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 $\frac{q}{N{\epsilon }_0}$ Find the value of $N$?

Answer 1

Answer: 24

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