Reduction of the classical electromagnetism to a two-dimensional curved surface
The reduction of the three-dimensional classical electromagnetism to a two-dimensional curved surface is performed in a twofold way. In the first case, the ordinary two-dimensional electromagnetism is obtained with sources in the form of conserved electric currents flowing along the surface. The ele...
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| Published in | Journal of modern optics Vol. 66; no. 9; pp. 1029 - 1037 |
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| Main Author | |
| Format | Journal Article |
| Language | English |
| Published |
Abingdon
Taylor & Francis
21.05.2019
Taylor & Francis Ltd |
| Subjects | |
| Online Access | Get full text |
| ISSN | 0950-0340 1362-3044 |
| DOI | 10.1080/09500340.2019.1599076 |
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| Abstract | The reduction of the three-dimensional classical electromagnetism to a two-dimensional curved surface is performed in a twofold way. In the first case, the ordinary two-dimensional electromagnetism is obtained with sources in the form of conserved electric currents flowing along the surface. The electric field is a two-vector tangent to the surface and magnetic field is a scalar quantity. In the second approach, the reduced theory is that of the two-vector magnetic field and a scalar electric one. The only source coupled to the fields is now a scalar, subject to no conservation law. In the redefined theory, this scalar source may be converted into an eddy magnetic current flowing in the surface. No magnetic monopoles appear. Our results can find some applications in the electrodynamics of thin layers and of metal-dielectric interfaces. |
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| AbstractList | The reduction of the three-dimensional classical electromagnetism to a two-dimensional curved surface is performed in a twofold way. In the first case, the ordinary two-dimensional electromagnetism is obtained with sources in the form of conserved electric currents flowing along the surface. The electric field is a two-vector tangent to the surface and magnetic field is a scalar quantity. In the second approach, the reduced theory is that of the two-vector magnetic field and a scalar electric one. The only source coupled to the fields is now a scalar, subject to no conservation law. In the redefined theory, this scalar source may be converted into an eddy magnetic current flowing in the surface. No magnetic monopoles appear. Our results can find some applications in the electrodynamics of thin layers and of metal-dielectric interfaces. |
| Author | Radożycki, Tomasz |
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| SubjectTerms | Eddy currents Electric fields Electrodynamics Electromagnetism low-dimensional theory Magnetic fields Magnetic monopoles Reduction Thin films thin layers wave propagation |
| Title | Reduction of the classical electromagnetism to a two-dimensional curved surface |
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