volume | PIER Journals

Abstract

A rigorous analytical procedure is developed that allows the exact evaluation of the complete integral representations for the time-harmonic electromagnetic (EM) field components generated by a vertical magnetic dipole (VMD) lying on the surface of a flat and homogeneous lossy half-space. Closed-form expressions for the radial distributions of the EM field components induced on the surface of the half-space are provided in terms of exponential functions and modified Bessel functions. Such expressions make it possible to overcome the limitations implied by the previously published quasi-static solutions, which are valid only in the low-frequency range. Numerical results are presented to show where the quasi-static approximations deviate from the exact solutions for a given homogeneous medium as frequency is changed. The computed amplitude and phase frequency spectra of the EM field components demonstrate that the quasi-static approach fails at frequencies higher than 1 MHz, and that, in particular, it leads to underestimating the EM field strength. Finally, it is also shown that at a frequency equal to or greater than 10 MHz excellent results in terms of accuracy may be obtained by using the high-frequency asymptotic forms of the exact solutions.

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Dr. Mauro Parise