Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

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



Electromagnetic field in the source region of continuously varying current density

Author: John G. Fikioris
Journal: Quart. Appl. Math. 54 (1996), 201-209
MSC: Primary 78A25
DOI: https://doi.org/10.1090/qam/1388012
MathSciNet review: MR1388012
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Abstract: Continuity, analyticity, and the singular points of the vector potential A and the field vectors H, E in a spherical source region $ \nu $ are investigated thoroughly for, practically, any continuous current density distribution J in $ \nu $. In other words, this is a study of the inhomogeneous Helmholtz equation in $ \nu $. Explicit results for A, H, E are obtained by direct integration, extending previous results for constant density in $ \nu $ to continuously varying ones. The importance of imposing the Hölder condition on J to insure existence of E and of certain second derivatives of A is explicitly demonstrated by a specific continuous J, violating this condition at a point; it is then seen that E and some second derivatives of A do not exist, tending to infinity, at that point.

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  • [1] O. D. Kellogg, Foundations of Potential Theory, Dover Publ., New York, 1953
  • [2] C. Müller, Foundations of the Mathematical Theory of Electromagnetic Waves, Springer-Verlag, Berlin, New York, 1969
  • [3] J. G. Fikioris, Electromagnetic fields inside a current-carrying region, J. Math. Phys. 6, no. 11, 1617-1620 (1965)
  • [4] J. G. Fikioris, The electromagnetic field of constant-density distributions in finite regions, J. Electromagnetic Waves and Applications 2, no. 2, 141 153 (1988); also, Erratum, J. Electromagnetic Waves and Applications 5, no. 9, 1035 (1991)
  • [5] S. W. Lee, J. Boersma, C. L. Law, and G. A. Deschamps, Singularity in Green's function and its numerical evaluation, IEEE Trans. Antennas Propag. AP-28, no. 3, 311-317 (1980)
  • [6] J. Boersma and P. J. de Doelder, Closed-form evaluation of the wave potential due to a spherical current source distribution, Dept. Math., Eindhoven Univ. Technol., Memo. 1979-11, Oct. 1979
  • [7] R. E. Collin, The dyadic Green's function as an inverse operator, Radio Science 21, no. 6, 883-890 (1986)
  • [8] J. Van Bladel, Singular Electromagnetic Fields and Sources, Clarendon Press, Oxford, 1991
  • [9] J. A. Stratton, Electromagnetic Theory, McGraw-Hill, New York, 1941

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DOI: https://doi.org/10.1090/qam/1388012
Article copyright: © Copyright 1996 American Mathematical Society

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