Published online by Cambridge University Press: 16 October 2026
This chapter develops a macroscopic description of electric dipole matter and shows how dielectrics are incorporated into classical electromagnetism. Starting from the near field of localized electric dipoles, it coarse-grains to a polarization density P(r,t), derives Maxwell’s equations in dielectric form, and connects the macroscopic polarization field to underlying dipole moments and local fields. Boundary value problems with piecewise constant polarization and permittivity are formulated using Green’s functions and solved for canonical planar and spherical geometries. Specializing to linear, isotropic dielectrics leads to constitutive relations, susceptibility and permittivity, and to the Clausius–Mossotti relation linking microscopic polarizability to macroscopic response. The chapter then analyzes energy storage in dielectrics, capacitance in simple geometries with and without dielectric fillings, and the forces exerted on polarizable media and on individual dipoles. A brief note on spherical harmonics introduces tools needed for multipole expansions and for evaluating fields of polarized spheres.
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