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

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

2004-12-20

arxiv.org/abs/physics/0412127v1

Physics

Classical Physics

Proceedings of The 8th World Multi-Conference on Systemics, Cybernetics and Informatics (SCI 2004), July 2004, Orlando, Florid

Scientific paper

A scalar field method to obtain transverse solutions of the vector Laplace and Helmholtz equations in spherical coordinates for boundary-value problems with azimuthal 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.

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