Electromagnetic Fields of a Uniform Sphere in a Uniform Conducting Medium withApplication to Dipole Sources

摘要

Vector spherical harmonic expansions are developed for the electromagnetic fieldof a uniform sphere in a uniform conducting medium in the presence of an arbitrary localized distribution of current. The source is either interior to or exterior to the sphere. Explicit expressions then are developed for all cases for magnetic and current dipole sources, and a complete numerical treatment is given for the case of exterior dipole and field point. The general treatment includes the transverse electric-transverse magnetic representation of the electromagnetic field in a source-free region, and demonstration of the formation of the electric and magnetic field vectors from E . r and B . r alone. General expressions are given relating the scattered field expansion coefficients to the source expansion coefficients, including the special case of a perfectly conducting sphere. The specialized treatment of dipole sources includes explicit expressions for the electric and magnetic field components both interior to and exterior to the sphere, for either internal or external dipoles, for the general ac case and for the dc limit. The detailed treatment of the dipole sources includes various series and asymptotic representations of the Bessel functions which are incorporated into Hewlett-Packard Basic 3.0 codes for the calculation of the dipole field components for the ac and dc cases for exterior dipole and field point.