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

<quiz display=simple> {A line of charge density λ situated 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)?
$Answer$ (assuming $ℬ>𝒜$) $is:\frac{1}{4\pi {ϵ}_0}\underset{𝒜}{\overset{ℬ}{\int }}\frac{𝒞\lambda ds}{{[{𝒟}^2+{ℰ}^2]}^{ℱ}}$, where $ℬ=$} - −7 - −3 - −3 - 3 + 2

{A line of charge density λ situated 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)?
$Answer$ (assuming $ℬ>𝒜$) $is:\frac{1}{4\pi {ϵ}_0}\underset{𝒜}{\overset{ℬ}{\int }}\frac{𝒞\lambda ds}{{[{𝒟}^2+{ℰ}^2]}^{ℱ}}$, where $𝒞=$} - 3−s - 3 - s−7 + 7−s - s−3

{A line of charge density λ situated 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)?
$Answer$ (assuming $ℬ>𝒜$) $is:\frac{1}{4\pi {ϵ}_0}\underset{𝒜}{\overset{ℬ}{\int }}\frac{𝒞\lambda ds}{{[{𝒟}^2+{ℰ}^2]}^{ℱ}}$, where$ℱ=$} - 2 - 3 + 3/2 - 1/2

{A line of charge density λ situated 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)?
$Answer$ (assuming $ℬ>𝒜$) $is:\frac{1}{4\pi {ϵ}_0}\underset{𝒜}{\overset{ℬ}{\int }}\frac{𝒞\lambda ds}{{[{𝒟}^2+{ℰ}^2]}^{ℱ}}$, where $𝒞=$:} - 2 - s − 2 - 2 − s - s − 9 + 9 − s

{A line of charge density λ situated 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)?
$Answer$ (assuming $ℬ>𝒜$) $is:\frac{1}{4\pi {ϵ}_0}\underset{𝒜}{\overset{ℬ}{\int }}\frac{𝒞\lambda ds}{{[{𝒟}^2+{ℰ}^2]}^{ℱ}}$, where ${𝒟}^2+{ℰ}^2=$:} - 9² + (7-s)² - 9² + (2-s)² - 7² + (2-s)² - 2² + (7-s)² + 2² + (9-s)²

{A line of charge density λ situated 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)?
$Answer$ (assuming $ℬ>𝒜$) $is:\frac{1}{4\pi {ϵ}_0}\underset{𝒜}{\overset{ℬ}{\int }}\frac{𝒞\lambda ds}{{[{𝒟}^2+{ℰ}^2]}^{ℱ}}$, where $𝒜=$:} - 1/2 + 4 - 2 - 8

{A line of charge density λ situated 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)?
$Answer$ (assuming $ℬ>𝒜$) $is:\frac{1}{4\pi {ϵ}_0}\underset{𝒜}{\overset{ℬ}{\int }}\frac{𝒞\lambda ds}{{[{𝒟}^2+{ℰ}^2]}^{ℱ}}$, where $𝒞=$:} - s−8 - 8−s - s−4 - 4−s + 4

{A line of charge density λ situated on the x axis extends from x = 4 to x = 8. What is the x component of the electric field at the point (8, 4)?
$Answer$ (assuming $ℬ>𝒜$) $is:\frac{1}{4\pi {ϵ}_0}\underset{𝒜}{\overset{ℬ}{\int }}\frac{𝒞\lambda ds}{{[{𝒟}^2+{ℰ}^2]}^{ℱ}}$, where $𝒞=$:} - s−8 + 8−s - s−4 - 4−s - 4

{A line of charge density λ situated on the y axis extends from y = 4 to y = 6. What is the x component of the electric field at the point (5, 1)?
$Answer$ (assuming $ℬ>𝒜$) $is:\frac{1}{4\pi {ϵ}_0}\underset{𝒜}{\overset{ℬ}{\int }}\frac{𝒞\lambda ds}{{[{𝒟}^2+{ℰ}^2]}^{ℱ}}$, where $𝒞=$:} + 5 - s−4 - 5−s - 1−s - s−1

{A line of charge density λ situated 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)?
$Answer$ (assuming $ℬ>𝒜$) $is:\frac{1}{4\pi {ϵ}_0}\underset{𝒜}{\overset{ℬ}{\int }}\frac{𝒞\lambda ds}{{[{𝒟}^2+{ℰ}^2]}^{ℱ}}$, where $𝒞=$:} - 5 - s−4 - 5−s + 1−s - s−1

{A line of charge density λ situated 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)?
$Answer$ (assuming $ℬ>𝒜$) $is:\frac{1}{4\pi {ϵ}_0}\underset{𝒜}{\overset{ℬ}{\int }}\frac{𝒞\lambda ds}{{[{𝒟}^2+{ℰ}^2]}^{ℱ}}$, where $ℱ=$:} - 1/2 - 2/3 - 2 + 3/2 - 3

{A line of charge density λ situated 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)?
$Answer$ (assuming $ℬ>𝒜$) $is:\frac{1}{4\pi {ϵ}_0}\underset{𝒜}{\overset{ℬ}{\int }}\frac{𝒞\lambda ds}{{[{𝒟}^2+{ℰ}^2]}^{ℱ}}$, where $𝒞=$:} - s−3 - 3−s - 8 - s−7 + 7−s

{A line of charge density λ situated 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)?
$Answer$ (assuming $ℬ>𝒜$) $is:\frac{1}{4\pi {ϵ}_0}\underset{𝒜}{\overset{ℬ}{\int }}\frac{𝒞\lambda ds}{{[{𝒟}^2+{ℰ}^2]}^{ℱ}}$, where ${𝒟}^2+{ℰ}^2=$:} - 7² + (8−s)² - 7² + 8² + (7-s)² + 8² - 7² + (3−s)² - 3² + 8² </quiz>