Question

Determine the electric field produced on any point in space by a very long line

(infinite) charged with a uniform density λ

Answer 1

$\phi=\oint E.dA$

$$\phi=\oint _{s_1}E.dA+\oint _{s_2}E.dA+\oint _{s_3}E.dA$$

$\phi=0+0+\smallint E.dA$

$\phi=E(2\pi r)\\2\pi xrE =\frac{x\lambda}{\epsilon}$

$E=\frac{\lambda}{2\pi\epsilon r}$