Development and generalization of the method of reflections in problems of electrostatics and thermal conductivity of plane-layered media

The method of mirror reflections of electrostatics for a point charge located next to a plane-layered medium consisting of a single film on a dielectric half-space is formulated. The method is generalized to the case of an arbitrary system of charges. The proposed approach is applied to mathematically similar problems of electrostatics and stationary heat conduction of plane-layered media. In particular, the problems of finding distributions of the electrostatic potential around a conducting sphere, an ellipsoid of revolution and a drop-shaped body located near the dielectric film on the dielectric half-space. It is shown how to apply the results obtained for electrostatic problems to similar problems of finding the temperature distribution of uniformly heated bodies of the same geometry located near a heat-conducting film in a heat-conducting half-space.