The Half-Space Sommerfeld Problem of a Horizontal Dipole for Magnetic Media
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 potenti...
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2025-01-01
|
| Series: | Mathematics |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2227-7390/13/1/169 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1841549128803287040 |
|---|---|
| author | Seil Sautbekov Merey Sautbekova |
| author_facet | Seil Sautbekov Merey Sautbekova |
| author_sort | Seil Sautbekov |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-32bd7eacbaa94381ad2c56b70f1ee92c |
| institution | Kabale University |
| issn | 2227-7390 |
| language | English |
| publishDate | 2025-01-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj-art-32bd7eacbaa94381ad2c56b70f1ee92c2025-01-10T13:18:29ZengMDPI AGMathematics2227-73902025-01-0113116910.3390/math13010169The Half-Space Sommerfeld Problem of a Horizontal Dipole for Magnetic MediaSeil Sautbekov0Merey Sautbekova1Department of Physics and Technology, Al-Farabi Kazakh National University, Almaty 050040, KazakhstanSchool of Applied Mathematics, Kazakh-British Technical University, 59 Tole bi st., Almaty 050000, KazakhstanA 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.https://www.mdpi.com/2227-7390/13/1/169Maxwell’s equationsconvolutionGreen functionelectromagnetic wave scatteringHertz dipoleSommerfeld integrals |
| spellingShingle | Seil Sautbekov Merey Sautbekova The Half-Space Sommerfeld Problem of a Horizontal Dipole for Magnetic Media Mathematics Maxwell’s equations convolution Green function electromagnetic wave scattering Hertz dipole Sommerfeld integrals |
| title | The Half-Space Sommerfeld Problem of a Horizontal Dipole for Magnetic Media |
| title_full | The Half-Space Sommerfeld Problem of a Horizontal Dipole for Magnetic Media |
| title_fullStr | The Half-Space Sommerfeld Problem of a Horizontal Dipole for Magnetic Media |
| title_full_unstemmed | The Half-Space Sommerfeld Problem of a Horizontal Dipole for Magnetic Media |
| title_short | The Half-Space Sommerfeld Problem of a Horizontal Dipole for Magnetic Media |
| title_sort | half space sommerfeld problem of a horizontal dipole for magnetic media |
| topic | Maxwell’s equations convolution Green function electromagnetic wave scattering Hertz dipole Sommerfeld integrals |
| url | https://www.mdpi.com/2227-7390/13/1/169 |
| work_keys_str_mv | AT seilsautbekov thehalfspacesommerfeldproblemofahorizontaldipoleformagneticmedia AT mereysautbekova thehalfspacesommerfeldproblemofahorizontaldipoleformagneticmedia AT seilsautbekov halfspacesommerfeldproblemofahorizontaldipoleformagneticmedia AT mereysautbekova halfspacesommerfeldproblemofahorizontaldipoleformagneticmedia |