Question

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

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

Answer 1

Answer: (B)

$\frac{Q}{6{ϵ}_0}$

Draw an imaginary square enclosing that point charge at the centre.

Then from gauss law, $\varphi =\frac{Q_{in}}{{ϵ}_o}$

This is the flux passing through all the six surfaces.

Therefore through one surface, $\frac{1}{6}$th of this flux will pass.