Question

A charge q is located at the centre of a cube. The electric flux thorugh 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. $\frac{4\pi q}{6\left(4\pi {\epsilon }_0\right)}$

Answer 1

The correct option is D $\frac{4\pi q}{6\left(4\pi {\epsilon }_0\right)}$

Gauss's law
$\varphi =\frac{q}{{\epsilon }_0}$
Electric flux through one face is $1/6$th of the total flux passing through the cube.
${\varphi }^{\prime }=\frac{\varphi }{6}=\frac{q}{6{\epsilon }_0}=\frac{4\pi q}{6\left(4\pi {\epsilon }_0\right)}$.