Hostname: page-component-78c5997874-s2hrs Total loading time: 0 Render date: 2024-11-11T00:34:18.426Z Has data issue: false hasContentIssue false
  • English
  • Français

The potential due to a circular parallel plate condenser

Part of: Higher-dimensional theory

Published online by Cambridge University Press:  26 February 2010

E. R. Love
E. R. Love
Affiliation:
Department of Mathematics, University of Melbourne, Parkville, Victoria, Australia 3052.
Get access

Extract

Atkinson, Young and Brezovich [1: 1983] gave a formula for the potential distribution due to a circular disc condenser with arbitrary spacing parameter к (the ratio of separation of the discs to their radius). This was simpler to calculate than the formulation which I gave in [8: 1949]; but unfortunately it fails to satisfy two requirements, as the present paper shows. Together with [8], this paper shows that the potential formulated in [8] satisfies all requirements.

MSC classification

Secondary: 31B20: Boundary value and inverse problems
Type
Research Article
Information
Mathematika , Volume 37 , Issue 2 , December 1990 , pp. 217 - 231
Copyright
Copyright © University College London 1990

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1. Atkinson, W. J., Young, J. H. and Brezovich, I. A.. An analytic solution for the potential due to a circular parallel plate capacitor. J. Phys. A: Math. Gen., 16 (1983), 2837–2841.Google Scholar
2. Chew, W. C. and Kong, J. A.. Asymptotic formula for the capacitance of two oppositely charged discs. Math. Proc. Cambridge Phil Soc., 89 (1981), 373–384.CrossRefGoogle Scholar
3. Chew, W. C. and Kong, J. A.. Microstrip capacitance for a circular disk through matched asymptotic expansions. SIAM J. Appl. Math., 42 (1982), 302–317.Google Scholar
4. Erdélyi, A., Magnus, W., Oberhettinger, F. and Tricomi, F. G.. Tables of Integral Transforms, vol. 2 (Bateman Manuscript Project, McGraw-Hill, 1954).Google Scholar
5. Fox, L. and Goodwin, E. T.. The numerical solution of non-singular linear integral equations. Phil. Trans. Roy. Soc. London (A), 245 (1953), 501–534. (esp. p. 507 and Table 3).Google Scholar
6. Hutson, R. L.. Modeling electric fields from implanted electrodes. Proc. Int. Syntp. on Cancer Therapy by Hyperthermia and Radiation, Washington D.C. (National Cancer Institute, 1975), 229–230.Google Scholar
7. Hutson, V.. The circular plate condenser at small separations. Proc. Cambridge Phil. Soc., 59 (1963), 211–224.Google Scholar
8. Love, E. R.. The electrostatic field of two circular coaxial conducting disks. Quart. J. Mech. Appl. Math., 2 (1949), 428–451.CrossRefGoogle Scholar