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An asymptotic solution of an integro-differential equation arising in magnetic coupling through thin shield walls

Published online by Cambridge University Press:  17 February 2009

G. F. Fitz-Gerald  and
N. A. McDonald
G. F. Fitz-Gerald
Affiliation:
Department of Mathematics, RMIT, Melbourne, Vic., Australia.
N. A. McDonald
Affiliation:
Department of Communication and Electronic Engineering, RMIT, Melbourne, Vic., Australia.
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An equation which has arisen in a study of the magentic coupling through a small rectangular aperture of dimension A × B in a thin shield wall is discussed. The magnetic polarisability of such an aperture in a conducting wall of zero thickness is known to be expressible as RHA3, in which RH is dimensionless and is a function of the aspect ratio α ≡ B/A. An asymptotic solution procedure of a certain variational formulation of this problem is described in the limiting case of large aspect ratio α. Explicit analytical formulase for the leading terms in the expansion are given. These analytical results justify the purely numerical procedures used previously to obtain approximate solutions of this formulation of the problem.

Type
Research Article
Information
The ANZIAM Journal , Volume 30 , Issue 4 , April 1989 , pp. 414 - 423
Copyright
Copyright © Australian Mathematical Society 1989

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