Electrostatic image theory for the dielectric sphere with an internal source

The electrostatic image theory for a point charge next to the conducting sphere, originally discovered by Lord Kelvin, was recently generalized to the dielectric sphere with external sources by one of the present authors. This article treats the corresponding problem of a source located inside the dielectric sphere, thus completing the theory. Image expressions corresponding to potentials both outside and inside the sphere are worked out and their validity is checked with numerous tests. The present theory can be applied for small dielectric spheres with internal sources or scatterers.