Hostname: page-component-745bb68f8f-v2bm5 Total loading time: 0 Render date: 2025-01-13T09:42:11.815Z Has data issue: false hasContentIssue false
  • English
  • Français

The potential of a circular current

Published online by Cambridge University Press:  24 October 2008

G. E. Pringle
G. E. Pringle
Affiliation:
School of Chemistry, The University of Leeds
Get access Rights & Permissions [Opens in a new window]

Extract

The 3-dimensional potential due to a charged circle can be derived in various ways which lead to the same expression in terms of the toroidal coordinate σ through Legendre functions of s (= cosh σ). Applying the same methods to the magnetic potential of a circular current we find various results: (a) Legendre's equation yields no solution (§4·1). (b) The appropriate transformation from cylindrical to toroidal coordinates gives a Fourier series (equation (48)) the coefficients of which, though not Legendre functions, are related to them by the identity (§4·2) By this method we also derive expressions in elliptic integrals (equations (56), (58)). (c) Direct integration of the solid angle gives an alternative expression in elliptic integrals (equation (59)).

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 57 , Issue 2 , April 1961 , pp. 385 - 392
Copyright
Copyright © Cambridge Philosophical Society 1961

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

(1)Bateman, H., Partial differential equations (Cambridge, 1932).Google Scholar
(2)Whittaker, E. T. and Watson, G. N.. A course of modern analysis, 4th ed. (Cambridge, 1927).Google Scholar
(3)Heine, E.. Anwendungen der Kugelfunktionen, pp. 283–301 (Berlin, 1881).Google Scholar
(4)Hicks, W. M., Phil. Trans. 171 (1881), 609–52.Google Scholar