Homogenization of laminated magnetic cores and the role of surface charges

Due to its theoretical and practical significance, homogenization of laminated magnetic cores has been studied by several research groups. Recently, Tsukerman and Markel proposed non-asymptotic and nonlocal homogenization theories for periodic electromagnetic structures at high frequencies. This paper explores the applicability of these theories to laminated magnetic cores at power frequencies. Particular attention is paid to the boundary condition for the electric current density: its normal component does not have to be zero and may produce surface charges. The eddy current problem inside conducting elements must be coupled with the quasi-static problem outside. The importance of the boundary condition for the current density extends far beyond the simulation of laminated cores - to a variety of eddy current and coupled field-circuit problems.