Answer to Question #185217 in Field Theory for Esmail

Question

Use Gauss’ Law to calculate the electric field due to a long line of charge, with linear charge density 

Answer 1

Answer

Let from to r distance of long line charge density $\lambda$ where we want to calculate electric field.

So this situation consider a cylinderical shape as gaussian surface of radius r and length l

So using gauss law

$E\times2\pi rl=\frac{\lambda l}{\epsilon _0}$

Where $Q=\lambda l$

So electric field

$E=\frac{2k\lambda}{r}$