Question

A point charge q is at a distance of d/2 directly above the centre of a square of side d, as shown the figure. Use Gauss' law to obtain the expression for the electric flux through the square.

Answer 1

If we imagine a cube of side d, then this point charge q will be at the centre of the cube. 
Now, the total electric flux due to this charge will pass evenly through the six faces of the cube. 
So, the electric flux through one face will be equal to 1/6 of the total electric flux due to this charge.

Now, the total electric flux generated by the charge will be given by Gauss's law as :

`triangle phi = vecE.vec(triangleS)` = q/6∈₀

So, the electric flux through the square = q/6∈∘">∈∘