Conductive Sphere on a Charged Conductive Plane

Statement of the Problem: If a conductive sphere is placed in contact with a semi-infinite, conductive plane, the configuration constitutes a three-dimensional equipotential surface. Assuming an isolated plane to be electrically charged to a known surface charge density (σ_°) originally, it is desired to determine the effect produced by placing a sphere on the plane. Specifically, the purpose of this investigation is to determine the force exerted on the sphere normal to the plane, the total charge acquired by the sphere and the perturbation in the electrical field due to its presence on the plane.