Low-frequency image theory for the dielectric sphere

Abstract

Kelvin's well-known and Neumann's lesser known image theories for the sphere, valid for static sources outside the sphere, are extended to low-frequency current sources involving a nondispersive dielectric, by expressing known field integrals as arising from suitable image currents. The image of a radial current element is seen to consist of a radial line current between the center of the sphere and the Kelvin point plus a dipole at the Kelvin point. The image of a transverse current element is a combination of a transverse current strip plus a radial bifilar line current between the center and the Kelvin point. These image currents can be interpreted as image charges of the corresponding static problem in harmonic motion. The theory is tested by known limiting cases.