RSS feeds
РусскийEnglish
Issue 10, 2026
Volume year page
Issues Authors PACS Subscription For authors

Issues

 / 

2012

 / 

September

←  →

Methodological notes


Some useful correspondences in classical magnetostatics, and the multipole representations of the magnetic potential of an ellipsoid


Moscow State Mining University, Leninskii 6, Moscow, 119991, Russian Federation

It is shown that for a given geometric body, the Ferrers theorem not only relates the potentials of volume- and surface-distributed scalar (charge or mass) sources (which it is known to do) but also relates the vector (scalar) magnetic field potentials produced by the volume- and surface-distributed densities of a stationary current (i.e., vector sources). For a body with a given magnetization, the magnetic multipole moments calculated from expressions for polarization magnetic charges are shown to be equal to those of AmpÉre currents. Using these results and noting the universality of the multipole expressions, multipole representations of the scalar magnetic potential of an ellipsoid can be (and, indeed, have been) obtained rather straightforwardly.

Fulltext pdf (523 KB)
Fulltext is also available at DOI: 10.3367/UFNe.0182.201209d.0987
PACS: 41.20.Cv, 41.20.Gz (all)
DOI: 10.3367/UFNe.0182.201209d.0987
URL: https://ufn.ru/en/articles/2012/9/c/
000312382200003
2-s2.0-84872100326
Citation: Muratov R Z "Some useful correspondences in classical magnetostatics, and the multipole representations of the magnetic potential of an ellipsoid" Phys. Usp. 55 919–928 (2012)
BibTexBibNote ® (generic)BibNote ® (RIS)MedlineRefWorks

Received: 21st, March 2011, 8th, June 2011

Оригинал: Муратов Р З «О некоторых полезных соответствиях в классической магнитостатике и o мультипольных представлениях магнитного потенциала эллипсоида» УФН 182 987–997 (2012); DOI: 10.3367/UFNr.0182.201209d.0987

References (25) ↓ Similar articles (20)

  1. ’sр’?’?’?’?’?ь Ya ’R ’l’?’?р’?’?’?’? ’?’?’?р’?’?’?ыkh тру’?’?’? ’n. 1 ’e’?’?’?тр’?’?’?’?’?’?’?’?’? (’d’?shch’?ya т’?’?р’?ya э’?’?’?тр’?ch’?ст’?’?) (’a. - ’’.: ’R’?’?-’?’? ’B’v ’l’l’l’i, 1956)
  2. ’sр’?’?’?’?’?ь Ya ’R ’e’?’?’?тр’?’?’?’?’?’?’?’?’? Vol. 2 (’’. - ’a.: ’d’v’n’R, 1935)
  3. Ferrers N M Quart. J. Pure Appl. Math. 14 (53) 1 (1877)
  4. ’aур’?т’?’? ’i ’O ’z’?т’?’?ts’?’?’?ы э’?’?’?’?с’?’?’?’? (’a.: ’Bт’?’?’?’?’?’?т, 1976)
  5. ’a’?’?’?’?’?’?’? ’G ’E ’v’?ch’?’?’? т’?’?р’?т’?ch’?с’?’?’? ф’?’?’?’?’? (’a.: ’v’?у’?’?, 1977)
  6. ’Mф’?’?’?’? ’l ’z, ’aур’?т’?’? ’i ’O Astron. Zh. 67 302 (1990); Efimov S P, Muratov R Z Sov. Astron. 34 152 (1990)
  7. ’Mф’?’?’?’? ’l ’z, ’aур’?т’?’? ’i ’O Astron. Zh. 67 314 (1990); Efimov S P, Muratov R Z Sov. Astron. 34 157 (1990)
  8. ’aур’?т’?’? ’i ’O Astron. Zh. 70 1271 (1993); Muratov R Z Astron. Rep. 37 641 (1993)
  9. Poisson S D Mémoir. L’Acad. Sci. Paris 5 247 (1821 - 1822)
  10. Mattis D C The Theory Of Magnetism: An Introduction To The Study Of Cooperative Phenomena (New York: Harper & Row, 1965); ’a’?тт’?с ’K ’n’?’?р’?ya ’?’?’?’?’?т’?’?’?’?. ’E’?’?’?’?’?’?’? ’? ’?’?уch’?’?’?’? ’?’?’?’?’?р’?т’?’?’?ыkh ya’?’?’?’?’?’? (’a.: ’a’?р, 1967)
  11. Whittaker E T A History Of The Theories Of Aether And Electricity Vol. 1 The Classical Theories (London: T. Nelson, 1951); ’p’?тт’?’?’?р ’e ’Rст’?р’?ya т’?’?р’?’? эф’?р’? ’? э’?’?’?тр’?ch’?ст’?’?. ’F’?’?сс’?ch’?с’?’?’? т’?’?р’?’? (’Rzh’?’?с’?: ’iKh’K, 2001)
  12. Maxwell J C A Treatise On Electricity And Magnetism Vol. 2 (London: Oxford Univ. Press, 1891); ’a’?’?с’?’?’?’? ’Kzh K ’nр’?’?т’?т ’?’? э’?’?’?тр’?ch’?ст’?’? ’? ’?’?’?’?’?т’?’?’?’? Т. 2 (’a.: ’v’?у’?’?, 1989)
  13. Ampère A-M J. Physique 93 447 (1821); ’B’?’?’?р A M ’e’?’?’?тр’?’?’?’?’?’?’?’?’? (’a.: ’R’?’?-’?’? ’B’v ’l’l’l’i, 1954) p. 283
  14. Ampère A-M M 6 175 (1827); ’B’?’?’?р A M ’e’?’?’?тр’?’?’?’?’?’?’?’?’? (’a.: ’R’?’?-’?’? ’B’v ’l’l’l’i, 1954) p. 7
  15. ’n’?’?’? ’R ’M ’dс’?’?’?ы т’?’?р’?’? э’?’?’?тр’?ch’?ст’?’? (’a.: ’v’?у’?’?, 1989); Tamm I E Fundamentals Of The Theory Of Electricity (Moscow: Mir Publ., 1979)
  16. ’aур’?т’?’? ’i ’O Zh. Tekh. Fiz. 67 (4) 1 (1997); Muratov R Z Tech. Phys. 42 325 (1997)
  17. ’Mф’?’?’?’? ’l ’z Teor. Mat. Fiz. 39 219 (1979); Efimov S P Theor. Math. Phys. 39 425 (1979)
  18. ’aур’?т’?’? ’i ’O Zh. Tekh. Fiz. 72 (4) 6 (2002); Muratov R Z Tech. Phys. 47 380 (2002)
  19. Thomson W, Tait P G Treatise On Natural Philosophy Vol. 2 (Cambridge: The Univ. Press, 1912)
  20. Routh E J A Treatise On Analytical Statics Vol. 2 (Cambridge: The Univ. Press, 1922)
  21. ’aур’?т’?’? ’i ’O, Sh’?ур’?т’?’?’? ’E ’’ Zh. Tekh. Fiz. 75 (8) 1 (2005); Muratov R Z, Shkuratnik V L Tech. Phys. 50 961 (2005)
  22. ’’’?’?’?’?у ’’ ’K, ’’’?фsh’?ts ’M ’a ’e’?’?’?тр’?’?’?’?’?’?’?’?’? с’?’?’?sh’?ыkh ср’?’? (’a.: ’v’?у’?’?, 1992); Landau L D, Lifshitz E M Electrodynamics Of Continuous Media (Oxford: Pergamon Press, 1984)
  23. Stratton J A Electromagnetic Theory (New York: McGraw-Hill, 1941); ’lтрэтт’?’? ’Kzh ’B ’n’?’?р’?ya э’?’?’?тр’?’?’?’?’?’?т’?’?’?’? (’a. - ’’.: ’I’R’n’n’’, 1948)
  24. Hobson E W The Theory Of Spherical And Ellipsoidal Harmonics (Cambridge: The Univ. Press, 1931); ’I’?’?с’?’? ’M ’E ’n’?’?р’?ya сф’?р’?ch’?с’?’?kh ’? э’?’?’?’?с’?’?’?’?’?ь’?ыkh фу’?’?ts’?’? (’a.: ’R’’, 1952)
  25. ’B’?р’? ’a Ya Usp. Fiz. Nauk 181 173 (2011); Agre M Ya Phys. Usp. 54 167 (2011)
© 1918–2026 Uspekhi Fizicheskikh Nauk
Email: ufn@ufn.ru Editorial office contacts About the journal Terms and conditions