Current on a Wire Parallel to Two Walls of a Rectangular Cavity

Abstract

A simple and efficient method is developed by treating electromagnetic problems of determining current induced on a wire oriented parallel to two walls of a rectangular cavity. The wire and the cavity interior are excited by electromagnetic sources exterior to the cavity. The formulation makes use of the theory of truncated Fourier series expansion to approximate the waveform of unknown current induced on the wire. The field, comprised of infinitely many orthogonal modes, is then determined in terms of unknown Fourier coefficients by employing the properties of orthogonality. Finally, a matrix equation for the unknown Fourier coefficients is obtained by enforcing appropriate boundary condition on surface of the wire under consideration. Each element of the resulting matrix equation, which is essentially a doubly infinite sum in nature, is simplified into a single infinite one by using a closed form solution. This method bypasses the dyadic Green's function approach thereby leading to a solution which is computationally easier to handle. Any arbitrary load conditions and excitations are easily treated. Selected numerical results in the form of current distributions are presented to illustrate the theory.