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20.—Inequalities for the Capacity of an Electrified Conducting Annular Disc

Published online by Cambridge University Press:  14 February 2012

E. R. Love  and
W. D. Collins
E. R. Love
Affiliation:
Department of Mathematics, University of Melbourne, Australia
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Synopsis

The simultaneous integral equations of Noble and Cooke, for inter alia the Dirichlet problem for an annular disc, are transformed into equations closely analogous to those recently given by Clements and Love for the corresponding Neumann problem. The transformed equations are relatively simple, and do not involve any artificial preliminary dissection of the known functions. They are also uncoupled, and admit iterative solution for virtually all radius ratios.

In the case of the conducting annular disc, iteration of these equations isused to obtain two series for the capacity, an interim one with all terms positive, and a final one with all terms after the first negative. The final series is more rapidly convergent as well as neater. It is used to provide a family of inequalities which enclose the capacity and determine it to high accuracy with very few terms, failing only when the radius ratio is close to 1.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 74 , 1976 , pp. 257 - 270
Copyright
Copyright © Royal Society of Edinburgh 1976

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