Use of surface integral equations for analysis of TM-induction problem

The problem considered is that of evaluating the induced fields and the power loss in a long conductor with arbitrary cross-section placed in a time-harmonic transverse magnetic (TM) field. Hitherto, the problem has been analysed by numerically solving the governing differential equations or a volume-type integral equation. The paper presents a new approach which uses Helmholtz single-and double-layer potentials to derive integral equations which relate the values of the axial current density and the tangential magnetic field at the surface of the conductor. These are two coupled Fredholm integral equations with weakly singular kernels. As an example, the eddy-current losses in a rectangular conductor placed in a uniform magnetic field are computed, and the results arecompared with previous ones. The proposed approach has two salient advantages. First, by reducing the dimensions of the problem by one, the computation time is considerably reduced. Consequently, many problems that are beyond the practical limit of previous approaches can be easily handled. Secondly, both magnetic and nonmagnetic conductors can be handled.