Bibliography

Wulf A. A., A Collection of Exercises in Electromagnetic Field Theory, 219 pp., price 7 rubles. State Publishing House for Literature on Communications and Radio, Moscow, 1939.

The book under review is a collection of 99 problems with very detailed solutions. Almost every problem is solved in two or even three different ways.

A. A. Wulf’s book is intended for persons studying a course in electromagnetic field theory according to the curriculum of higher technical educational institutions of communications. This circumstance is reflected in the specific selection of problems.

As far as we know, neither in our country nor abroad has a collection of problems in electromagnetic field theory been published. A small collection of problems is given as an appendix to Abraham’s course on the theory of electricity; problems from the field of electromagnetic theory are selected more thoroughly and in the greatest number in the Russian translation of Jeans’s classical course. In these two books, however, the solution of the problems is left to the reader: for the most part only the answer to the problem is given, or the path to the solution is outlined. The acute need for a collection sufficiently extensive in the number of problems for a course in the theory of electromagnetism has not been met by A. A. Wulf’s book. The author set himself the goal of showing, through a number of examples, methods for solving problems in field theory, thus leaving unfilled so significant a gap in the scientific literature on questions of the electromagnetic field as the absence of a problem book.

The distribution of the material by volume in the book under review is very uneven. Of the total volume of 219 pages, constant fields are allotted 180–190 pages. Accordingly, the title of the book should be changed. Electrostatics is allotted 140 pages, i.e., approximately \(2/3\) of the volume of the book. A whole series of the most important questions of field theory is not touched upon at all (for example, induction in linear conductors); only 3 pages are devoted to solving problems by the vector-potential method. The sections set forth on pp. 179–219—the electromagnetic field, the Poynting vector, Maxwell’s equations, the vector potential—as is clear from comparing the list of sections with the space assigned to them, cannot give and do not give the student any conception of the methods for solving the corresponding problems. These pages could be removed from the book almost without being noticed, without detriment to its content.

Thus we regard A. A. Wulf’s book as a collection of exercises devoted to electrostatics (pp. 3–143) and to calculations in different systems of units (pp. 144–179).

In the section on electrostatics, 33 pages are devoted to the field of a uniformly charged sphere, the most elementary problem in electrostatics. In his calculations the author is tiresomely detailed. All computations are carried out down to trifles (for example, on p. 8 the following chain of equalities:

\[ \frac{1}{r^2}\frac{d}{dr}(r^2 E)=0, \]

\[ \frac{d}{dr}(r^2 E)=0,\qquad r^2E=C,\qquad E=\frac{C}{r^2}\ \text{etc.}). \]

The author’s mathematical exposition, without loss for the average student’s understanding, could have been compressed by half. The solutions, given over these 33 pages, of the equation \(\operatorname{div} E = 4\pi\rho\) are, in our opinion, superfluous: students, undoubtedly, should be given some conception of solving problems by means of differential equations for the potential, and therefore it is natural to demonstrate to them the application of this equation to a more easily solved problem; as for the equation \(\operatorname{div} E = 4\pi\rho\), the student will certainly not have to encounter its application, and therefore there is no point in presenting this method of solution.

The remaining 76 pages of the section on electrostatics in vacuum are devoted to computing the field of one and two cylinders. The exposition suffers from the same shortcomings: excessively detailed calculation, and the solution of a problem, in addition to the simple method, by a second—complicated—method that has no practical significance.

Even in this, the most thoroughly presented section of the collection, a number of the most important methods for solving problems are omitted (the method of images, conformal mapping), and here the author does not give the student a complete survey of the methods of field theory. It is also quite obvious that on 219 pages, by means of making the mathematical language more concise, the volume of the material presented could have been considerably increased.

The sections “dielectrics” and “calculations in various systems of units” suffer from the same shortcomings, though to a somewhat lesser degree. Our pedagogical experience, however, allows us to doubt the necessity of introducing the cumbersome systematics used by the author in the chapter “Systems of Units.”

A number of particular questions considered for the problems mentioned should not have been posed: for example, why prove (problem 33), for a special case, the general proposition that the integral \(\int E_l\,dl\) does not depend on the path of integration, or (problem 15) prove that vectors of the type \(f(r)\mathbf r\) are potential vectors, if it is known that \(\operatorname{rot} f(r)\mathbf r = 0\). Here it is appropriate to note that the author does not use vector analysis in the calculations. For a course in field theory this is a fundamental shortcoming. In some problems (for example, 82–83) the author does not dwell sufficiently on the limits of applicability of the simplified solutions.

Special mention should be made of the author’s extremely ponderous and, to say no more, unliterary language. Let us cite a few quotations (p. 29): “Three fluxes through three faces will be accompanied by a minus sign”; (p. 110) “… for the molecule they take \(p = \beta E\), and for \(1\ \mathrm{cm}^3\) of dielectric they make \(P = kE_m\)”; (p. 61) “… the difference is only that (4) is written in complex form, where the components along the axes of the real and imaginary parts are visible, while (13) is written in symbolic form, when the modulus and argument of a complex expression are visible,” and so on, on every page.

On the whole, we consider A. A. Wulf’s book unsuccessful. Owing to the complete absence of similar literature, the book will evidently find wide circulation. It will nevertheless bring some benefit to the student. In a reprint, should one follow, A. A. Wulf’s exercise collection on electromagnetic field theory must be fundamentally reworked.

A. Kitaigorodsky, Moscow