Bibliography

J. A. Stratton, Electromagnetic Theory. Pp. XV + 615. McGraw-Hill Book Comp., New York and London, 1941.

Stratton’s book represents a significant event in the physics literature. As is clear from the title, it is a course in electromagnetic field theory. However, it is not an elementary course intended for beginners; to study it, one must already have familiarity with the general exposition of field theory. The author’s point of view, formulated in his preface, is as follows. The textbooks existing in Anglo-American literature, beginning with Maxwell’s classic Treatise, are characterized by the fact that their chief attention is devoted to electrostatics and direct current. Thus, in Maxwell’s book, only a few of the 1,000 pages in the entire book are devoted to the general equations of the field, the propagation of plane waves, and electromagnetic theory of light. The same, approximately, is the character of Jeans’s very widespread textbook in England and America. In contrast to this, Stratton set himself the task of giving “a more adequate exposition of the theory of the variable electromagnetic field and of the propagation of waves. Some attention is also given to the stationary state, but for the purpose of introducing the fundamental concepts under simpler conditions and always with a view to their later applications in general cases” (Preface, p. V).

In accordance with this formulated point of view, the book is constructed as follows:

Chapter I, “Field Equations.” Here, in the first section, the Maxwell equations are first postulated, written at first in differential and then in integral form. In the next section the macroscopic properties of matter are taken into account (the coefficients \(\varepsilon\) and \(\mu\), electric and magnetic polarization, conductivity).

Next the electromagnetic potentials are introduced—the scalar and the vector. In §§ 1.13 the boundary conditions are established. The following section (§§ 1.14—1.19) is devoted to curvilinear coordinates; after deriving the basic formulas, the field equations are written in general orthogonal coordinates, and the properties of various concrete coordinate systems are considered in detail (cylindrical, spherical, elliptic, parabolic, etc.—8 different systems in all).

The last section of the first chapter is “Field Tensors.” In this section the elements of tensor analysis are presented, after which the field equations are reduced to four-dimensional symmetric form and the foundations of the special theory of relativity are set forth.

The foregoing survey of the contents of the first chapter already sufficiently characterizes the book. The next chapter, II, is “Stresses and Energy.” The task of this chapter is formulated as follows: “In order to reconcile the mathematical structure developed in the preceding chapter with experiments that can be performed in the laboratory, we must be able to calculate the mechanical forces experienced in the field by elements of charges and currents, and also by neutral bodies. In the present chapter will be...

it is shown how, by a suitable choice of the vectors \(E\) and \(B\), these forces can be derived directly from Maxwell’s equations.”

The next two chapters, III and IV, are devoted to static fields—electric and magnetic. Beginning with Chapter V and to the end of the book (pp. 268–569), questions of wave propagation are considered in connection with electric waves and radiation. The extensive and interestingly composed Chapter V is devoted specifically to plane waves. The properties of plane waves of general type are investigated, as well as harmonic waves in space and time in nondissipative and dissipative media. Along the way, mathematical questions are set forth: an analysis of the Fourier transform and of the Laplace transform. We note the exceptionally careful and rigorous exposition of the difficult question of the velocities of propagation of plane waves (phase velocity, group velocity, and signal velocity). In the following two chapters cylindrical and spherical waves are examined in detail.

In the introduction to these chapters it is pointed out that, whereas the scalar three-dimensional wave equation separates in eleven different coordinate systems, the complete solution of the vector wave equation in a form suitable for solving boundary-value problems is known only for certain separable cylindrical coordinates and for spherical coordinates. These chapters are devoted to the exposition of the corresponding mathematical methods, which are of great importance for modern radio engineering.

Chapter VIII is “Radiation.” Chapter IX is “Boundary-Value Problems.” Here the theory of reflection and refraction for dielectrics and metals is given, the propagation of waves along wires and inside conductors is examined, the problem of the diffraction of plane waves by a sphere is solved, including the theory of light scattering, and finally the influence of the earth on the propagation of electromagnetic waves is discussed.

The book is furnished with a large number of interesting, though difficult, problems, borrowed chiefly from the original literature. These problems are not merely exercises in mathematical calculation, but have an entirely concrete physical or technical character. Such, too, is the general character of the whole book: the reader is always clear as to the purpose for which it is necessary to consider one or another complicated question; a large number of practical applications are shown in special paragraphs or in the problems; the formulas are carried through to numerical coefficients. Any physicist engaged in optics or in electromagnetic oscillations, as well as any radio engineer, on leafing through this book, will feel the desire always to have it at hand, to study it and use it for reference, since it at once becomes clear that the labor spent in studying this book will be amply repaid by the benefit it brings.

E. Shpolsky