QUASI-STATIC IMAGE THEORY FOR THE BI-ISOTROPIC SPHERE

Image theory for the static point charge and the conducting sphere, produced by Kelvin's inversion theory, was recently extended to the dielectric and permeable spheres by the present author. The objective of the present communication is to further extend the image theory to the more general bi-isotropic sphere, including the chiral sphere as a special case. Image expressions for the bi-isotropic sphere can be derived in a manner similar to that of the dielectric sphere except that the quasi-static problem now involves both electric and magnetic scalar potentials, coupled through the interface conditions at the spherical surface. The image is a combination of electric and magnetic line charges along the axis connecting the point charge and the center of the sphere, and their expressions are obtained through what can be labeled as finite Mellin transformation. The expressions derived can find application in more complete quasi-static analyses of interactions of bi-isotropic spherical particles in artificial bi-isotropic media.