ 7-s }

{ |type="{}"} $𝒟=${ 7-s }

{ |type="{}"} $ℰ=${ 8 }

{ |type="{}"} $ℱ=${ 3/2 }

</quiz>