Question

define electric flux is it a scalar or vector quantity ? A point charge q is at a distance of d/2 directly above the centre of a square of side d, use Gauss law to obtain the expression for the electric flux through the square.

Answer 1

Hello,
Electric flux is a measurer of electric field passing through a specific object. It is defined as- f = E.dS

Now, Coming to your problem,
Consider a cube of sides 'd' and a charge Q placed at center of the cube. Clearly, the charge Q is at distance d/2 from all of the sides.
Now, flux passing through whole cube-
f = Q/e
where e is permittivity of free space.

Also, the charge is placed symettric to all the 6 faces and hence flux passing through one of the faces- f/6 = Q/6e.

This situation is similar to which described in your question.

Answer 2

If the charge is at a distance d/2 from the center of a square surface of side length d then the charge is at the centre of a cube of side length d.

That means the cube has 6 equal area faces. Invoke gauss law which states that total flux out of a surface is charge / epsilon naught. Since we are talking about one sixth of the total surface area hence the net flux should also go down six times. Hence your answer will be charge/ six times epsilon naught.