Question

A point charge q is located at a distance l from an infinite conducting plane. Determine the surface density of charges induced on the plane as a function of separation r from the base of the perpendicular drawn to the plane from the charge.

Answer 1

To find the surface charge density, we must know the electric field at the point P (Fig.) which is at a distance r from the point O.

Using the image mirror method, the field at P,

Now from Gauss’ theorem the surface charge density on conductor is connected with the electric field near its surface (in vaccum) through the relation  where E_n is the projection  of the outward normal vector n(with respect to the conductor).