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On energy and momentum conservation laws for an electromagnetic field in a medium or at diffraction on a conducting plate


Chernyshevskii Saratov State University, ul. Astrakhanskaya 83, Saratov, 410071, Russian Federation

For a field—matter system, general nonstationary balance equations for energy and momentum densities and their transport velocities are obtained based on a rigorous nonstationary definition of these densities depending on the creation history of the field. We analyze the simplest dispersion law determined by conductivity dissipation; we find the electromagnetic energy density, phase velocity, group velocity, and energy and momentum transport velocities of a plane monochromatic wave. The low-frequency energy density is shown to be given by the electrostatic density in which the dielectric constant is replaced with its real part and the energy transport velocity is equal to the phase velocity. The group velocity can exceed the speed of light. We prove that the Minkowski form of momentum density must be used in the medium, and find the corresponding transport velocity, which in the case under consideration also coincides with the phase velocity. Energy and momentum conservation laws are shown to hold for a plane electromagnetic wave propagating in a medium or diffracted by a conducting plate.

Fulltext pdf (475 KB)
Fulltext is also available at DOI: 10.3367/UFNe.0180.201006e.0623
PACS: 03.50.De, 41.20.Jb, 42.25.Fx (all)
DOI: 10.3367/UFNe.0180.201006e.0623
URL: https://ufn.ru/en/articles/2010/6/d/
000281644500004
2-s2.0-77958538442
2010PhyU...53..595D
Citation: Davidovich M V "On energy and momentum conservation laws for an electromagnetic field in a medium or at diffraction on a conducting plate" Phys. Usp. 53 595–609 (2010)
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Оригинал: Давидович М В «О законах сохранения энергии и импульса электромагнитного поля в среде и при дифракции на проводящей пластине» УФН 180 623–638 (2010); DOI: 10.3367/UFNr.0180.201006e.0623

References (58) ↓ Cited by (14) Similar articles (20)

  1. Minkowski H Gött. Nachr. 53 11 (1908)
  2. Abraham M Palermo Rend. 28 1 (1909)
  3. Ginzburg V L Usp. Fiz. Nauk 110 309 (1973); Ginzburg V L Sov. Phys. Usp. 16 434 (1973)
  4. Skobel’tsyn D V Usp. Fiz. Nauk 110 253 (1973); Skobel’tsyn D V Sov. Phys. Usp. 16 381 (1973)
  5. Ginzburg V L, Ugarov V A Usp. Fiz. Nauk 118 175 (1976); Ginzburg V L, Ugarov V A Sov. Phys. Usp. 19 94 (1976)
  6. Brevik I Mat. Phys. Medd. Dan. Vid. Selsc. 37 (13) 1 (1970)
  7. de Groot S R, Suttorp L G Physica 39 84 (1968)
  8. de Groot S R, Suttorp L G Foundations Of Electrodynamics (Amsterdam: North-Holland, 1972); de Groot S R, Sattorp L G Elektrodinamika (M.: Nauka, 1982)
  9. Skobel’tsyn D V Usp. Fiz. Nauk 122 295 (1977); Skobel’tsyn D V Sov. Phys. Usp. 20 528 (1977)
  10. Ginzburg V L Usp. Fiz. Nauk 122 325 (1977); Ginzburg V L Sov. Phys. Usp. 20 546 (1977)
  11. Leonhardt U Nature 444 823 (2006)
  12. Pfeifer R N C et al. Rev. Mod. Phys. 79 1197 (2007)
  13. Obukhov Y N Ann. Physik 17 830 (2008)
  14. Davidovich M V Usp. Fiz. Nauk 179 443 (2009); Davidovich M V Phys. Usp. 52 415 (2009)
  15. Akhiezer A I, Akhiezer I A Elektromagnetizm i Elektromagnitnye Volny (M.: Vysshaya shkola, 1985)
  16. Davidovich M V Pis’ma ZhTF 32 (22) 53 (2006); Davidovich M V Tech. Phys. Lett. 32 982 (2006)
  17. Landau L D, Lifshits E M Elektrodinamika Sploshnykh Sred (M.: Nauka, 1982); Landau L D, Lifshitz E M Electrodynamics Of Continuous Media (Oxford: Pergamon Press, 1984)
  18. Vinogradov A P Usp. Fiz. Nauk 172 363 (2002); Vinogradov A P Phys. Usp. 45 331 (2002)
  19. Feynman R P, Leighton R B, Sands M The Feynman Lectures On Physics Vol. 2 (Reading, Mass.: Addison-Wesley Publ. Co., 1964); Feinman R, Leiton R, Sends M Feinmanovskie Lektsii Po Fizike Vol. 6 (M.: Mir, 1966)
  20. Hietler W The Quantum Theory Of Radiation 3rd ed. (Oxford: Clarendon Press, 1954); Geitler V Kvantovaya Teoriya Izlucheniya (M.: IL, 1956)
  21. Umov N F Beweg-Gleich. Energie Contin. Kopern. Z. Math. Phys. Slomilch 1 9 (1874)
  22. Okun’ L B Usp. Fiz. Nauk 158 511 (1989); Okun’ L B Sov. Phys. Usp. 32 629 (1989)
  23. Okun’ L B Usp. Fiz. Nauk 170 1366 (2000); Okun’ L B Phys. Usp. 43 1270 (2000)
  24. Kotel’nikov I A Zh. Tekh. Fiz. 74 (9) 91 (2004); Kotel’nikov I A Tech. Phys. 49 1196 (2004)
  25. Ordal M A et al. Appl. Opt. 22 1099 (1983)
  26. Markov G T, Chaplin A F Vozbuzhdenie Elektromagnitnykh Voln 2-e izd. (M.: Radio i svyaz’, 1983)
  27. Zil’bergleit A S, Kopilevich Yu I Zh. Tekh. Fiz. 50 241 (1980); Zilbergleit A S, Kopilevich Iu I Sov. Phys. Tech. Phys. 25 147 (1980)
  28. Zil’bergleit A S, Kopilevich Yu I Zh. Tekh. Fiz. 50 449 (1980); Zilbergleit A S, Kopilevich Iu I Sov. Phys. Tech. Phys. 25 273 (1980)
  29. Gureev A V Zh. Tekh. Fiz. 61 (11) 23 (1990); Gureev A V Sov. Phys. Tech. Phys. 35 1244 (1990)
  30. Silin R A Periodicheskie Volnovody (M.: Fazis, 2002)
  31. Mandel’shtam L I Lektsii Po Optike, Teorii Otnositel’nosti i Kvantovoi Mekhanike (M.: Nauka, 1972)
  32. Bhatnagar P L Nonlinear Waves In One-Dimensional Systems (Oxford: Clarendon Press, 1979); Bkhatnagar P Nelineinye Volny v Odnomernykh Dispersnykh Sistemakh (M.: Mir, 1983)
  33. Ginzburg V L Rasprostranenie Elektromagnitnykh Voln v Plazme (M.: Fizmatgiz, 1960); Ginzburg V L Propagation Of Electromagnetic Waves In Plasma (New York: Gordon and Breach, 1962)
  34. Vainshtein L A Elektromagnitnye Volny 2-e izd. (M.: Radio i svyaz’, 1988)
  35. Gol’dshtein L D, Zernov N V Elektromagnitnye Polya i Volny (M.: Sovetskoe radio, 1971)
  36. Vinogradova M B, Rudenko O V, Sukhorukov A P Teoriya Voln (M.: Nauka, 1979)
  37. Vainshtein L A Usp. Fiz. Nauk 118 339 (1976); Vainshtein L A Sov. Phys. Usp. 19 189 (1976)
  38. Vainshtein L A, Vakman D E Razdelenie Chastot v Teorii Kolebanii i Voln (M.: Nauka, 1983)
  39. Stratton J A Electromagnetic Theory (New York: McGraw-Hill, 1941); Stretton D A Teoriya Elektromagnetizma (M.: Gostekhizdat, 1948)
  40. Schulz-DuBois E O Proc. IEEE 57 1748 (1969)
  41. Ostrovskii L A, Potapov A I Vvedenie v Teoriyu Modulirovannykh Voln (M.: Fizmatlit, 2003)
  42. Polevoi V G, Rytov S M Usp. Fiz. Nauk 125 549 (1978); Polevoi V G, Rytov S M Sov. Phys. Usp. 21 630 (1978)
  43. Rytov S M Zh. Eksp. Teor. Fiz. 17 930 (1947)
  44. Lighthill M J J. Inst. Math. Appl. 1 1 (1965)
  45. Biot M A Phys. Rev. 105 1129 (1957)
  46. Olver F W G Introduction To Asymptotics And Special Functions (New York: Academic Press, 1974); Olver F Vvedenie v Asimptoticheskie Metody i Spetsial’nye Funktsii (M.: Nauka, 1978)
  47. Mayergoyz I D IEEE Trans. Magn. 29 1301 (1993)
  48. Savin M G Problema Kalibrovki Lorentsa v Anizotropnykh Sredakh (M.: Nauka, 1979)
  49. Hinds E A, Barnett S M Phys. Rev. Lett. 102 050403 (2009)
  50. Marklund M J. Phys. A Math. Gen. 38 4265 (2005)
  51. Garrison J C, Chiao R Y Phys. Rev. A 70 053826 (2004)
  52. Leonhardt U Phys. Rev. A 73 032108 (2006)
  53. Brevik I Mat. Phys. Medd. Dan. Vid. Selsc. 37 (11) 1 (1970)
  54. Brevik I Mat. Phys. Medd. Dan. Vid. Selsc. 37 (13) 1 (1970)
  55. Gribov V N Kvantovaya Elektrodinamika (M. - Izhevsk: RKhD, 2001)
  56. Landau L D, Lifshits E M Teoriya Polya (M.: Nauka, 1973) p. 107; Landau L D, Lifshitz E M The Classical Theory Of Fields (Oxford: Pergamon Press, 1975)
  57. Veselago V G Usp. Fiz. Nauk 179 689 (2009); Veselago V G Phys. Usp. 52 649 (2009)
  58. Veselago V G Usp. Fiz. Nauk 180 331 (2010); Veselago V G Phys. Usp. 53 317 (2010)
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