Question

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

• A. $\frac{\pi q}{6\left(4 \pi \varepsilon_{0}\right)}$
• B. $\frac{q}{6\left(4 \pi \varepsilon_{0}\right)}$
• C. $\frac{2 \pi q}{6\left(4 \pi \varepsilon_{0}\right)}$
• D. $\frac{4 \pi q}{\frac{1}{6}\left(4 \pi \varepsilon_{0}\right)}$

Answer 1

Answer: (D)

By Gauss law in electrostatics, electric flux through any closed surface is
$\frac{q}{\varepsilon_{0}}$.
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
$\frac{1}{6} \frac{q}{\varepsilon_{0}}$
$=\frac{1}{6} \frac{4 \pi q}{\left(4 \pi \varepsilon_{0}\right)}$