Published online by Cambridge University Press: 16 October 2026
This chapter develops the far-field, or radiation-zone, approximation of classical electromagnetism and uses it to analyze how accelerated charges radiate energy and momentum. Starting from the retarded integral solutions of Maxwell’s equations, it isolates the 1/𝑟 radiation fields, derives compact expressions for 𝐸rad, 𝐵rad, and the radiative Poynting vector, and shows how total radiated power follows from angular integration. Specializing to localized sources leads to the Larmor formula for nonrelativistic point charges and to explicit formulas for radiation from a one-dimensional harmonic oscillator. The chapter then confronts the back-reaction of radiation on the source, introducing the radiation–reaction force, the radiation relaxation time, and a local self-interaction picture, and it discusses the “classical radiation catastrophe” for bound electrons. Finally, it contrasts radiating, time-dependent currents with steady currents, introduces the energy density carried by radiation from extended current distributions, and describes the geometric–optics picture of radiation in terms of phase fronts and plane waves, before closing with problems.
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