Hostname: page-component-cb9f654ff-kl2l2 Total loading time: 0 Render date: 2025-08-25T16:26:41.479Z Has data issue: false hasContentIssue false
  • English
  • Français

The EM response due to a plane sheet of arbitrary shape and conductivity profile

Published online by Cambridge University Press:  17 February 2009

D. G. Hurley  and
P. F. Siew
D. G. Hurley
Affiliation:
University of Western Australia, Nedlands, WA 6009.
P. F. Siew
Affiliation:
School of Mathematics and Statistics, Curtin University of Technology, WA.
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

The eddy currents induced in a thin sheet of variable conductivity by a sinusoidally varying primary magnetic field are investigated in the low frequency limit when the depth of penetration of the primary field is much greater than the thickness of the sheet. The problem is formulated in terms of a set of integro-differential equations. The method of solution is applicable to bodies with arbitrary planar shape and the result is particularly useful in inverse problems involving bodies with conductivity inhomogeneities.

Information

Type
Research Article
Information
The ANZIAM Journal , Volume 37 , Issue 2 , October 1995 , pp. 267 - 278
Copyright
Copyright © Australian Mathematical Society 1995

References

[1]Ashour, A. A., “The induction of electric currents in a uniform circular disc”, Q. J. Mech. Appl. Math. 3 (1950) 119–28.CrossRefGoogle Scholar
[2]Ashour, A. A. and Price, A. T., “The induction of electric currents in a non-uniform ionosphere”, Proc. R. Soc. Lond. A 195 (1948) 198–224.Google Scholar
[3]Hurley, D. G. and Siew, P. F., “The decay of eddy currents in thin sheets and related water wave problems”, IMA J. Appl. Math. 34 (1985) 1–21.CrossRefGoogle Scholar
[4]Hurley, D. G. and Siew, P. F., “A first-order correction to the theory for the electromagnetic response of a thin conducting sheet”, Geophys. Prosp. 39 (1991) 527–41.CrossRefGoogle Scholar
[5]Jeffreys, H. and Jeffreys, B. S., Methods of mathematical physics, 3rd ed. (Camb. Univ. Press, 1962).Google Scholar
[6]Lamontague, Y. and West, G. F., “EM response of a rectangular thin plate”, Geophysics 36 (1971) 1204–22.CrossRefGoogle Scholar
[7]Landau, L. D. and Lifshitz, E. M., Electrodynamics of continuous media, 2nd. ed. (Pergamon Press, Oxford, 1984).Google Scholar
[8]Maxwell, J. C., A Treatise on electricity and magnetism. Vol. 2, 3rd ed. (Dover Publications Inc., 1891) 291–295.Google Scholar
[9]Price, A. T., “The induction of electric currents in non-uniform thin sheets and shells”, Q. J. Mech. Appl. Math. 2 (1949) 282–310.CrossRefGoogle Scholar
[10]Siew, P. F., “A numerical scheme for the electromagnetic response in thin conductors of arbitrary planar shape”, J. Aust. Math. Soc. (B) 35 (1994) 479–497.CrossRefGoogle Scholar
[11]Siew, P. F. and Hurley, D. G., “Electromagnetic response of thin disks”, J. Appl. Math. Phys. (ZAMP) 39 (1988) 619–33.CrossRefGoogle Scholar
[12]Smythe, W. R., Static and dynamic electricity (McGraw Hill, London, 1968).Google Scholar