Question

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

• A. $\frac{\pi q}{6\left(4\pi {\epsilon }_0\right)}$
• B. $\frac{q}{6\left(4\pi {\epsilon }_0\right)}$
• C. $\frac{2\pi q}{6\left(4\pi {\epsilon }_0\right)}$
• D. $\frac{4\pi q}{\frac{1}{6}\left(4\pi {\epsilon }_0\right)}$

Answer 1

Answer: (D)

By Gauss law in electrostatics, electric flux through any closed surface is
$\frac{q}{{\epsilon }_0}$.
If the charge is located at the center of the cube it is placed symmetrically with respect to each other.
$\therefore$ Electric flux through each face is
$\frac{1}{6}\frac{q}{{\epsilon }_0}$
$=\frac{1}{6}\frac{4\pi q}{\left(4\pi {\epsilon }_0\right)}$