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On the problem of the electrified disc

Published online by Cambridge University Press:  20 January 2009

E. T. Copson
E. T. Copson
Affiliation:
University College, University of St Andrews, Dundee.
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When a perfectly conducting uniform thin circular disc is kept at a potential V0 in an external electrostatic field of potential Φ, electric charge is induced on the surface of the disc; the problem is to find the surface-density σ of this induced charge and its potential V so that the total potential V + Φ has the constant value V0 on the surface of the disc. This problem was first discussed by Green in 1832, and the solution in the case when there is no external field was deduced by Lord Kelvin from the known formula for the gravitational potential of an elliptic homoeoid. The problem is still of interest since similar ideas occur in the theory of diffraction by a circular disc and in the theory of the generation of sound waves by a vibrating disc when the wave-length is large compared with the radius of the disc.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 8 , Issue 1 , October 1947 , pp. 14 - 19
Copyright
Copyright © Edinburgh Mathematical Society 1947

References

page 14 note 1 By σ we mean the total surface density on the two faces of the disc.

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