Free Maxwell equations in vacuum in orthogonal curvilinear coordinates and some applications: Helmholtz equation, poynting vector, and energy density
In this paper, we present a generalized method of solving the Free Maxwell Equations in Vacuum employing the process of separation of variables, which can be used for different systems of orthogonal curvilinear coordinates. This method leads us to obtain the Helmholtz equation for the distinct syste...
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Published in | European physical journal plus Vol. 139; no. 9; p. 792 |
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Main Authors | , , |
Format | Journal Article |
Language | English |
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Berlin/Heidelberg
Springer Berlin Heidelberg
06.09.2024
Springer Nature B.V |
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Abstract | In this paper, we present a generalized method of solving the Free Maxwell Equations in Vacuum employing the process of separation of variables, which can be used for different systems of orthogonal curvilinear coordinates. This method leads us to obtain the Helmholtz equation for the distinct systems of curvilinear coordinates. We show the case for the prolate spheroidal coordinates, obtaining the solutions dependent on the spatial and time coordinates. An analysis of the Poynting vector field of the solutions is presented together with the energy density analysis. It is shown that prolate spheroidal coordinates do not allow the existence of closed surfaces of the magnetic field; in addition, the nodal surfaces (geometric places where the energy density does not change in time) are not closed surfaces either. Our results may be helpful to the scientific community because they provide us with a systematic method for solving the system of Free Maxwell Equations in Vacuum for such coordinate systems. |
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AbstractList | In this paper, we present a generalized method of solving the Free Maxwell Equations in Vacuum employing the process of separation of variables, which can be used for different systems of orthogonal curvilinear coordinates. This method leads us to obtain the Helmholtz equation for the distinct systems of curvilinear coordinates. We show the case for the prolate spheroidal coordinates, obtaining the solutions dependent on the spatial and time coordinates. An analysis of the Poynting vector field of the solutions is presented together with the energy density analysis. It is shown that prolate spheroidal coordinates do not allow the existence of closed surfaces of the magnetic field; in addition, the nodal surfaces (geometric places where the energy density does not change in time) are not closed surfaces either. Our results may be helpful to the scientific community because they provide us with a systematic method for solving the system of Free Maxwell Equations in Vacuum for such coordinate systems. |
ArticleNumber | 792 |
Author | Pérez-Carlos, David A. Puga-Candelas, Alejandro Gutiérrez-Rodríguez, A. |
Author_xml | – sequence: 1 givenname: David A. orcidid: 0000-0003-0304-5346 surname: Pérez-Carlos fullname: Pérez-Carlos, David A. email: dperezcarlos@gmail.com organization: Unidad Académica de Física, Universidad Autónoma de Zacatecas – sequence: 2 givenname: A. surname: Gutiérrez-Rodríguez fullname: Gutiérrez-Rodríguez, A. organization: Unidad Académica de Física, Universidad Autónoma de Zacatecas – sequence: 3 givenname: Alejandro surname: Puga-Candelas fullname: Puga-Candelas, Alejandro organization: Unidad Académica de Física, Universidad Autónoma de Zacatecas |
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Cites_doi | 10.1088/0305-4470/35/38/307 10.1088/0253-6102/70/1/19 10.1088/0741-3335/51/12/124017 10.1051/0004-6361/202243471 10.1007/s41116-020-00027-4 10.1088/2040-8978/17/12/125610 10.1086/383025 10.1140/epjp/s13360-023-04780-x 10.1140/epjp/s13360-023-03945-y |
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Copyright | The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2024. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law. |
Copyright_xml | – notice: The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2024. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law. |
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SubjectTerms | Applied and Technical Physics Atomic Charged particles Complex Systems Condensed Matter Physics Electrons Fields (mathematics) Helmholtz equations Magnetic fields Mathematical and Computational Physics Maxwell's equations Molecular Optical and Plasma Physics Parity Physics Physics and Astronomy Prolate spheroids Regular Article Spherical coordinates Theoretical Time dependence Variables |
Title | Free Maxwell equations in vacuum in orthogonal curvilinear coordinates and some applications: Helmholtz equation, poynting vector, and energy density |
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