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

Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: Continuity, analyticity, and the singular points of the vector potential **A** and the field vectors **H**, **E** in a spherical source region are investigated thoroughly for, practically, any continuous current density distribution **J** in . In other words, this is a study of the inhomogeneous Helmholtz equation in . Explicit results for **A**, **H**, **E** are obtained by direct integration, extending previous results for constant density in 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.

**[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

Retrieve articles in *Quarterly of Applied Mathematics*
with MSC:
78A25

Retrieve articles in all journals with MSC: 78A25

Additional Information

DOI:
https://doi.org/10.1090/qam/1388012

Article copyright:
© Copyright 1996
American Mathematical Society