Question

A point charge q is located at the center of a cube whose sides are of length a. If there are no other charges in this system, what is the electric flux through one face of the cube?

Answer 1

Answer:

$\phi_E=\frac{q}{6\epsilon_o}$

Explanation:

Given: A charge q is enclosed within the cube

The length of the one side of cube = a

Now, according to the Gauss Law the net flux ($\phi_E$) through the closed surface containing the charge q is:

$\phi_E=\oint \vec{E}.\vec{ds}=\frac{q_o}{\epsilon_o}$

where, $\epsilon_o}$ is the permittivity

This electric flux is for the 6 faces of the cube

thus, for the one face of the cube the electric flux will be $\phi_E=\frac{q}{6\epsilon_o}$