A charge Q is placed at a distance a/2 above the centre of a horizontal, square of edge a as shown in figure. Find the flux of the electric field through the square surface.
Given:
Length of square edge=a
Distance of charge Q above the center=a/2
Concept: Imagine the square to be one face of a cube of side a with the center at a point where charge Q is placed.
Since charge is placed at centre it is placed symmetrically with respect to all the faces of the cube . therefore we can say that equal flux passes through all the six surfaces.
∴ flux passing through each surface
By Gauss’s law, flux of net electric field through a closed surface equals the net charge enclosed by the surface divided by ϵ0
⇒
(as qin=Q)
Therefore flux of electric field through square surface is given by Q/6ϵ0