EXACT ELECTROMAGNETIC FIELD EXCITED BY A VERTICAL MAGNETIC DIPOLE ON THE SURFACE OF A LOSSY HALF-SPACE

Abstract

A rigorous analytical procedure is developed that allows the exact evaluation of the complete integral representations for the time-harmonic electromagnetic (EM) fleld components generated by a vertical magnetic dipole (VMD) lying on the surface of a ∞at and homogeneous lossy half-space. Closed-form expressions for the radial distributions of the EM fleld components induced on the surface of the half-space are provided in terms of exponential functions and modifled 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 fleld components demonstrate that the quasi-static approach produces inaccurate results at frequencies higher than 1MHz, and that, in particular, it leads to underestimating the EM fleld strength. Finally, it is also shown that at a frequency equal to or greater than 10MHz excellent results in terms of accuracy may be obtained by using the high-frequency asymptotic forms of the exact solutions.