Field Distributions Around a Long Opening in a Metallic Half Space Excited by Arbitrary-Frequency Alternating Current-Carrying Wires of Arbitrary Shape

We propose a semianalytical solution for evaluation of field distributions around a long opening in a metallic conductive half space excited by a three-dimensional current-carrying inducer at arbitrary frequency. The governing Helmholtz equation is solved in three dimensions by separation of variables. The solution is obtained by developing a two-dimensional (2-D) Fourier series model and using exponential functions in the third dimension. To expand all possible field distributions in the metal, we assume it as a lossy material with very large loss-tangent. The displacement current in the metal opening is regarded to have a nonzero value accordingly. After imposing boundary conditions and mode matching technique, a system of AX=B is solved to obtain the unknown coefficients. The proposed model is found to be consistent with the existing 2-D model and in excellent agreement with those obtained numerically using a finite integration code.