Static Field Solutions and Image Theory for a Conducting Sphere with RadialAnisotropy

摘要

Static problems involving a conducting sphere with radial anisotropy (radial andtangential conductivity, denoted alpha and eta) are considered. Conditions for alpha, eta and the external isotropic conductivity sigma(0) are given, for which the sphere becomes transparent in a homogeneous current flow, i.e., the dipole moment totally vanishes. Also problems involving external and internal point sources of current are examined, and simple interpretations in terms of image sources are presented for cases where alpha much > eta and alpha approx = eta. Image expressions for radial and tangential dipole sources are finally elaborated.