Question

A charge $q$ is located at the centre of a cube. The electric flux through any face is

• A. $\frac{\pi q}{6(4\pi {\epsilon }_0)}$
• B. $\frac{q}{6(4\pi {\epsilon }_0)}$
• C. $\frac{2\pi q}{6(4\pi {\epsilon }_0)}$
• D. $\frac{4\pi q}{6(4\pi {\epsilon }_0)}$

Answer 1

Answer: (D)

Gauss's law states that, "the net electric flux through any closed surface is equal to the net charge inside the closed surface divided by ${\epsilon }_0"$
From Gauss's law
$\varphi =\frac{q}{{\epsilon }_0}$
This is the net flux coming out of the cube.
Since, a cube has $6$ sides so electric flux through any face is
${\varphi }^{\prime }=\frac{\varphi }{6}=\frac{q}{6{\epsilon }_0}=\frac{4\pi q}{6(4\pi {\epsilon }_0)}$