Question

A charge $Q$ is placed at a distance $a/2$ above the centre of a horizontal, square surface of edge $a$ as shown in figure. Find the flux of the electric field through the square surface.

• A. $\frac{Q}{{\in }_0}$
• B. $\frac{Q}{3{\in }_0}$
• C. $\frac{Q}{6{\in }_0}$
• D. $\frac{Q}{4{\in }_0}$

Answer 1

The correct option is C $\frac{Q}{6{\in }_0}$

To close the charge, we can assume $5$ more square surfaces having length $a$ which forms a cube of length $a$ as shown in figure.


Now, by Gauss's law, electric flux through the entire closed surface,

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

This flux is through 6 square surfaces. The electric flux through the given square surface will be one-sixth of the electric flux through all the six surfaces.

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