Transverse Solutions of the Vector Laplace and Helmholtz Equations for Spherical Coordinates and Boundary Conditions with Azimutal Symmetry

摘要

A scalar field method to obtain transverse solutions of the vector Laplace and Helmholtz equations in spherical coordinates for boundary-value problems with azimutal symmetry is described. Neither scalar nor vector potentials are used. Solutions are obtained by use of separation of variables instead of dyadic Green's functions expanded in terms of vector spherical harmonics. Applications to the calculations of magnetic fields from steady and oscillating localized current distributions are presented.