Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

Online ISSN 1552-4485; Print ISSN 0033-569X



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 | References | Additional Information

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.

References [Enhancements On Off] (What's this?)

  • [1] O. D. Kellogg, Foundations of potential theory, Dover Publications, Inc., New York, N. Y., Chapter XI (1953)
  • [2] John David Jackson, Classical electrodynamics, 2nd ed., John Wiley & Sons, Inc., New York-London-Sydney, 1975. MR 0436782
  • [3] Philip M. Morse and Herman Feshbach, Methods of theoretical physics. 2 volumes, McGraw-Hill Book Co., Inc., New York-Toronto-London, 1953. MR 0059774
  • [4] W. R. Smythe, Charged right circular cylinder, J. Appl. Phys. 27 (1956), 917–920. MR 0079946
  • [5] W. R. Smythe, Charged sphere in cylinder, J. Appl. Phys. 31 (1960), 553–556. MR 0109610
  • [6] P. C. Waterman, Matrix formulation of electromagnetic scattering, Proc. IEEE 53, 805-812 (1965)
  • [7] P. C. Waterman, Symmetry, unitarity, and geometry in electromagnetic scattering, Phys. Rev. D3, 825-839 (1971)

Additional Information

DOI: https://doi.org/10.1090/qam/99707
Article copyright: © Copyright 1973 American Mathematical Society

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