Electrostatic image theory for an anisotropic boundary

An image theory for electrostatic problems involving the anisotropic impedance boundary is introduced through Heaviside operator calculus. The image of a point charge in front of an anisotropic boundary plane is given in terms of a combination of point charge and a surface-charge distribution consisting of a planar angular sector of exponentially decaying surface charge bounded by two line charges. The angle of the sector depends on the anisotropy of the boundary. For vanishing anisotropy the sector contracts to an exponentially decaying line charge coinciding with the result derived previously for the isotropic boundary. The theory is validated numerically by computing potential values from the image and through inverse Fourier transform techniques.