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IEEE Transactions on Antennas and Propagation
Volume 48 Number 10, October 2000

Radiation of a Hertzian Dipole Immersed in a Dissipative Medium

Page 1501.

Abstract:

The general radiation formula for a Hertzian dipole immersed in an isotropic dissipative medium of infinite extent has been derived. As a boundary condition of the source, it is assumed that the dipole moment is a given quantity. When the conductivity of the medium is finite, the total radiating power is found to be infinite. Thus, in order to define a finite physically meaningful quantity, the dipole must be"insulated."The total radiating power is then a function of the thickness of the insulator and the constants of the media. When the radius of the spherical insulator is large compared to a wavelength, the reflection coefficient of the wave traveling from the dielectric to the dissipative medium with the dipole as a source reduces to that of a plane wave as derived from Fresnel's equations. The similarity between this and the problem by Weyl is discussed in this paper.

References

1. H. Weyl, "Ausbreitung elektromagnetischer Wellen über einem ebenen Leiter", Ann. Phys., vol. 60, pp.  481-500,  1919.
2. P. Frank and R. v. Mises, Differential gleichungen der Physik, New York: Rosenberg, 1943,vol. 11, pp.  953-963. 
3. A. Sommerfeld, "Über die Ausbreitung der Wellen in der drohtlosen Telegraphie", Ann. Phys., vol. 28, pp.  665-756,  1909.
4. J. A. Stratton, Electromagnetic Theory, New York: McGraw-Hill, 1941.