A uniform linear charge of 3.0 nC/m is distributed along the y axis from y = -3 m to y = 2m.Which of the following integrals is correct for the magnitude of the electric field at y = 4 m on the y axis?
A) $\int _ { - 3 } ^ { 2 } \frac { 27 d y } { ( 4 - y ) ^ { 2 } }$
B) $\int _ { - 3 } ^ { 2 } \frac { 27 d y } { 16 + y ^ { 2 } }$
C) $$\int _ { - 3 } ^ { 2 } \frac { 135 d y } { ( 4 - y ) ^ { 2 } }$$
D) $\int _ { - 3 } ^ { 2 } \frac { 135 d y } { 16 + y ^ { 2 } }$
E)none of these

Question

Quizplus · Accepted Answer

The correct integral is $\int _ { - 3 } ^ { 2 } \frac { 27 d y } { ( 4 - y ) ^ { 2 } }$ because the electric field due to a uniform linear charge distribution is given by the integral of $\frac { \lambda } { ( r ) ^ { 2 } }$ where $\lambda$ is the linear charge density and r is the distance from the charge distribution to the point where the electric field is being calculated. In this case, the linear charge density is 3.0 nC/m and the distance from the charge distribution to the point where the electric field is being calculated is 4 m - y.

A Uniform Linear Charge of 3 ∫−3227dy(4−y)2\int _ { - 3 } ^ { 2 } \frac { 27 d y } { ( 4 - y ) ^ { 2 } }∫−32​(4−y)227dy​

A Uniform Linear Charge of 3 $\int _ { - 3 } ^ { 2 } \frac { 27 d y } { ( 4 - y ) ^ { 2 } }$