volume | PIER Journals

Abstract

This paper investigates the low-frequency excitation of a non-magnetic stratified conducting sphere by external sources, using a classical quasi-static approach. We focus on point-impressed sources represented by charges or electric dipoles, which predominantly generate electric fields. The findings have implications for low-frequency scattering theory and can potentially support the assessment of localized human exposure to low-frequency electric fields, such as those from Wireless Power Transfer using capacitive coupling technology. For a sphere with an arbitrary number of homogeneous layers, we develop a numerical-analytical solution inspired by the Exact Difference Scheme. This approach yields a tridiagonal discretized representation of the continuous problem, ensuring uniqueness and computational stability, and allowing for efficient solution via the Thomas algorithm. For a sphere with general radial inhomogeneity, we apply the Finite Difference method. Computational experiments show a strong agreement between these two approaches. We also examine the physical aspects of electric field interaction with a four-layer model of the human head, using the concept of coupling coefficients for the electric field and the generated heat. Our results show that these coupling coefficients increase with the separation between the point sources and the sphere, converging in certain cases to those for a uniform incident electric field. A comparison with the relevant ICNIRP reference levels for the incident electric field is also provided. The comprehensive Wolfram Mathematica code, consisting of multiple modules and including theoretical definitions and explanations of the computed quantities, is available as a supplement to the paper.

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Dr. Mykola Bogomolov

Dr. Gregory B. Gajda

Dr. Mykola Zhuk