Screening of a point charge by an anisotropic medium: Anamorphoses in the method of images

We extend the classical dielectric image problem for an external point char ge interacting with a semi-infinite medium to the case of an anisotropic di electric; We show that the exterior potential is a solution to an unconvent ional image problem. By contrast the interior potential is not a solution t o any simple image system; instead it can be obtained through an anamorphic transformation of an image solution. We calculate the volume bound charge density that is induced within the anisotropic dielectric and distinguishes it from an isotropic medium where the volume density vanishes. This soluti on provides a very simple and physically relevant example in which the phys ics of the surface and volume bound charge densities in a polarized dielect ric can be analyzed. (C) 2001 American Association of Physics Teachers.