Classical Electrodynamics

Citation

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

Chapter Summary

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

Introduction and Survey

A short opening section surveys several foundations:

• 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
• the idealizations used in electromagnetism

Chapter 1: Introduction to Electrostatics

The chapter starts with Coulomb's law, the electric field, Gauss's law and the scalar potential. It then moves to the 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 opening says most readers will find much of it review, so the book does not start from first principles.

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

Two chapters cover solving for potentials. Chapter 2 starts with the method of images. It then treats 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. It covers Legendre polynomials, associated Legendre functions, spherical harmonics, the addition theorem and Bessel functions. It also expands 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. Topics include 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 chapter opens with the Biot–Savart law, Ampère's law and the vector potential. Next come the force, torque and energy of a localized current distribution, and the macroscopic equations with their boundary conditions. Later sections cover magnetic shielding, numerical methods for two-dimensional fields, Faraday's law, field energy, inductances and eddy currents. The publisher notes that this edition moved Faraday's law and quasi-static fields into this chapter, alongside magnetostatics.

Chapter 6: Maxwell Equations, Macroscopic Electromagnetism, Conservation Laws

The chapter begins with Maxwell's displacement current and the full equations. It then covers potentials, gauge transformations (Lorenz and Coulomb gauges), Green functions for the wave equation and retarded solutions. Next it derives macroscopic electromagnetism and Poynting's theorem. It also treats how fields and sources behave 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

The chapter covers plane waves in a nonconducting medium, polarization and Stokes parameters, and reflection and refraction. It also treats frequency dispersion in dielectrics, conductors and plasmas. Further sections cover 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

Topics include fields at conducting surfaces and waveguides of rectangular and general cylindrical cross-section. The chapter also covers 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 brings together radiation from localized sources. It runs 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 these methods to scattering at long wavelengths, including Rayleigh's explanation of the blue sky. It also covers 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. It covers Lorentz transformations, four-velocity, Thomas precession and the covariance of electrodynamics.

Chapter 12 treats Lagrangians and Hamiltonians for a charged particle and motion in static fields. It also covers adiabatic invariants, the Darwin Lagrangian, stress tensors and conservation laws.

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

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

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 choosing 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: the 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. The opening survey of the Maxwell equations sets out the organizing view early.
• Systematic treatment of solution methods. Three chapters cover potentials and boundary-value problems. They teach images, Green functions, separation of variables in three coordinate systems and an introduction to finite elements. The result is 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. The publisher counts over 110 new problems in this edition.
• Still adopted in current courses. Both Spring 2025 graduate courses described below list this third edition as a textbook.

Limitations

• Not a first course. Chapter 1 calls its own material largely review for most readers, and the publisher describes the book as a graduate-level text. Readers without undergraduate electromagnetism and vector calculus will need another book first.
• Two systems of units. Chapters 1–10 use SI units and the later chapters use Gaussian units, so readers must switch between systems. The appendix on units and dimensions includes conversion between SI and Gaussian.
• Numerical methods are brief. Numerical techniques appear only as short sections, such as finite element analysis in Chapter 2 and numerical methods for magnetic fields in Chapter 5. They are not a continuing thread.
• Too long for one course. At 832 pages and sixteen chapters, the book is usually taught in selected chapters. Chapters 13, 15 and 16 treat narrower topics.
• Listed with companion books. Both courses below name other books alongside Jackson, though in different roles.

Where It Fits in the Course

Jackson is the graduate-level treatment in this course list.

• Gentle first introductions: Fleisch's A Student's Guide to Maxwell's Equations and the electromagnetism volume of OpenStax's University Physics.
• Calculus-based first serious course: Purcell and Morin's Electricity and Magnetism.
• Natural step before Jackson: Griffiths's Introduction to Electrodynamics, the comprehensive advanced-undergraduate text.
• Specialized sequel: Bittencourt's Fundamentals of Plasma Physics, which applies electromagnetism to charged-particle motion, kinetic theory and waves in plasmas. Jackson's Chapters 7 and 12 are relevant background for it.

In actual courses, the link with Griffiths is looser than a strict sequence. The two courses below pair the books in different ways, and neither says Griffiths must be read first.

How to Use This Book

Take Jackson after a full undergraduate course in electricity and magnetism. You should also have a mathematical methods course that covers partial differential equations, special functions and vector analysis. Use Chapter 1 as a check: 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. Use Chapters 2–3 as practice in solving boundary-value problems; Chapters 5–7 are 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, and use the end-of-chapter references for further reading. Check which unit system a chapter uses before comparing formulas across chapters.

How current courses use it

Both course titles below carry "I," and both use the edition listed here. Lehigh's syllabus dates it Wiley, 1999; the 1998 date in the citation above is for the same third edition. Neither the SMU course page nor the Lehigh syllabus gives a full chapter-by-chapter Jackson schedule, so follow your own instructor's assignments.

• SMU, Physics 7311 Electromagnetic Theory I (Spring 2025; course page):
  • Role: Jackson is the only book under "Text," which makes it the primary textbook. The page does not explicitly designate it a required textbook.
  • Assigned reading: the one explicit Jackson reference is §1.12, paired with Feynman Lectures 2-19 for variational techniques. This connects to the variational approach at the end of Chapter 1.
  • Other topics: the lecture resources also cover Green functions, conformal mapping, relativity-related material, hidden momentum, superconductivity, radiation from accelerated charges and ponderomotive force. The page does not tie these topics to Jackson chapters.
  • Recommended reading: Griffiths, Lorrain and Corson's Fundamentals of Electromagnetic Phenomena, and Haus and Melcher's Electromagnetic Fields and Energy.
• Lehigh, Physics 421 Electricity and Magnetism I (Spring 2025; syllabus):
  • Role: the syllabus describes a graduate class. It lists Jackson together with Griffiths's 4th edition (2013) and does not say which is primary or how the two divide the work.
  • Course topics: electrostatics, magnetostatics, Maxwell's equations, charged-particle dynamics, multipole fields and the potential formulation.
  • Detailed goals: Coulomb's and Gauss's laws; Laplace's equation, Green's theorem and boundary-value problems; polarization in materials; the Biot–Savart law and vector potential; Ampère's and Faraday's laws; the Lorentz force; charge conservation; and gauge transformations.
  • Chapter coverage: these goals overlap with the early chapters summarized above, but the syllabus gives no chapter numbers.
  • Homework: set through CourseSite, so the syllabus does not show which Jackson problems are assigned.

Read selectively, following your course, rather than cover to cover.