Question

A positive point charge (+q) is kept in the vicinity of an uncharged conducting plate. Sketch electric field lines originating from the point on to the surface of the plate. Derive the expression for the electric field at the surface of a charged conductor.

Answer 1

Let us consider an infinite plane sheet of charge of uniform charge density where q is charge in area A on sheet of charge σ = q/a.

Let P be any point on the one side of sheet and P’ on the other side of sheet, at same distance r from it. We draw a Gaussian cylindrical surface S of cross section area A cutting through the plane sheet of charge, such that points P and P’ lie on its plane faces. Then electric flux linked with cylindrical surface S is

But by Gauss's theorem

Where q is the charge in area A of sheet, enclosed by cylindrical surface S.

By equation (ii) and (iii) we get

This gives the electric field intensity at any point near or on the surface of the infinite thin plane sheet of charge.