This chapter provides a comprehensive treatment of electromagnetic radiation, focusing on how time-varying charge and current distributions generate fields that can propagate independently through space, carrying energy to infinity. It begins by deriving the general solutions to Maxwell’s equations in the presence of time-dependent sources, introducing the concept of retarded potentials (Liénard–Wiechert potentials) to account for the finite speed of light and the causal relationship between sources and fields. The chapter then analyzes the electromagnetic field generated by a point charge, demonstrating that only an accelerating charge produces radiation fields that decay as 1/r and transport energy to large distances. It distinguishes between near fields (which behave like static fields at short distances) and far fields (radiation fields), emphasizing that the latter are responsible for electromagnetic radiation. Generalizing from a point charge, the chapter develops expressions for the radiation fields produced by arbitrary time-varying charge and current distributions confined within a finite volume. It introduces the Poynting vector to quantify the radiated power and its angular distribution, defining the radiation pattern as a key characteristic of emitting systems like antennas. A significant portion is dedicated to electric dipole radiation, which represents the dominant term in the multipole expansion for sources much smaller than the wavelength of the emitted radiation. The scalar and vector potentials for electric dipole radiation are derived, leading to the expressions for the electric and magnetic radiated fields, which exhibit the structure of a quasi-plane wave propagating radially. Larmor’s formula for the total power radiated by an accelerating charge is derived, and its implications for classical atomic models (e.g., the instability of the classical hydrogen atom) are discussed. A significant portion is dedicated to electric dipole radiation, which represents the dominant term in the multipole expansion for sources much smaller than the wavelength of the emitted radiation. The scalar and vector potentials for electric dipole radiation are derived, leading to the expressions for the electric and radiated magnetic fields, which exhibit the structure of a quasi-plane wave propagating radially. Larmor’s formula for the total power radiated by an accelerating charge is derived, and its implications for classical atomic models (e.g., the instability of the classical hydrogen atom) are discussed. Finally, the chapter explores the phenomenon of scattering of electromagnetic waves by matter. It details Thomson scattering (scattering by free electrons) and extends the analysis to scattering from atoms and molecules, incorporating Lorentz model to account for the binding forces on electrons. This leads to the derivation of the scattering cross section, which quantifies the effective area for scattering, and explains phenomena like Rayleigh scattering (responsible for the blue color of the sky) and resonant scattering.

Electromagnetic Radiation

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发表日期：

2025年

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Fabian Cadiz,
Arnaud Couairon

摘要

This chapter provides a comprehensive treatment of electromagnetic radiation, focusing on how time-varying charge and current distributions generate fields that can propagate independently through space, carrying energy to infinity. It begins by deriving the general solutions to Maxwell’s equations in the presence of time-dependent sources, introducing the concept of retarded potentials (Liénard–Wiechert potentials) to account for the finite speed of light and the causal relationship between sources and fields. The chapter then analyzes the electromagnetic field generated by a point charge, demonstrating that only an accelerating charge produces radiation fields that decay as 1/r and transport energy to large distances. It distinguishes between near fields (which behave like static fields at short distances) and far fields (radiation fields), emphasizing that the latter are responsible for electromagnetic radiation. Generalizing from a point charge, the chapter develops expressions for the radiation fields produced by arbitrary time-varying charge and current distributions confined within a finite volume. It introduces the Poynting vector to quantify the radiated power and its angular distribution, defining the radiation pattern as a key characteristic of emitting systems like antennas. A significant portion is dedicated to electric dipole radiation, which represents the dominant term in the multipole expansion for sources much smaller than the wavelength of the emitted radiation. The scalar and vector potentials for electric dipole radiation are derived, leading to the expressions for the electric and magnetic radiated fields, which exhibit the structure of a quasi-plane wave propagating radially. Larmor’s formula for the total power radiated by an accelerating charge is derived, and its implications for classical atomic models (e.g., the instability of the classical hydrogen atom) are discussed. A significant portion is dedicated to electric dipole radiation, which represents the dominant term in the multipole expansion for sources much smaller than the wavelength of the emitted radiation. The scalar and vector potentials for electric dipole radiation are derived, leading to the expressions for the electric and radiated magnetic fields, which exhibit the structure of a quasi-plane wave propagating radially. Larmor’s formula for the total power radiated by an accelerating charge is derived, and its implications for classical atomic models (e.g., the instability of the classical hydrogen atom) are discussed. Finally, the chapter explores the phenomenon of scattering of electromagnetic waves by matter. It details Thomson scattering (scattering by free electrons) and extends the analysis to scattering from atoms and molecules, incorporating Lorentz model to account for the binding forces on electrons. This leads to the derivation of the scattering cross section, which quantifies the effective area for scattering, and explains phenomena like Rayleigh scattering (responsible for the blue color of the sky) and resonant scattering.