The potential distribution in a constricted cylinder: an exact solution
Authors:
A. M. Rosenfeld and R. S. Timsit
Journal:
Quart. Appl. Math. 39 (1981), 405-417
MSC:
Primary 78A30; Secondary 35J05
DOI:
https://doi.org/10.1090/qam/636244
MathSciNet review:
636244
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Abstract: An exact solution to the Laplace equation is derived for the distribution of electric potential within a long cylinder carrying a circular constriction along its axis. The expression obtained for the potential distribution is reduced to a form which may be readily evaluated and is highly accurate for a ratio of constriction radius to cylinder radius approaching unity. Exact expressions both for the electric current density within the constriction and for the spreading resistance (i.e., the increase in resistance of the cylinder due to constriction of current flow lines) are also obtained.
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M. Abramowitz and I. A. Stegun, Handbook of mathematical functions, Dover, New York, 1972
W. R. Smythe, J. Appl. Phys. 23, 170 (1952)
L. C. Roess, Theory of spreading conductance, Appendix A of an unpublished report of the Beacon Laboratories of Texas Company, Beacon, New York
A. M. Clausing, University of Illinois Department of Mechanical and Industrial Engineering, ME Technical Report 242-2, Urbana, 1965
R. S. Timsit, J. Phys. D, Appl. Phys. 10, 2011 (1977)
F. Llewellyn-Jones, The physics of electrical contacts, Oxford Press, 1957
I. N. Sneddon and R. P. Srivastav, Proc. Roy. Soc. Edin. A66, 150 (1964)
G. N. Watson, A treatise on the theory of Bessel functions, Cambridge University Press, 1966
F. G. Tricomi, Integral equations, Interscience, New York, 1957
I. S. Gradshtyn and I. M. Ryzhik, Table of integrals, series and products, Academic Press, New York, 1965
W. R. Smythe, Phys. Fluids Vol. 7, 633 (1964)
M. Abramowitz and I. A. Stegun, Handbook of mathematical functions, Dover, New York, 1972
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Article copyright:
© Copyright 1981
American Mathematical Society
