Radiation of a Hertzian dipole immersed in a dissipative medium

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 (1919) is discussed.