Hostname: page-component-78c5997874-ndw9j Total loading time: 0 Render date: 2024-11-09T05:35:00.356Z Has data issue: false hasContentIssue false
  • English
  • Français

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
Get access Rights & Permissions [Opens in a new window]

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

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

REFERENCES

(1)Copson, E. T.Proc. Edinb. Math. Soc. (2), 8 (1947–1950), 14–19.CrossRefGoogle Scholar
(2)Watson, G. N.Theory of Bessel functions (Cambridge, 1922).Google Scholar
(3)Cooke, J. C. and Tranter, C. J.Quart. J. Mech. App. Math. 12 (1959), 379–86.CrossRefGoogle Scholar
(4)Smythe, W. R. J.Appl. Phys. 31 (1960), 553–6.CrossRefGoogle Scholar
(5)Ling, C. B.Quart. Appl. Maths. 10 (1952–1953), 149–56.CrossRefGoogle Scholar
(6)Green, A. E. and Zerna, W.Theoretical elasticity (Oxford, 1954).Google Scholar
(7)Collins, W. D.Quart. J. Mech. App. Math. 14 (1961), 101–17.CrossRefGoogle Scholar