Why Another EM Book?

Several textbooks are currently available for teaching electromagnetics to students majoring in electrical engineering. So, why do we need another one? The answer is simple: (1) the curriculum for a bachelor's degree in electrical engineering is undergoing a radical change, perhaps more radical in both outlook and content than any of the curricular changes we have witnessed over the past several decades, and (2) available textbooks are incompatible with the philosophy of the new curriculum proposed for the twenty-first century (see, for example, the article by Director *et al.* in the *Proceedings of the IEEE,* September 1995).

The Changing Curriculum

For a bachelor's degree in electrical engineering, the curriculum has undergone about one major change per decade. In the 1960s, courses concerning solid-state devices were introduced and those on vacuum-tube electronics were slowly phased out. In the 1970s, courses on electric machinery nearly disappeared from the curricula of most universities and were replaced with computer-programming courses. More computer-related and digital processing courses were added in the 1980s, mainly by increasing the volume of required courses and reducing the number of technical and free electives. Also, there has been a sustained effort to incorporate new knowledge and assimilate the rapidly evolving role of technology in the undergraduate curriculum. More material was added to courses, greater effort was expected from students, and the number of elective credit hours rapidly approached zero. By the early 1990s, the average student at a U.S. university needed closer to five years to complete what was originally designed as a four-year program.

This scenario was not limited to electrical engineering; indeed, in almost any engineering discipline, the curriculum had become too demanding in terms of time to complete the B.S. degree and too inflexible to accommodate changes. From these pressures was born a new philosophy embracing the following tenets: (1) the B.S. degree program should be scaled back to four years, (2) the required part of the B.S. degree program should focus on the teaching of fundamentals, but with greater exposure to engineering applications, and (3) the electives portion of the program should be increased substantially to allow the student to explore both engineering and nonengineering areas of interest. While this new philosophy has been adopted, as least in principle, by many engineering schools, the task of revising the curriculum has been a major challenge, particularly at the course level. The new electrical engineering curriculum calls for allocating fewer credit hours in many of the traditionally core areas—electromagnetics (EM) among them. At many universities the required EM content of the program has been reduced from two courses down to one. For some, the intent is to continue to offer a two-course sequence, but with only the first being part of the required core and the second being for students interested in deepening their knowledge in electromagnetics.

Course Contents

Given these objectives and associated boundary conditions, what then should be the contents of a one-semester or a two-course sequence in electromagnetics and what texts might one use for this purpose? To answer these questions, we should briefly review the traditional approaches that have been in use over the past two decades. Most EM books share a common template. They begin with one or more chapters on vector calculus and coordinate systems, followed by two or more chapters on statics (electrostatics and magnetostatics). These topics typically constitute half of the total material, and the second half usually covers dynamics (time-varying fields, wave propagation and reflection, waveguides and resonators, and antennas). Such an arrangement of topics presents two problems. First, starting a course with a heavy dose of mathematics tends to "turn the students off." And second, whereas electrostatics and magnetostatics are interesting subjects in themselves and have many practical applications, their importance pales in comparison with the many applications of time-varying fields to communication systems, radar, optics, computers, and solid-state electronics, among others. Thus, teaching statics only in the required portion of the B.S. degree curriculum would leave an electrical engineering student seriously lacking in ability to deal with most electromagnetic phenomena.

Because of the heavy emphasis on mathematical manipulations using vector calculus and the relatively dry character of electrostatics and magnetostatics, the student who completes such a required course is unlikely to select to take the second course in the sequence, which is where many of the topics relevant to engineering practice are covered. Clearly, teaching from a book based on this traditional sequence of topics is no longer compatible with the format of the new curriculum proposed for the twenty-first century.

In past years, attempts have been made by educators at various universities to teach the dynamics of electromagnetics without preceding it with a study of statics. These attempts have not been very successful, primarily because in dynamics students must deal with several fundamental parameters simultaneously. These include spatial coordinates denoting location, vectors denoting direction, time, and the interconnection between the electric and magnetic fields. In statics, the electric and magnetic fields are independent of one another and time is not a variable, thereby reducing the number of parameters from four to two. By studying electrostatics and magnetostatics first, the student can much more easily tackle situations involving time-varying fields.

This Book

In view of this background, how then does one design an appropriate one-semester or two-course sequence in electromagnetics? My answer to this question is characterized in this book by the following elements:

**1.** I wanted to begin by building a bridge between what was already familiar to a third-year electrical engineering student and the electromagnetics material. Prior to enrolling in an EM course, a typical student will have taken two or more courses in circuits. Thus, he or she is familiar with circuit analysis, Ohm's law, Kirchoff's current and voltage laws, and related topics. Transmission lines constitute a *natural* bridge between electric circuits and electromagnetics. Without having to deal with vectors or fields, the student uses already familiar concepts to learn about wave motion, the reflection and transmission of power, phasors, impedance matching, and many of the properties of wave propagation in a guided structure. All of these newly learned concepts will prove invaluable later (in Chapters 7 though 9) and will facilitate the learning of how plane waves propagate in free space and in material media. Transmission lines are covered in Chapter 2, which is preceded in Chapter 1 with reviews of complex numbers and phasor analysis.

**2.** The next part of the book, contained in Chapters 3 through 5, covers vector analysis, electrostatics, and magnetostatics. Compared with most EM textbooks written for undergraduate instruction, the present book differs in terms of its presentation of these three topics in the following two ways: Of the total number of pages contained in the book, about 30% are allocated to these topics, compared with 50% or more in most EM textbooks. The electrostatics chapter begins with Maxwell's equations for the time-varying case, which are then specialized to electrostatics and magnetostatics, thereby 'providing the student with an overall framework for what is to come and showing him or her why electrostatics and magnetostatics are special cases of the more a general time-varying case.

**3.** Unlike most EM textbooks, this book does not have a chapter on waveguides and resonators. Space limitations and the fact that waveguides are no longer used as widely as they had been prior to 1980 dictated this change.

**4.** Chapter 6 deals with time-varying fields and sets the stage for the material in Chapters 7 through 9. Chapter 7 covers plane-wave propagation in dielectric; and conducting media, and Chapter 8 covers reflection and transmission at discontinuous boundaries and introduces the student to fiber optics and the imaging properties of mirrors and lenses.

In Chapter 9, the student is introduced to the principles of radiation by currents flowing in wires, such as dipoles, as well as to radiation by apertures, such as a horn antenna or an opening in an opaque screen illuminated by a light source.

**5.** To give the student a taste of the wide-ranging applications of electromagnetics in today's technological society, Chapter 10 concludes the book with overview presentations of two system examples: satellite communication systems and radar sensors.

**6.** The material in this book was written for a two-semester sequence of six credits, but it is possible to trim it down to generate a syllabus for a one-semester four-credit course. The table on the preceding page provides syllabi for each of these two options.

In writing this book, I avoided lengthy derivations of theorems, particularly those involving extensive use of vector calculus. My goal has been to help the student to develop competence in applying vector calculus to solve electromagnetic problems of practical interest. 1 view vector calculus and mathematics in general as useful tools and not as ends in themselves. Throughout the material, emphasis is placed on using the mathematics to explain and clarify the physics, followed with practical examples intended to demonstrate the engineering relevance of physical concepts. I believe the combination of the approach used in presenting the material, the arrangement of topics covered in the book, and the relative emphasis in favor of dynamics constitutes an effective algorithm for equipping our future graduates with a relevant foundation in applied electromagnetics.

*--This text refers to an out of print or unavailable edition of this title.*