A Semi-Analytical Approach for Low Frequency Plane Eddy Current Problem in Conductors with Various Cross-Sections

An area of conducting and permeable material with infinite length in the direction perpendicular to its cross section is placed in an external time-harmonic low-frequency magnetic field. This plane eddy current problem is solved by coupling the integral equation for the vector potential outside the conductor with a series representation for the vector potential inside the conductor that results from separation and allows orthogonalization of the resulting resulting boundary integral equation (BIE). Solving the resulting matrix equation yields unknown coefficients of the series. Focus of this paper are the kernel functions and series representations for differently shaped conductors.