Question

A charge $Q$ is placed at the centre of a cube. Find the flux of the electric field through three surfaces of the cube.

• A. $\frac{Q}{{\in }_0}$
• B. $\frac{Q}{6{\in }_0}$
• C. $\frac{Q}{2{\in }_0}$
• D. $\frac{Q}{3{\in }_0}$

Answer 1

The correct option is C $\frac{Q}{2{\in }_0}$


By Gauss's law, electric flux through the closed surface,

$\varphi =\frac{q_{\text{enclosed}}}{{\in }_0}=\frac{Q}{{\in }_0}$

This flux is through all the six surfaces of the cube.

So, through 1 surface of the cube the flux is,

${\varphi }_1=\frac{Q}{6{\in }_0}$

Through 3 surfaces of the cube the flux will be,
${\varphi }_3=3\times \frac{Q}{6{\in }_0}=\frac{Q}{2{\in }_0}$