I= JPVdv - IEEE Xplore

IEEE TRANSACTIONS ON EDUCATION, VOL. E-23, NO. 2, MAY 1980

125

Book Reviews Engineering Electromagetics-W. H. Hayt (New York: McGrawHill, 1974, 3rd ed., 487 pp., $25.50). Reviewed by A. David Wunsch. Engineering Electromagnetics by W. H. Hayt must be one of the most popular intermediate level books on electromagnetic theory written for electrical engineering students. Although this text has some serious defects which I will discuss, it is very well liked by my students at the University of Lowell. We have used it for the past ten years, in various editions, for a two-semester course. One year we switched to the Durney and Johnson text [11 and the outcry of the students was so great that we reverted back to our old book. Hayt's popularity is not hard to explain. The author has recognized that he is treating a difficult and often sterile subject and has written a book pitched at a slightly lower level than its competitors. His writing is clear and succinct. Most of the required mathematics, beyond freshman calculus, is developed in the first chapter or is spread in a leisurely way throughout the book. What makes this text special, however, is the way in which it is designed. The page size is rather small and the margins generous, so that the quantity of material on any page rarely looks forbidding. The important equations are circled in color, and a great deal of space surrounds each equation. The book looks easy to read, and it is. The diagrams are especially good, some using as many as three colors. Even various equations are multicolored. Durney and Johnson, also a McGraw-Hill book and similar in level to this one, is not nearly as tempting. One is reminded of McLuhan's aphorism, "the medium is the message." Perhaps, "the design is the book," is equally true. Each chapter is divided into relatively small sections which are followed by easy exercises called drill problems. They enable the reader to test his or her knowledge at short intervals without waiting to finish the chapter. I have to confess that some of my students use the book as a self-study course and skip my lectures. The problems at the end of the chapter are more difficult than the drill problems. Unfortunately, they lack novelty; there are few which are "fun" or contain the sort of paradoxes and puzzles which are possible in this subject. One minor defect of the text, which the teacher can mitigate, is its lack of any suggestion in the early chapters of the enormous number of applications of electromagnetic theory. The student may rightly wonder for quite awhile why this subject is being required. There are more serious weaknesses, however. The discussion of electric flux and the development of Gauss's Law in Sections 3.1 and 3.2 is confusing. The author introduces the electric flux density vector X earlier than he should. There is no reason to define X until one deals with polarizable media. By taking X = eO in Section 3.1, Hayt must renounce this definition when he reaches dielectrics some 80 pages later. In anticipation of this difficulty, he attaches the phrase "free space only" to certain equations in this section and sometimes lands in difficulty. The equation on page 62 E

v

p dvaR

4reR2

(free space only)

is incorrect. If we use the total charge density this integral gives t correctly under all static conditions. The notion of the flux of a vector through a surface is a The reviewer is with the University of Lowell, Lowell, MA 01854.

mathematical concept not limited to electrostatics. I doubt whether a student realizes this after reading Chapter 3. The flux of eo over a closed surface is the total charge inside, while the flux of 15 e0=c + l over this surface is the free charge inside. This first statement of Gauss's Law should appear in Section 3.2, while the second should be delayed until dielectrics are treated. Another difficulty pops up in Sections 3.4 through 3.7. The discussion of the divergence theorem given here is so intimately tied to electrostatics that the student often believes it to be a physical statement rather than a mathematical theorem. Indeed, the author never does prove the divergence theorem but infers its validity from Gauss's Law. An actual proof at the level of this text is given in many books, e.g., Corson and Lorrain [2]. Section 4.8 on stored electrostatic energy has a derivation of

we

PVdv

obtained through the assembly of an array of point charges. This procedure neglects the self-energy of the charges in the array. Nevertheless, the above integral for We contains all the stored energy of a continuous distribution of charge. No explanation for this paradox is given. The author is again in difficulty here because of his premature use of the i} vector. The student may later wonder if the energy equation We=

2fJ

D

*E

dv

derived under the assumption D = coE is applicable in dielectrics where 15 # con. Section 4.8 should be postponed until 15 has been properly defined. Drill problem 4.10 at the end of this section is fatuous as it presupposes that stored electric energy can be ascribed to a particular region of space. A student using

I= JPV dv

we -fPvdL

to work out this exercise will not get the same answer as Hayt who uses

We

D * E dv.

Both procedures are equally questionable. Section 5.6 is weak because of the "hand waving argument" which derives Pb = - V . A rigorous derivation is not too difficult at this point since it involves only the divergence theorem, the field of a dipole, and a vector identity. Moreover, it yields the additional information that the surface density of bound charge is Ob = n , an equally important result appearing nowhere in the text. Chapter 8, with its discussion of the I fleld, Stokes Theorem, and curl, suffers from the same defects as Chapter 3 with its discussion of 1 and the divergence theorem. i} is introduced sooner than it should be. The author should instead rely on /,o as long as he is in nonmagnetic material. By introducing X too early and then having to redefine it on page 299, Hayt stumbles into an equation which is clearly false: -

v X H=J +Jb

IEEE TRANSACTIONS ON EDUCATION, VOL. E-23, NO. 2, MAY 1980

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where J is free current. Students want to know if this does not contradict V X I = Jpresented on page 300. The der-

ivation of Stokes Theorem uses the letter .7, which makes the student think that this is a physical formula rather than a mathematical theorem. In Chapter 9 the expression for stored magnetic energy B .Hdv

is pulled out of thin air. A justification for the formula is promised in the section of Poynting's Theorem in Chapter 11. Because there are several terms in Poynting's Theorem which will need explaining, the student is not easily convinced that one of them is stored magnetic energy. The author should have given a simple derivation of his WH in Chapter 9 based on circuit theory. One is given by Kraus and Carver [3 ]. Such a proof would help strengthen the later discussion of Poynting's Theorem.

The most inconvenient feature of the book is the order in which transmission lines and plane waves are treated. Hayt takes up plane waves first (Chapter I 1) and then transmission lines (Chapter 12). Many of the equations derived in Chapter 11 are transcribed wholesale, with little discussion, into corresponding expressions for transmission lines in Chapter 12. Unfortunately, concepts such as input impedance, standing waves, and standing wave ratio are more easily grasped by the student who learns them for transmission lines rather than for the more abstract plane waves. The order of these chapters should be reversed. It is easier to learn plane waves having first been exposed to transmission lines. REFERENCES [1] Dumey and Johnson, Introduction to Modern Electromagnetics. New York: McGraw-Hill, 1969. [21 P. Lorrain and D. Corson, Electromagnetic Fields and Waves, 2nd ed. San Francisco, CA: Freeman, 1970, sect. 1.5. [31 J. Kraus and K. Carver, Electromagnetics. New York: McGrawHill, 1973, p. 174.