ELECTROSTATIC IMAGE THEORY FOR AN ANISOTROPIC HALF-SPACE SLIGHTLY DEVIATING FROM TRANSVERSE ISOTROPY

Electrostatic image theory developed earlier for a point charge in an isotropic half-space in front of an anisotropic half-space with transv erse isotropy is extended to an anisotropic half-space with a slight d eviation from transverse isotropy. Two alternative image solutions are found: a combination of a point charge and a planar surface charge, o r a combination of a point charge and a half-infinite line charge of q uadrifilar nature. Both images are shown theoretically to give the sam e potential in the isotropic half-space, which is tested by finding th e potential function at the interface. As an example, image expression s for a point charge above the interface of a uniaxial anisotropic med ium with its axis tilted from the vertical are found, and the effect o f 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 us e of the simple Green function corresponding to the isotropic space.