Question

A charge q is located at the centre 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. $\frac{4\pi q}{6\left(4\pi {\epsilon }_0\right)}$
• D. $\frac{4\pi q}{\frac{1}{6}\left(4\pi {\epsilon }_0\right)}$

Answer 1

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

$\text{Step 1: Charge inclosed in cube [Refer Fig.]}$

Charge enclosed in cube $=q$

$\text{Step 2: Apply Gauss Law}$

Assuming gaussian surface as the cube, Applying Gauss Law:

Electric flux passing through cube $=\frac{\text{Charge Enclosed}}{{ϵ}_0}=\frac{q}{{ϵ}_0}$

As charge is placed at the center, Therefore, due to symmetry, all the six faces of cube being equivalent, so same flux will pass through each face.

$\therefore$ Flux through each face $=\frac{\text{Total flux through cube}}{6}=\frac{q}{6{ϵ}_0}=\frac{4\pi q}{6\left(4\pi {ϵ}_0\right)}$

Hence Correct Option is $C$