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

Author

Listed:
  • Seil Sautbekov

    (Department of Physics and Technology, Al-Farabi Kazakh National University, Almaty 050040, Kazakhstan
    These authors contributed equally to this work.)

  • Merey Sautbekova

    (School of Applied Mathematics, Kazakh-British Technical University, 59 Tole bi st., Almaty 050000, Kazakhstan
    These authors contributed equally to this work.)

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.

Suggested Citation

  • Seil Sautbekov & Merey Sautbekova, 2025. "The Half-Space Sommerfeld Problem of a Horizontal Dipole for Magnetic Media," Mathematics, MDPI, vol. 13(1), pages 1-11, January.
    • Handle: RePEc:gam:jmathe:v:13:y:2025:i:1:p:169-:d:1560842
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