Question

Compute the electric flux through a square surface of edges $2l$ due to a charge $+Q$ whose geometric centre is located on the x-axis at a perpendicular distance $l$ from the centre of the square.

• A. $\frac{Q}{{ϵ}_0}$
• B. $\frac{Q}{2{ϵ}_0}$
• C. $\frac{Q}{4{ϵ}_0}$
• D. $\frac{Q}{6{ϵ}_0}$

Answer 1

The correct option is D $\frac{Q}{6{ϵ}_0}$

According Gauss' Law,

$\varphi \overrightarrow{E}.\overrightarrow{dS}=\frac{Q}{{ϵ}_0}$

Therefore the total flux through the cube is $\frac{Q}{{ϵ}_0}$.

The flux through a square surface

$⟹\frac{1}{6}\frac{Q}{{ϵ}_0}$

where $Q⟹\frac{Q}{6{ϵ}_0}$ [$Q\to$charge enclosed in the surface.]