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

Published online by Cambridge University Press:  24 October 2008

W. D. Collins
W. D. Collins
Affiliation:
King's CollegeNewcastle upon Tyne
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Extract

Copson(1) has shown that the problem of determining the surface density of electric charge induced on a thin circular disk maintained at a constant potential in an external electrostatic field can be solved by two applications of the known solution of Abel's integral equation. This note shows that Copson's method can be extended to determine the surface charge density induced on the disk when situated inside an earthed coaxial infinitely long hollow cylinder. Whilst this problem is not solved in closed form, it is shown to be governed by a Fredholm integral equation of the second kind, which can be solved approximately by iteration when the radius of the cylinder is large compared with that of the disk.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 57 , Issue 3 , July 1961 , pp. 623 - 627
Copyright
Copyright © Cambridge Philosophical Society 1961

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References

REFERENCES

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