1. A charge q is located at  and a second charge  at  above an infinite grounded conducting plane occupying  the xy plane at . Calculate the force exerted on the charge q.

The charge  and the charge   gives rise to two images, the former an image charge located at a distance  below the plane and the latter an image at a distance  below the plane.  Thus the force (away from the plane) on the charge   is

2. A point charge  is located at a distance d above a grounded,  infinite,  conducting plane. A second charge  is free to move along the perpendicular from the position of the charge q on to the plane. Where should this charge –q be placed so that the net  force on it is zero?

The image charges due to the charges  and  are shown. Let the charge be at a distance from the plane.

Force on –q in upward direction is to be equated to zero. This gives,

This simplifies to , which has the solution