Use of surface-integral equations for the analysis of the TE-induction problem

A surface-integral-equations approach for the analysis of the linear transverse-electric (TE) induction problem at an arbitrary frequency is presented. It parallels an earlier analysis of the TM induction problem, and uses Helmholtz potentials to derive integral equations correlating the surface values of the tangential current density and axial magnetic field. Two Fredholm integral equations with weakly singular kernels reduce to a single equation for a quasistatic magnetic field. The present approach reduces the dimensions of the numerical problem by one, and is valid for arbitrary cross-sectional shapes, arbitrary material properties and arbitrary frequencies. It is free of the limitations of the separation of variables method used in the low-frequency range and perfect-conductor analysis used in the high-frequency range. It is an exact dual of the TM analysis. This approach is used to compute the power loss over the whole frequency range for a rectangular conducting cylinder placed normal to an H-wave. It is shown that, in the low-frequency range, the surface charges have no appreciable effect on the power loss.