Electrostatic image theory for the dielectric sphere

Abstract

The image of a point charge in a conducting sphere, produced by Kelvin's inversion theory, has become well known since its formulation in 1848. The corresponding theory in terms of point charges does not exist for the dielectric sphere. In the present paper, electrostatic image theory for the dielectric sphere, both for the field outside and inside of the sphere, is developed. Simple analytic expressions in terms of a point charge and a line charge are seen to arise in both cases. The theory is extended to give simple images for dipole and line sources. Possible application of the new expressions in simplified quasi‐static analyses of interactions of dielectric spherical particles in artificial dielectric media is pointed out.