Eddy current analysis of a conductor with a groove by surface integral equation with one unknown

In this paper, we study how to solve eddy currents induced in a conductor with a narrow groove in the case of thick skin depth by using surface integral equations, of which unknowns are the surface electric and magnetic currents. When the skin depth is small, the surface integral equations give accurate solutions except around the sharp edge and corner. Some edges and corners of the groove are so close that it is difficult to get accurate solutions; moreover, as the width of the groove becomes narrower, the surface integral equations become ill conditioned. In order to solve these problems, we propose a method to analyze the eddy currents induced in a conductor with a groove by introducing a lumped loop magnetic current, which is formulated by a surface integral equation derived from the normal component of the electric field.