Electrostatic image theory of layered dielectric sphere

Static image theory for a homogeneous dielectric sphere, recently formulated by one of the authors, is generalised to the problem of a multilayer dielectric sphere in terms of a line-image charge. The image line source is seen in this case to be in relation to the so-called static reflection coefficient that could be labelled as a finite Mellin transformation. This transformation is discussed and a table of corresponding transforming functions is given. The result can be applied in a more complete quasistatic analysis of interactions of layered dielectric spherical particles in an artificial dielectric media. More closely, a two-layer sphere is considered with special cases of a thin layer, and that of a low contrast between the layers. Numerical results are calculated for the radiowave propagation problem of attenuation due to melting hail particles, assumed to be composed of a spherical ice core with a spherical water shell