Some Axisymmetric Solutions of the System of Maxwell’s Equations
https://doi.org/10.56304/S2304487X2202002X
Abstract
The system of Maxwell’s equations is considered after the transition from the Cartesian to cylindrical coordinate system. Instead of the first two traditional components of magnetic and electric field strength, radial and circumferential components of these vectors are introduced. The resulting system of partial differential equations does not explicitly include the dependence on the polar angle. In the case where the desired functions depend only on time and the radial coordinates, specific solutions of the system of Maxwell’s equations are constructed using the separation of variables.
About the Authors
S. P. Bautin
Snezhinsk Institute of Physics and Technology, National Research Nuclear University MEPhI (Moscow Engineering Physics Institute)
Russian Federation
Russian Federation
Snezhinsk, Chelyabinsk oblast, 456776
A. G. Obukhov
Tyumen Industrial University
Russian Federation
Russian Federation
Tyumen, 625000
References
1. Landau L.D., Lifcsych E.M. Teoreticheskaja fizika. Tom 2. Teorija polja [Theoretical physics. Volume 2. Field Theory]. Moscow, gos. izd-vo fiz.-mat. Literatury Publ., 1960. 400 p. (in Russian)
2. Kurant R. Uravnenija s chastnymi proizvodnymi [Partial differential equations]. Moscow, Mir Publ., 1964, 830 p.
3. Tamm I.E. Osnovy teorii electrichestvf [Fundamentals of the theory of electricity]. Moscow, Nauka Publ., 1976, 616 p.
4. Parsell E. Electrichestvo i magnetizm [Electricity and magnetism]. Moscow, Nauka Publ., 1975. 440 p.
5. Sidorov A.F., Shapeev V.P., Janenko N.N. Metod differencyalnyh svjazei i ego prilozenija v gazovoi dinamike [Differential coupling method and its applications in gas dynamics]. Novosibirsk, Nauka Publ., 1984. 272 p.
6. Bautin S.P. Charakteristicheskaja zadaca Koshy i ee prilozenija v gazovoi dinamike [The characteristic Cauchy problem and its applications in gas dynamics]. Novosibirsk, Nauka Publ., 2009. 368 p.
7. Goldshtein L.D., Zernov N.V. Elektromagnitnye polja i volny [Electromagnetic fields and wave]. Moscow, Sovetskoe radio Publ., 1971, 665 p.
8. Korn G., Korn Т. Spravocnik po matematike dlaj nauchnyh rabotnikov i inzenerov [Handbook of Mathematics for researchers and engineers]. Moscow, Nauka Publ., 1970. 720 p.
9. Zaitsev V.F., Polyanin A.D. Spravocnik po obyknovennym differencyalnym uravneniajm [Handbook of ordinary differential equations]. Moscow, Fizmatlit Publ., 2001, 576 p.
Review
For citations:
Bautin S.P., Obukhov A.G. Some Axisymmetric Solutions of the System of Maxwell’s Equations. Vestnik natsional'nogo issledovatel'skogo yadernogo universiteta "MIFI". 2022;11(2):133–142. (In Russ.) https://doi.org/10.56304/S2304487X2202002X
Views:
103
Email this article 