*Modern Electrodynamics* is a recent entry into the list of texts available for a first-year graduate course in electricity and magnetism, a rite of passage for every beginning physics graduate student. The consequences of Maxwell's equations connect experiment and theory across a wide range of disciplines and scales in contemporary physics research, from devising field configurations to contain plasmas or hold single electrons to using electromagnetic probes to deduce the structures of the early universe. The subject matter is not always easy to grasp. It requires both mathematical facility and physical insight. Zangwill provides a quotation from Max Planck to begin Chap. 15 on general electromagnetic fields: “When we turn our attention to the general case of electrodynamics…our first impression is surprise at the enormous complexity of the problems to be solved.” However, in my course using Zangwill's text I conclude the syllabus with the observation that “The material is formidable, but truly worth mastering.”

Zangwill, a condensed matter theorist, has taken a different point of view in developing his text than most of his recent predecessors. Condensed matter physics and biological physics present some challenging applications of electromagnetic theory in understanding the energetics of charge transport or magnetic dipole orientation in cells or novel materials. Zangwill covers the important conventional topics of classical electrodynamics, but enlivens his discussion with well-chosen examples from a range of current topics to justify the adjective “Modern” in the title.

The challenge of understanding classical electrodynamics has attracted extraordinarily talented investigators over the past four centuries. Zangwill supplies quotes and examples from early biological physics investigators (Galvani studying electrical stimulation of frogs) through the amazing experimental achievements of Priestly, Ampère, and Faraday in delineating the fundamental properties of electrical and magnetic forces and into our time. Each chapter has a section entitled Sources, References, and Additional Reading that contains intriguing articles and books. Many of the entries in those sections were new to me, and I found them well worth exploring. Zangwill writes as a story-teller as well as physics lecturer. In discussing the concept of the Faraday cage, he quotes from Faraday's diary about building a cube 12 ft on a side, covered with tinfoil and copper wire. Faraday went inside and had the conducting surface charged by a static electric generator, while he looked for evidence of a field. This was no microscopic investigation of the Faraday cage concept. The book also boasts some superb graphics, like the figure showing Maxwell's depiction of the field lines and equipotentials at the edge of a long parallel plate capacitor.

The preface gives insight into the somewhat idiosyncratic structure of the text. Zangwill experimented with different organizational styles. The current version presents material—998 pages worth—in a style that he finds most logical. Overall, the organization is traditional, beginning with mathematical preliminaries. Statics and dynamics are treated separately, then unified via special relativity. Each chapter has a generous set of problems, chosen from a wide variety of sources. Some problems are quite specific, aiming to elucidate one particular point in the text. Others invite the student to expand his/her understanding of the link between electrical and magnetic fields such as a problem showing that there is an electrostatic equivalent of the magnetic Helmholtz coil configuration. A few problems present significant challenges in identifying the physics needed to make a solution.

Some of the material presented is quite innovative and non-traditional. Because physics graduate programs in many institutions have students heading into diverse specialties via interdisciplinary research, these expansions of topics are a real strength of this text. Examples of this sort are discussions of the energy barrier for a potassium ion in aqueous solution to move through a channel in a low-dielectric protein tubule and of the relation between Fick's law for the diffusion current of charge carriers and the resting potential across a cell wall due to potassium ion diffusion.

Using the text has presented me with some unexpected challenges. Zangwill notes that each instructor will want to decide on topics and order of presentation—always true, of course. What is different here is that topics pop up in pieces in unexpected places, to be referenced several chapters later in a different discussion. One such case is the treatment of the expansion of 1/|**r – r′**| in spherical polar coordinates. I would expect to find this as part of a systematic treatment of formal solutions to the Laplace equation in potential theory. Zangwill not only introduces it three chapters before his potential theory section but also relegates formal treatment of spherical harmonics, Legendre functions, and Bessel functions to an Appendix. This discontinuity in treatment can be solved, of course, by appropriate course notes. However, the scattered nature of the material here, in contrast to more coherent presentations in other texts, bothered some of my students. Another surprise is the treatment of stored energy in electrostatic or magnetostatic fields for: (a) a source-free configuration and (b) an attached charge or current source. Zangwill introduces a Legendre transformation to modify the source-free energy in going from (a) to (b), rather than making a physics argument based on the difference in what constitutes an isolated system in the two configurations. Using a Legendre transformation to introduce the additional energy term may be natural from a condensed matter point of view, but it does not seem to me to contribute to the clarity of this important discussion. Zangwill's use of the Minkowski metric in the discussion of special relativity is also unusual.

For a book entitled *Modern Electrodynamics*, I am disappointed at the mere passing mention of computational electrodynamics, rather than a serious treatment of the power of computational approaches to static and dynamic real-world problems. The accuracy of the electromechanical and magnetostatic force calculations by such methods makes possible the design of large superconducting magnets for MRI scanners and particle accelerators and detectors, for example.

The classic electrodynamics text for the past four decades has been the monumental work by J. D. Jackson, the book from which most current-generation physicists took their first course. In Jackson's work, the examples are sophisticated and fine points of the physics are often relegated to problems. The Zangwill approach is different. For example, he compares the average of quantum calculations with classical models for material properties like dielectric constants, magnetic permeability, and skin depth in conductors; areas in which the classical approximation of an abrupt change at a surface is unphysical but nevertheless gives a good description of observations for distances large compared with atomic sizes. The quantum computations demonstrate that the distance scale for field variations from equilibrium values inside and outside material is indeed characterized by an atomic distance scale, justifying the classical approach. While I find that Zangwill's presentation is frequently not as thorough as that of Jackson on a given topic, Zangwill's approach is easier for a beginning student to navigate. I am happy to have both resources on my bookshelf.

*James S. Russ is professor of physics at Carnegie Mellon University. His research area is experimental high energy physics. In his career, he has been involved in building and testing many pieces of experimental equipment that rely heavily on the topics discussed in this book.*