Issues

 / 

1979

 / 

May

←  →

Methodological notes


Virial theorem for a system of charged particles


National Research Centre ‘Kurchatov Institute’, pl. Akademika Kurchatova 1, Moscow, 123182, Russian Federation

Two formulations of the virial theorem are used in practice: one for separate particles and one for a continuous medium. The virial theorem for a system of charged particles which was given by Landau and Lifshitz in their book \emph{The Classical Theory of Fields} should incorporate both these formulations. However, there is an error there in the derivation of this theorem, which is based on transformation from a discussion in terms of particles to a discussion in terms of a continuous medium. Specifically, the selfeffect force of the charges is not eliminated. As a result, the infinite self-energy of the charges is not eliminated, and the corresponding final equation cannot be satisfied. In the present note, a refined formulation of the virial theorem for a system of charged particles is given. The renormalization of the total electromagnetic field energy is taken into account.

Fulltext pdf (221 KB)
Fulltext is also available at DOI: 10.1070/PU1979v022n05ABEH005500
PACS: 03.50.Kk
DOI: 10.1070/PU1979v022n05ABEH005500
URL: https://ufn.ru/en/articles/1979/5/e/
Citation: Shafranov V D "Virial theorem for a system of charged particles" Sov. Phys. Usp. 22 368–370 (1979)
BibTexBibNote ® (generic)BibNote ® (RIS)MedlineRefWorks

Оригинал: Шафранов В Д «О теореме вириала для системы заряженных частиц» УФН 128 161–164 (1979); DOI: 10.3367/UFNr.0128.197905f.0161

Cited by (2) Similar articles (20) ↓

  1. A.M. Fridman “Modified criterion for the Landau stabilization of the instability of a tangential velocity discontinuity in a compressible medium” Sov. Phys. Usp. 33 (10) 865–867 (1990)
  2. B.M. Bolotovskii, S.N. Stolyarov “Radiation from and energy loss by charged particles in moving media” Sov. Phys. Usp. 35 (2) 143–150 (1992)
  3. V.A. Saranin “On the interaction of two electrically charged conducting balls” Phys. Usp. 42 385–390 (1999)
  4. V.A. Saranin “Electric field strength of charged conducting balls and the breakdown of the air gap between them” Phys. Usp. 45 1287–1292 (2002)
  5. E.G. Batyev “Pauli paramagnetism and Landau diamagnetism” Phys. Usp. 52 1245–1246 (2009)
  6. V.P. Kazantsev, O.A. Zolotov et al “Interaction energy of point electric multipoles” Phys. Usp. 68 843–849 (2025)
  7. V.L. Ginzburg, V.A. Ugarov “Remarks on forces and the energy-momentum tensor in macroscopic electrodynamics” Sov. Phys. Usp. 19 94–101 (1976)
  8. N.P. Klepikov “Radiation damping forces and radiation from charged particles” Sov. Phys. Usp. 28 506–520 (1985)
  9. I.M. Frank “On the moments of a magnetic dipole moving in a medium” Sov. Phys. Usp. 32 456–458 (1989)
  10. L.B. Okun’ “The concept of mass (mass, energy, relativity)” Sov. Phys. Usp. 32 629–638 (1989)
  11. V.N. Tsytovich “Description of collective processes and fluctuations in classical and quantum plasmas” Sov. Phys. Usp. 32 911–932 (1989)
  12. V.S. Krivitskii, V.N. Tsytovich “Average radiation-reaction force in quantum electrodynamics” Sov. Phys. Usp. 34 (3) 250–258 (1991)
  13. A.A. Kolokolov, G.V. Skrotskii “Interference of reactive components of an electromagnetic field” Sov. Phys. Usp. 35 (12) 1089–1093 (1992)
  14. V.I. Klyatskin, A.I. Saichev “Statistical and dynamic localization of plane waves in randomly layered media” Sov. Phys. Usp. 35 (3) 231–247 (1992)
  15. B.M. Bolotovskii, S.N. Stolyarov “Law of conservation of energy for the electromagnetic field as applied to radiation by moving charged particles” Sov. Phys. Usp. 35 (3) 248–254 (1992)
  16. A.L. Barabanov “Angular momentum in classical electrodynamics” Phys. Usp. 36 (11) 1068–1074 (1993)
  17. A.V. Belinskii “Bell’s theorem without the hypothesis of locality” Phys. Usp. 37 219–222 (1994)
  18. A.V. Belinskii “Bell’s paradoxes without the introduction of hidden variables” Phys. Usp. 37 413–419 (1994)
  19. B.M. Bolotovskii, A.V. Serov “Details of the motion of charged nonrelativistic particles in a variable field” Phys. Usp. 37 515–516 (1994)
  20. B.N. Shvilkin “On measuring the Debye radius in an unstable gas discharge plasma” Phys. Usp. 41 509–510 (1998)

The list is formed automatically.

© 1918–2026 Uspekhi Fizicheskikh Nauk
Email: ufn@ufn.ru Editorial office contacts About the journal Terms and conditions