Electrostatic image theory for two anisotropic half-spaces

An image solution for the canonical electrostatic problem of a point charge in an anisotropic half-space bounded by another anisotropic half-space is presented. The image source is obtained in operator form by using Fourier-transformed Maxwell equations and transmission line theory. After applying Heaviside operator calculus the image operator can be interpreted as a combination of a point charge and a sector of planar charge. The new theory is shown to coincide with the previously known image solutions of less general anisotropic media. In addition to being applicable to any physically feasible anisotropic medium of electrostatics, the method can be used for steady-current conductivity problems via a duality transformation.