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The circular plate condenser at small separations

Published online by Cambridge University Press:  24 October 2008

V. Hutson
V. Hutson
Affiliation:
Department of Applied Mathematics, Sheffield University
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Abstract

The problem considered is the oppositely charged, circular disk condenser when the disks are very close together. An integral equation due to Love(5) is used as the governing equation of the problem. This equation is solved asymptotically for small separations by splitting the field into regions, one being an annulus containing the edges, the other being the rest of the domain, and combining these solutions. Bounds for the error in the solution of the integral equation are obtained rigorously; the error is shown to approach zero as the separation approaches zero. The capacity of the system is deduced from this solution. The problem of finding the capacity has previously been attempted by various authors, whose results have differed. The present treatment establishes which of these results is correct.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 59 , Issue 1 , January 1963 , pp. 211 - 224
Copyright
Copyright © Cambridge Philosophical Society 1963

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References

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