Question

A charge q is situated at the centre of a cube. Electric flux through one of the faces of the cube is

• A. $\frac{q}{{ϵ}_0}$
• B. $\frac{q}{3{ϵ}_0}$
• C. $\frac{q}{6{ϵ}_0}$
• D. Zero

Answer 1

The correct option is C $\frac{q}{6{ϵ}_0}$

According to Gauss's Law,
$\oint \overrightarrow{E}.\overrightarrow{ds}=\frac{q}{{ϵ}_0}\dots \dots \left(i\right)$
Cube has six equal faces, so electric flux pass through each would be equal.
If A = area of face
and E = field intensity
Then total flux $=6(E\times A)=\frac{q}{{ϵ}_0}$
So, net electric flux passing through each face of the cube is given by
$E\times A=\frac{q}{6{ϵ}_0}$