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A note on the magnetic scalar potential of an electric current-ring

Published online by Cambridge University Press:  24 October 2008

A. Hulme
A. Hulme
Affiliation:
University of Manchester
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Abstract

This paper considers the problem of expressing the magnetic scalar potential associated with the steady flow of an electric current around a thin circular wire, in terms of ‘local’ toroidal coordinates. This potential is known to be a multi-valued function of position and so cannot be expressed directly in terms of fundamental (i.e. single-valued) solutions of Laplace's equation. It is shown that the potential can however be expressed quite simply, as an infinite series of multi-valued toroidal harmonics and that this series is rapidly convergent in the neighbourhood of the current-ring.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 92 , Issue 1 , July 1982 , pp. 183 - 191
Copyright
Copyright © Cambridge Philosophical Society 1982

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References

REFERENCES

(1)Bateman, H.Partial differential equations of mathematical physics (Cambridge University Press, 1932).Google Scholar
(2)Erdélyi, A. (ed). Higher transcendental functions, vol. I (McGraw-Hill, 1953).Google Scholar
(3)Hulme, A.The potential of a horizontal ring of wave sources in a fluid with a free surface. Proc. Roy. Soc. Lond. A 375 (1981), 295–305.Google Scholar
(4)Morse, P. M. and Feshbach, H.Methods of theoretical physics, part II (McGraw-Hill, 1953).Google Scholar
(5)Pringle, G. E.The potential of a circular current. Proc. Cambridge Philos. Soc. 57 (1961), 385–392.CrossRefGoogle Scholar
(6)Stratton, J. A.Electromagnetic theory (McGraw-Hill, 1941).Google Scholar
(7)Watson, G. N.A treatise on the theory of Bessel functions (Cambridge University Press, 1944).Google Scholar