Question

An infinite line of charge with charge density λ1 = -2 μc/cm is aligned with the y-axis as shown. 1) what is ex(p), the value of the x-component of the electric field produced by

Answer 1

As we know by Gauss's law that

$\int E.dA = \frac{q}{\epsilon_0}$

so for line charge the gaussian surface is cylindrical in shape

so we will have

$E(2\pi RL) = \frac{\lambda L}{\epsilon_0}$

now by rearranging the terms

$E = \frac{\lambda}{2\pi \epsilon_0 R}$

so here we will have to find the x component of electric field so it is given by above equation

$E_x = \frac{\lambda}{2\pi \epsilon_0 x}$

here x = distance from the wire where we need to find electric field