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The field of current in a thin wire ring

Published online by Cambridge University Press:  06 March 2017

G. W. Carter ,
S. C. Loh  and
C. Y. K. Po
G. W. Carter
Affiliation:
Department of Electrical Engineering, University of Leeds
S. C. Loh
Affiliation:
Department of Electrical Engineering, University of Leeds
C. Y. K. Po
Affiliation:
Department of Electrical Engineering, University of Leeds
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Abstract

A simple expression is derived for the magnetic vector potential of current in a thin ring, in terms of the first derivative of toroidal functions of zero order. The axial and radial field components and the mutual inductance between two wire rings are obtained. These expressions are evaluated on a digital computer and the results are summarized in a series of graphs.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 60 , Issue 3 , July 1964 , pp. 613 - 619
Copyright
Copyright © Cambridge Philosophical Society 1964

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References

REFERENCES

(1) Carter, G. W. and Loh, S.-C. The approximate calculation of the electric field between a rod and a concentric ring by means of toroidal functions. Proc. Inst. Elec. Engrs. C, 105 (1958), 13–17.Google Scholar
(2) Gaugain, . Boussole des tangentes établie sur un principe nouveau d'electrodynamique. C.R. Acad. Sci., Paris, 36 (1853), 191–193.Google Scholar
(3) Hammond, P. The calculation of the magnetic field of rotating machines: part 3-eddy currents induced in a solid slab by a circular current loop. Proc. Inst. Elec. Engrs. C, 109 (1962), 508–515.Google Scholar
(4) Hicks, W. M. On toroidal functions. Philos. Trans. Roy. Soc. London, Ser. A, 172 (1881), 609–652.Google Scholar
(5) Jeans, J. H. The mathematical theory of electricity and magnetism (5th edition; Cambridge, 1951).Google Scholar
(6) Mascart, E. and Joubert, J. (transl. Atkinson, E.). A treatise on electricity and magnetism, vol. 2 (De la Rue, 1888).Google Scholar
(7) Morse, P. M. and Feshbach, H. Methods of theoretical physics (McGraw-Hill; 1953).Google Scholar
(8) Pringle, G. E. The potential of a circular current. Proc. Cambridge Philos. Soc. 57 (1961), 385–392.CrossRefGoogle Scholar
(9) Stratton, J. A. Electromagnetic theory (McGraw-Hill; 1941).Google Scholar
(10) Thomson, J. J. Elements of the mathematical theory of electricity and magnetism (5th edition; Cambridge, 1921).Google Scholar
(11) Wolfe, R. A. Calculation of intensity of field due to a circular coil (A. E.I. (Rugby) Limited).Google Scholar
(12) Wolfe, R. A. Subroutine to calculate self-inductance of circular coils (A. E. I. (Rugby) Limited).Google Scholar