CLASSICAL MULTIPOLE THEORY

Abstract Multipole expansions are derived of the scalar and vector potentials at a point far from finite static charge and current distributions. Force, torque, and potential energy are expanded in multipole series for these distributions. Also expressed as multipole expansions are the electrodynamic potentials of time-dependent distributions, together with their far- and near-zone limits. Macroscopic media are then considered and macroscopic multipole moment densities introduced, in terms of which bound charge and current densities (both volume and surface) are expressed. The two volume densities are then used in Maxwell's equations to express D and H fields as multipole expansions. The origin dependence of multipole moments, a crucial feature in this book, is considered, and the use of traceless moments shown to be inapplicable in many instances.