Potential and Electric Fields of a Conducting Sphere in the Presence of a Charged Conducting Plane

摘要

The solution is given to Laplace's equation for a conducting sphere above a ground plane. The solution includes the presence of a uniform electric field perpendicular to the ground plane. The arbitrary constants in the solution are determined by applying the boundary conditions on the plane and on the sphere. Formulas are given for the evaluation of the potential and electric fields at an arbitrary field point. All the resulting formulas are expressed in a style for computation. The computational results will form the basis of a future comparison report. (rh)