On Magnetostatics in the Lobachevsky Space
- Authors: Trepalin A.M.1
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Affiliations:
- Марийский государственный университет
- Issue: Vol 223 (2023)
- Pages: 123-127
- Section: Articles
- URL: https://journals.rcsi.science/2782-4438/article/view/270838
- DOI: https://doi.org/10.36535/0233-6723-2023-223-123-127
- ID: 270838
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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.
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About the authors
A. M. Trepalin
Марийский государственный университет
Author for correspondence.
Email: trefa50@mail.ru
Russian Federation, Йошкар-Ола
References
- Широков П. А. Преобразование винтовых интегралов в пространствах постоянной кривизны // In memoriam N. I. Lobatschevskii. — 1927. — 2. — С. 119—134.
- Широков А. П. Винтовая регулярная прецессия в пространстве Лобачевского // Уч. зап. Казан. ун-та. — 1963. — 123, № 1. — С. 196–207.
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