Electrostatic image theory for the dielectric sphere with an internal source
Abstract
The well known electrostatic image theory for a point charge next to a conducting sphere, originally discovered by Lord Kelvin, was recently generalized to the dielectric sphere, by one of the present authors, for sources located outside the sphere. The present paper treats the problem of a source located inside the dielectric sphere, thus completing the theory. Image expressions corresponding to potentials both inside and outside the spheres are worked out and their validity is checked with numerous tests. The image expression consists of simple functions easily handled with a pocket calculator. The theory can be straightforwardly transformed to cover direct current problems involving a current source inside a sphere located in a surrounding medium with different conductivity, which can be of interest, for example, to problems of electrocardiography.
 Publication:

NASA STI/Recon Technical Report N
 Pub Date:
 March 1991
 Bibcode:
 1991STIN...9223667S
 Keywords:

 Dielectrics;
 Electrostatics;
 Imagery;
 Mathematical Models;
 Point Sources;
 Spheres;
 Electric Dipoles;
 Mellin Transforms;
 Potential Theory;
 Spherical Harmonics;
 Communications and Radar