Question

Flux due to $q$ through square plate is

• A. $\frac{q}{6{ϵ}_o}$
• B. $\frac{q}{6{ϵ}_o}$
• C. $\frac{q}{12{ϵ}_o}$
• D. $\frac{q}{24{ϵ}_o}$

Answer 1

The correct option is D $\frac{q}{24{ϵ}_o}$


Let's make a surface such that the charge is at the centre of the surface.(as shown below)
Let us consider that this surface is a face of the cube. So, the flux through the cube will be : $\frac{q}{{ϵ}_0}$
So, flux through the face of the cube will be : $\frac{q}{6{ϵ}_0}$
Four squares fit on face of the cube. Hence,
${\varphi }_{square}=\frac{1}{4}\frac{q}{6{ϵ}_0}$
${\varphi }_{square}=\frac{q}{24{ϵ}_0}$