THE EXTERIOR PROBLEM FOR THE VECTOR WAVE EQUATION IN AN INHOMOGENEOUS ANISOPTROPIC MEDIUM
BOEING SCIENTIFIC RESEARCH LABS SEATTLE WA
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The vector wave equation for an electromagnetic field outside a perfectly conducting sphere situated in an inhomogeneous an isotropic medium is reduced, by means of a dyadic Stratton-Chu formula, to an equivalent vector integral equation. The anisotropy is presumed to arise from a magnetic dipole at the center of the sphere, so that the kernel of the integral equation consists of the inner product of the appropriate conductivity tensor and the Greens dyadic in a form due to C. T. Tai for a sphere in free space. The spherical vector wave functions involved are discussed, and various transformations are applied to render the vector integral equation more tractable. Finally, the vector system is reduced to a single scalar integral equation apparently more suited to numerical solution through proper redefinition of the domain of integration.
- Electricity and Magnetism