Question

A uniform linear charge of 2.0 nC/m is distributed along the x axis from x = 0 to x = 3 m. What is the x component of the electric field at y = 2 m on the y axis?

Answer 1

Answer:

The x component of the electric field at y=2m is $E_{x}=17.97\frac{N}{C}$

Explanation:

For a linear charge, using Gauss Law, we get that the Electric field (radial) has the following form

$E=\frac{\lambda}{2\pi\epsilon_{0}r}$

where λ is the charge for longitud unit given in the problem, r is replaced by the y coordinate, and there are two known more data. So

$E=\frac{2*10x^{-9}}{2*2\pi\epsilon_{0}}=17.97\frac{N}{C}$

is the x component of the Electric field at y=2m on the y axis, which is what we wanted to know.