DC fields and analytical image solutions for a radially anisotropic spherical conductor

Static problems involving a conducting sphere with radial anisotropy (radial and tangential conductivity, denoted α and η) are considered. The internal and external fields and the dipole moment are derived for a radially anisotropic sphere, and a condition relating α, η and the external isotropic conductivity α ₀ is given, for which the dipole moment vanishes, implying that the sphere becomes transparent in an homogeneous current flow. 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 α≫η and α≈η. Image expressions for radial and tangential dipole sources are elaborated