Question

A charge ${}^{\prime }{q}^{\prime }$ is placed at the centre of a cube of side $l$. What is the electric flux passing through each face to the cube?

Answer 1

$\text{Step 1: Applying Gauss Law for cube}$

Assuming the cube as gaussian surface, total flux passing through the cube of side $l$ can be given as,

$\varphi =\frac{q}{{ϵ}_o}$

$\text{Step 2: Flux through each face of the cube}$

As the charge is placed symmetrically to each face of the cube, thus electric flux passing through each face is equal.

$\therefore$ Electric flux passing through each face, ${\varphi }^{\prime }=\frac{\varphi }{6}=\frac{q}{6{ϵ}_o}$