Itogi Nauki i Tekhniki. Sovremennaya Matematika i ee Prilozheniya. Tematicheskie Obzory
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Itogi Nauki i Tekhniki. Sovremennaya Matematika i ee Prilozheniya. Tematicheskie Obzory, 2023, Volume 223, Pages 123–127
DOI: https://doi.org/10.36535/0233-6723-2023-223-123-127 (Mi into1161) 		 
On magnetostatics in the Lobachevsky Spac

A. M. Trepalin

Mari State University, Ioshkar-Ola
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DOI: https://doi.org/10.36535/0233-6723-2023-223-123-127
Abstract: An analog of the Biot–Savart law in the Lobachevsky space is obtained by a kinematic method. We find an expression for the Lorentz force in the case where a charge moves in electric and magnetic fields and prove the work is done only by electric forces. The Poynting theorem is proved and the cyclotron problem is solved.
Keywords: Lobachevsky space, magnetic field.
Document Type: Article
UDC: 514.83
MSC: 53Z05
Language: Russian
Citation: A. M. Trepalin, “On magnetostatics in the Lobachevsky Spac”, Proceedings of the International Conference «Classical and Modern Geometry» dedicated to the 100th anniversary of the birth of Professor Levon Sergeyevich Atanasyan (July 15, 1921—July 5, 1998). Moscow, November 1–4, 2021. Part 4, Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz., 223, VINITI, Moscow, 2023, 123–127
Citation in format AMSBIB
\Bibitem{Tre23}
\by A.~M.~Trepalin
\paper On magnetostatics in the Lobachevsky Spac
\inbook Proceedings of the International Conference «Classical and Modern Geometry» dedicated to the 100th anniversary of the birth of Professor Levon Sergeyevich Atanasyan (July 15, 1921—July 5, 1998). Moscow, November 1–4, 2021. Part 4
\serial Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz.
\yr 2023
\vol 223
\pages 123--127
\publ VINITI
\publaddr Moscow
\mathnet{http://mi.mathnet.ru/into1161}
\crossref{https://doi.org/10.36535/0233-6723-2023-223-123-127}
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