On Solving Electrostatics and Heat Conduction Problems for Double-Film Plane Layered Media

The electrostatics reflection method for a point charge located near a plane layered medium consisting of two films on a dielectric half-space is proposed. The method is generalized to the case of an arbitrary system of charges and applied to solving mathematically similar problems of electrostatics and steady-state heat conduction of plane layered media. The proposed version of the reflection method involves the distributed representation of virtual charges and double integration related to it. As an example of using the method, problems of finding the electrostatic potential distributions around a conducting sphere and a drop-shaped body of rotation located near a plane layered structure of two dielectric films on a dielectric half-space are solved. Similar problems of finding the temperature distributions are solved for uniformly heated bodies located near a heat-conducting plane layered structure consisting of two heat-conducting films placed on a thermal-conducting half-space.