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Note on an electrified circular disk situated inside a coaxial infinite hollow cylinder*

Published online by Cambridge University Press:  24 October 2008

I. N. Sneddon
I. N. Sneddon
Affiliation:
The UniversityGlasgow, W.2
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Extract

In a recent paper Collins (l) has shown that Copson's method of solution of the problem of determining the electrostatic field due to an electrified disk (2) can be extended to determine the surface charge density induced on an electrified disk when it is situated inside an earthed coaxial infinitely long hollow cylinder. In Collins's solution the problem is reduced to that of solving a Fredholm integral equation of the second kind. The object of the present note is to show that Collins's solution can be obtained more simply by making use of a technique in the theory of dual integral equations developed recently by the author (3) and Copson(4).

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 58 , Issue 4 , October 1962 , pp. 621 - 624
Copyright
Copyright © Cambridge Philosophical Society 1962

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References

REFERENCES

(1)Collins, W. D., Proc. Cambridge Philos. Soc. 57 (1961), 623–;627.CrossRefGoogle Scholar
(2)Copson, E. T., Proc. Edinburgh. Math. Soc. (2), 8 (1947–1950), 14–19.Google Scholar
(3)Sneddon, I. N., Proc. Glasgow Math. Assoc. 4 (1960), 108–110.Google Scholar
(4)Copson, E. T., Proc. Glasgow Math. Assoc. 5 (1961), 21–24.CrossRefGoogle Scholar
(5)Erdélyi, A. et al. , Tables of integral transforms (McGraw-Hill; New York, 1954).Google Scholar
(6)Cooke, J. C., and Tranter, C. J., Quart. J. Mech. Appl. Math. 12 (1959), 379–385.CrossRefGoogle Scholar