Electrostatic Image Method for the Anisotropic Half Space

摘要

Electrostatic image theory, well known for a point charge in front of anisotropic dielectric half space, is generalized to the case where the half space may be anisotropic, characterized by a symmetric and positive-definite permittivity dyadic. The theory is derived through Heaviside operational calculus involving manipulations with pseudo-differential operators. As a result, the image of a point charge is seen to consist of a point charge at the mirror image point plus a continuous distribution of surface charge filling an angular sector whose apex lies at the image point. The surface charge is shown to obey a simple analytic law. The angle of the image sector depends on the amount of transverse anisotropy of the half space. For decreasing anisotropy the angle becomes small and the angular image can be approximated by a quadrifilar line charge coinciding with the result recently obtained by these authors for the case of small anisotropy. Numerical tests confirm the validity of the image expression.