Applied Mathematics and Physics
ISSN (Print): 2333-4878 ISSN (Online): 2333-4886 Website: Editor-in-chief: Vishwa Nath Maurya
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Applied Mathematics and Physics. 2021, 9(1), 5-9
DOI: 10.12691/amp-9-1-2
Open AccessArticle

Boundary Charge Layer and Current for Spherical Inclusion in Conducting System

Michael Grinfeld1, and Pavel Grinfeld2

1The US Army Research Laboratory, Aberdeen Proving Ground, USA

2Department of Mathematics, Drexel University, Philadelphia, USA

Pub. Date: April 09, 2021

Cite this paper:
Michael Grinfeld and Pavel Grinfeld. Boundary Charge Layer and Current for Spherical Inclusion in Conducting System. Applied Mathematics and Physics. 2021; 9(1):5-9. doi: 10.12691/amp-9-1-2


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

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