Question

A flat, square surface with sides of length $L$ is described by the equations $x=L,0\le y\le L,0\le z\le L$
The electric flux through the square due to a positive point charge $q$ located at the origin $(x=0,y=0,z=0)$ is

• A. $\frac{q}{4{\epsilon }_0}$
• B. $\frac{q}{6{\epsilon }_0}$
• C. $\frac{q}{24{\epsilon }_0}$
• D. $\frac{q}{48{\epsilon }_0}$

Answer 1

The correct option is C $\frac{q}{24{\epsilon }_0}$

Imagine a charge $q$ at the centre of a cube of edge length $2L$ (Fig.). Then
$\varphi =\frac{q}{{ϵ}_0}$
Here, the square is one ${24}^{th}$ of the surface area of the imaginary cube, so it intercepts $1/24$ of the flux. That is,
$\Phi =\frac{q}{24{ϵ}_0}$.