On the boundary-value problem of a spheroid
Author:
John G. Fikioris
Journal:
Quart. Appl. Math. 31 (1973), 143-146
DOI:
https://doi.org/10.1090/qam/99707
MathSciNet review:
QAM99707
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Abstract |
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Abstract: The surface charge density of a charged spheroid is obtained in exact, closed form using a Green’s function expansion in spherical coordinates. The possibility is thus established of solving boundary-value problems analytically using coordinates that do not correspond to boundary shapes. The present approach, used previously in numerical solutions of related problems, requires the potential function to be constant in the interior of the conductor. Its advantages from the theoretical standpoint and its further possibilities are discussed.
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P. C. Waterman, Symmetry, unitarity, and geometry in electromagnetic scattering, Phys. Rev. D3, 825–839 (1971)
O. D. Kellogg, Foundations of potential theory, Dover Publications, Inc., New York, N. Y., Chapter XI (1953)
J. D. Jackson, Classical electrodynamics, John Wiley & Sons, Inc., New York, N. Y., Chapter 1 (1962)
P. M. Morse and H. Feshbach, Methods of theoretical physics, McGraw-Hill Book Company, Inc., New York, N. Y., pp. 1274 and 1284–96 (1953)
W. R. Smythe, Charged right circular cylinder, J. Appl. Phys. 27, 917–920 (1956)
W. R. Smythe, Charged sphere in cylinder, J. Appl. Phys. 31, 553–556 (1960)
P. C. Waterman, Matrix formulation of electromagnetic scattering, Proc. IEEE 53, 805–812 (1965)
P. C. Waterman, Symmetry, unitarity, and geometry in electromagnetic scattering, Phys. Rev. D3, 825–839 (1971)
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Article copyright:
© Copyright 1973
American Mathematical Society
