Classical Electrodynamics

Citation

Jackson, J. D. (1998). Classical Electrodynamics (3rd ed.). Wiley.

Chapter Summary

The third edition runs to 832 pages: an introduction and survey, sixteen chapters and an appendix on units and dimensions. Each chapter ends with a list of references and suggested reading and a set of problems. The publisher states that SI units are used in the first ten chapters and Gaussian units are retained in the later ones.

Introduction and Survey

A short opening section surveys the Maxwell equations in vacuum and in macroscopic media, the inverse square law and the mass of the photon, linear superposition, boundary conditions at interfaces, and some remarks on the idealizations used in electromagnetism.

Chapter 1: Introduction to Electrostatics

The chapter covers Coulomb's law, the electric field, Gauss's law and the scalar potential, then moves to Poisson and Laplace equations, Green's theorem, Dirichlet and Neumann boundary conditions and the Green function. It closes with electrostatic energy, a variational approach and a relaxation method for two-dimensional problems. The chapter's own opening says that most readers will find much of it a review, which signals that the book does not start from first principles.

Chapters 2–3: Boundary-Value Problems in Electrostatics: I and II

Two chapters are given to solving for potentials. Chapter 2 starts with the method of images, then Green functions for the sphere, orthogonal functions, separation of variables in rectangular coordinates, and an introduction to finite element analysis. Chapter 3 turns to spherical and cylindrical coordinates: Legendre polynomials, associated Legendre functions and spherical harmonics, the addition theorem, Bessel functions, and expansions of Green functions in these bases.

Chapter 4: Multipoles, Electrostatics of Macroscopic Media, Dielectrics

The multipole expansion and the energy of a charge distribution in an external field lead into dielectrics: the elementary treatment, boundary-value problems with dielectrics, molecular polarizability, models of polarization and electrostatic energy in dielectric media.

Chapter 5: Magnetostatics, Faraday's Law, Quasi-Static Fields

The Biot–Savart law, Ampère's law and the vector potential come first, followed by the force, torque and energy of a localized current distribution and macroscopic equations with boundary conditions. The chapter then covers magnetic shielding, numerical methods for two-dimensional fields, Faraday's law, field energy, inductances and eddy currents. The publisher notes that Faraday's law and quasi-static fields were moved here in this edition, alongside magnetostatics.

Chapter 6: Maxwell Equations, Macroscopic Electromagnetism, Conservation Laws

Maxwell's displacement current and the full equations are followed by potentials, gauge transformations (Lorenz and Coulomb gauges), Green functions for the wave equation and retarded solutions. The chapter then derives macroscopic electromagnetism and Poynting's theorem, and treats the behaviour of fields and sources under rotations, reflections and time reversal. Later sections take up magnetic monopoles, the Dirac quantization condition and polarization potentials.

Chapter 7: Plane Electromagnetic Waves and Wave Propagation

Plane waves in a nonconducting medium, polarization and Stokes parameters, reflection and refraction, and frequency dispersion in dielectrics, conductors and plasmas. Further sections treat propagation in the ionosphere and magnetosphere, magnetohydrodynamic waves, group velocity, pulse spreading and the Kramers–Kronig relations.

Chapter 8: Waveguides, Resonant Cavities, and Optical Fibers

Fields at conducting surfaces, waveguides of rectangular and general cylindrical cross-section, energy flow and attenuation, resonant cavities and their Q, and Schumann resonances. The publisher adds that two sections on optical fibers and dielectric waveguides are new to this edition.

Chapters 9–10: Radiating Systems, Multipole Fields and Radiation; Scattering and Diffraction

Chapter 9 consolidates radiation from localized sources, from the oscillating dipole and the center-fed linear antenna to the exact multipole expansion with its angular momentum and angular distribution. Chapter 10 applies the machinery to scattering at long wavelengths (including Rayleigh's explanation of the blue sky), scattering by a sphere, scalar and vectorial diffraction theory, Babinet's principle and the optical theorem.

Chapters 11–12: Special Theory of Relativity; Dynamics of Relativistic Particles and Electromagnetic Fields

Chapter 11 develops special relativity from Einstein's postulates through Lorentz transformations, four-velocity, Thomas precession and the covariance of electrodynamics. Chapter 12 treats Lagrangians and Hamiltonians for a charged particle, motion in static fields, adiabatic invariants, the Darwin Lagrangian, stress tensors and conservation laws.

Chapters 13–16: Collisions and Energy Loss; Radiation by Moving Charges; Bremsstrahlung; Radiation Damping

These chapters cover energy loss and scattering of charged particles with Cherenkov and transition radiation (13), the Liénard–Wiechert potentials, Larmor's formula, synchrotron radiation, undulators and wigglers, and Thomson scattering (14), bremsstrahlung and the method of virtual quanta (15), and radiation reaction with classical models of charged particles (16).

Key Concepts

Chapters 1–4: Electrostatics and Dielectrics

• Green functions: solutions for a point source used to build potentials for given boundary conditions.
• Boundary-value methods: images, separation of variables and expansions in orthogonal functions.
• Multipole expansion: representing a localized charge distribution by its leading moments.

Chapters 5–8: Magnetostatics, Maxwell's Equations, Waves and Guided Fields

• Gauge transformations: the freedom in the potentials, with the Lorenz and Coulomb gauges as standard choices.
• Poynting's theorem: energy and momentum conservation for the fields and charges together.
• Dispersion and causality: frequency dependence of media and the Kramers–Kronig relations.
• Waveguide modes: field patterns that can propagate in a guide or cavity.

Chapters 9–16: Radiation, Relativity and Charged Particles

• Multipole radiation: emission from localized sources organized by multipole order.
• Lorentz covariance: writing electrodynamics so that it holds in every inertial frame.
• Liénard–Wiechert potentials: fields of a point charge in arbitrary motion.
• Radiation reaction: the effect of emitted radiation on the emitting charge.

Critical Analysis

Strengths

• Coverage. Sixteen chapters take the subject from electrostatics through radiation, relativity and radiation reaction, and the opening survey of the Maxwell equations sets out the organizing view early.
• Systematic treatment of solution methods. Three chapters on potentials and boundary-value problems, with images, Green functions, separation of variables in three coordinate systems and an introduction to finite elements, give a toolbox rather than a list of examples.
• Radiation and relativistic material. Chapters 9–16 cover multipole radiation, scattering, diffraction, relativity, radiation by moving charges and radiation reaction in one place; the synchrotron section includes wigglers and undulators as light sources.
• A built-in reading list and problem set per chapter. Each chapter ends with suggested reading and problems, and the publisher counts over 110 new problems in this edition.

Limitations

• Not a first course. Chapter 1 describes its own material as largely review for most readers, and the publisher describes the book as a text for the graduate-level course. Readers without undergraduate electromagnetism and vector calculus will need another book first.
• Two systems of units. SI units are used in Chapters 1–10 and Gaussian units in the later chapters, so readers must move between systems; the appendix on units and dimensions includes conversion between SI and Gaussian.
• Numerical methods are brief. Numerical techniques appear as short sections (finite element analysis in Chapter 2, numerical methods for magnetic fields in Chapter 5) rather than as a continuing thread.
• Too long for one course. At 832 pages with sixteen chapters, a typical course selects chapters; Chapters 13, 15 and 16 treat narrower topics.

Where It Fits in the Course

Jackson is the graduate-level treatment in this course list. Fleisch's A Student's Guide to Maxwell's Equations and the electromagnetism volume of OpenStax's University Physics are gentle first introductions, and Purcell and Morin's Electricity and Magnetism is a calculus-based first serious course. Griffiths's Introduction to Electrodynamics is the comprehensive advanced-undergraduate text and the natural step before Jackson. Bittencourt's Fundamentals of Plasma Physics is a specialized sequel that applies electromagnetism to charged-particle motion, kinetic theory and waves in plasmas, and Jackson's Chapters 7 and 12 are relevant background for it.

How to Use This Book

Take Jackson after a full undergraduate course in electricity and magnetism and a course in mathematical methods that includes partial differential equations, special functions and vector analysis. Treat Chapter 1 as a calibration: if it reads as review, the book is at the right level.

A practical plan for a two-semester sequence:

• Core, first semester: Chapters 1–8, with Chapters 2–3 as practice in solving boundary-value problems and Chapters 5–7 as the heart of Maxwell theory.
• Core, second semester: Chapters 9–11 and 14, covering radiation, scattering, relativity and radiation from moving charges.
• Optional or selective: Chapter 4's molecular models, the plasma and ionosphere sections of Chapter 7, Chapters 12, 13, 15 and 16, and the finite element and numerical-method sections.

Work problems alongside every chapter; the end-of-chapter references point to further reading. Keep track of which unit system a chapter uses before comparing formulas across chapters.