The Half-Space Sommerfeld Problem of a Horizontal Dipole for Magnetic Media

Seil Sautbekov and Merey Sautbekova ()
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Seil Sautbekov: Department of Physics and Technology, Al-Farabi Kazakh National University, Almaty 050040, Kazakhstan
Merey Sautbekova: School of Applied Mathematics, Kazakh-British Technical University, 59 Tole bi st., Almaty 050000, Kazakhstan

Mathematics, 2025, vol. 13, issue 1, 1-11

Abstract: A Hertz radiator’s Sommerfeld boundary value problem is considered for the case when its electric moment is directed horizontally relative to the plane interface between two media with different values of magnetic permeability. An integral representation of the exact expression for the Hertz potential, which generalizes the classical solution for non-magnetic media, both in cylindrical and spherical coordinate systems, is obtained. The corresponding expressions for the scattered wave fields are given in the form of Sommerfeld integrals. It is shown that the potential components can be represented as the sum of an infinite series in powers of the Green function.

Keywords: Maxwell’s equations; convolution; Green function; electromagnetic wave scattering; Hertz dipole; Sommerfeld integrals (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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