Question

An infinite wire having charge density $\lambda$ passes through one of the edges of a cube having edge length $L$. Find the total flux passing through the cube.

Answer 1

Electric field at distance r $\Rightarrow E=\frac{\lambda }{2\pi r{ϵ}_0}$

Flux through Gaussian cylinder

$\varphi =E.2\pi rL$

$\varphi =\frac{\lambda L}{{ϵ}_0}$

Acc. to ques., If we set up 3 or more identical cube around it, to cover its area then we get flux equal to that of cylindrical Gaussian surface $i.e.\frac{\lambda L}{{ϵ}_0}$

But as we are covered with only $\frac{1}{4}$ of area thus

Flux would be = $\frac{\lambda L}{4{ϵ}_0}$