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The boundary-value problem for the perturbation of an electric potential by ahomogeneous anisotropic dielectric sphere in vacuum was formulated. The totalpotential in the exterior region was expanded in series of radial polynomialsand tesseral harmonics, as is standard for the Laplace equation. A bijectivetransformation of space was carried out to formulate a series representation ofthe potential in the interior region. Boundary conditions on the sphericalsurface were enforced to derive a transition matrix that relates the expansioncoefficients of the perturbation potential in the exterior region to those ofthe source potential. Far from the sphere, the perturbation potential decays asthe inverse of the distance squared from the center of the sphere, as confirmednumerically.

Theory of perturbation of electrostatic field by an anisotropic dielectric sphere