Michael Grinfeld^1,, Pavel Grinfeld²

The steady-state current in heterogeneous conducting system is considered. One of the goals is to generate a battery of establish exact solutions for the analysis of steady-state currents in the current-conducting heterogeneous system. These solutions are to be used a) for Validation and Verification purposes the electromagnetic software and b) for deeper understanding of some features that were not explored sufficiently so far. The system under study consists of an isotropic unbounded isotropic matrix containing spherical inclusion (the inclusion can be either isotropic or anisotropic, and even nonlinear). This was analyzed in the classical textbooks and monographs. However, the solutions of previous studies miss analysis of the boundary charge layer and the current in this layer. In this paper, we establish these elements of the exact solution.

electric current in conductors, irreversible thermodynamics, boundary value problems, exact solution