Question

The length of each side of a cubical closed surface is $l$. If charge $q$ is situated on one of the vertices of the cube, then if the flux passing through shaded face of the cube is $\frac{q}{x{\in }_0}$. Find $x$:

Answer 1

The cube has six surfaces . When a charge q at center of the cube , the flux through each surface is $\varphi =\frac{q}{6{ϵ}_0}$
When q is placed at one of the vertices of the cube, the charge inside the cube is $q/4$.
now flux $\varphi =\frac{\left(q/4\right)}{6{ϵ}_0}=\frac{q}{24{ϵ}_0}$
thus, $x=24$