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

Abstract

We extend the classical dielectric image problem for an external point charge interacting with a semi-infinite medium to the case of an anisotropic dielectric. We show that the exterior potential is a solution to an unconventional image problem. By contrast the interior potential is not a solution to 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 solution provides a very simple and physically relevant example in which the physics of the surface and volume bound charge densities in a polarized dielectric can be analyzed.