Question

What is the electric flux φ through each of the six faces of the cube? Use ϵ0 for the permittivity of free space?

Answer 1

If total charge Q is enclosed in the surface of cube

then we will have say that total flux linked with all surfaces of the cube will be given by

$\phi = \frac{Q}{\epsilon_0}$

since the position of charge is symmetric with respect to the center of the cube so here this whole flux will be equally linked with each of the face of the cube

So here total 6 faces of the cube is there and the total flux of the charge will equally divide in these 6 faces

so flux linked with each face is given by formula

$\phi = \frac{Q}{6\epsilon_0}$

so each face will have above flux due to central position of charge Q