Electrostatic image theory for an anisotropic half-space slightly deviating from transverse isotropy

摘要

Electrostatic image theory developed earlier for a point charge in an isotropic half-space in front of an anisotropic half-space with transverse isotropy is extended to an anisotropic half-space with a slight deviation from transverse isotropy. Two alternative image solutions are found: a combination of a point charge and a planar surface charge, or a combination of a point charge and a half-infinite line charge of quadrifilar nature. Both images are shown theoretically to give the same potential in the isotropic half-space, which is tested by finding the potential function at the interface. As an example, image expressions for a point charge above the interface of a uniaxial anisotropic medium with its axis tilted from the vertical are found, and the effect of the tilt angle is studied numerically. The image expressions can be applied, for example, in scattering problems involving an obstacle in the presence of an anisotropic half-space, which allows one to make use of the simple Green function corresponding to the isotropic space.