Engineering Electromagnetics provides a solid foundation in electromagnetics fundamentals by emphasizing physical understanding and practical applications. Electromagnetics, with its requirements for abstract thinking, can prove challenging for students. The authors' physical and intuitive approach has produced a book that will inspire enthusiasm and interest for the material. Benefiting from a review of electromagnetic curricula at several schools and repeated use in classroom settings, this text presents material in a rigorous yet readable manner.

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**Aziz S. Inan** is Associate Professor of Electrical Engineering at the University of Portland, where he has also served as Department Chairman. A winner of the University,s faculty teaching award, he conducts research in electromagnetic wave propagation in conducting and inhomogeneous media.

This book provides engineering students with a solid grasp of electromagnetic fundamentals by emphasizing physical understanding and practical applications. The topical organization of the text starts with an initial exposure to transmission lines and transients on high-speed distributed circuits, naturally bridging electrical circuits and electromagnetics.

Engineering Electromagnetics is designed for upper-division (3rd and 4th year) college and university engineering students, for those who wish to learn the subject through self-study, and for practicing engineers who need an up-to-date reference text. The student using this text is assumed to have completed typical lower-division courses in physics and mathematics as well as a first course on electrical engineering circuits.

**KEY FEATURES**

The key features of this textbook are:

- Modern chapter organization, covering transmission lines before the development of fundamental laws
- Emphasis on physical understanding
- Detailed examples, selected application examples, and abundant illustrations
- Numerous end-of-chapter problems, emphasizing selected practical applications
- Historical notes and abbreviated biographies of the great scientific pioneers
- Emphasis on clarity without sacrificing rigor and completeness
- Hundreds of footnotes providing physical insight, leads for further reading, and discussion of subtle and interesting concepts and applications

**Modern Chapter Organization**

We use a physical and intuitive approach so that this engineering textbook can be read by students with enthusiasm and with interest. We provide continuity with cir-cuit theory by first covering transmission lines-an appropriate step, in view of the newly emerging importance of transmission line concepts,not only in microwave and millimeter-wave applications but also in high-speed digital electronics, microelectronics, integrated circuits, packaging, and interconnect applications. We then cover the fundamental subject material in a logical order, following the historical development of human understanding of electromagnetic phenomena. We base the fundamental laws on experimental observations and on physical grounds, including brief discussions of the precision of the fundamental experiments, so that the physical laws are easily understood and accepted. Once the complete set of fundamental laws is established, we then discuss their most important manifestation: the propagation, reflection, transmission, and guiding of electromagnetic waves.

**Emphasis on Physical Understanding**

Future engineers and scientists need a clear understanding and a firm grasp of the basic principles so that they can understand, formulate, and interpret the results of complex practical problems. Engineers and scientists nowadays do not and should not spend time working out formulas and obtaining numerical results by substitution. Most of the number crunching and formula manipulations are left to computers and packaged application and design programs, so a solid grasp of fundamentals is now more essential than ever before. In this text we maintain a constant link with established as well as new and emerging applications (so that the reader's interest remains perked up), while at the same time emphasizing fundamental physical insight and solid understanding of basic principles. We strive to empower the reader with more than just a working knowledge of a dry set of vector relations and formulas stated axiomatically. We supplement rigorous analyses with extensive discussions of the experimental bases of the laws, of the microscopic versus macroscopic concepts of electromagnetic fields and their behavior in material media, and of the physical nature of the electromagnetic fields and waves, often from alternative points of view. Description of the electrical and magnetic properties of material media at a sufficiently simple, yet accurate manner at the introductory electromagnetics level has always been a challenge, yet a solid understanding of this subject is now more essential than ever, especially in view of many applications that exploit these properties of materials. To this end we attempt to distill the essentials of physically-based treatments available in physics texts, providing quantitative physical insight into microscopic behavior of materials and the representation of this behavior in terms of macroscopic parameters. Difficult three-dimensional vector differential and integral concepts are discussed when they are encountered-again, with the emphasis being on physical insight.

**Detailed Examples and Abundant Illustrations**

We present the material in a clear and simple yet precise and accurate manner, with interesting examples illustrating each new concept. Many examples emphasize selected applications of electromagnetics. A total of 180 illustrative examples are detailed over eight chapters, with four of the chapters having more than 30 examples each. Each example is presented with an abbreviated topical title, a clear problem statement, and a detailed solution. In recognition of the importance of visualization in the reader's understanding, especially in view of the three-dimensional nature of electromagnetic fields, over 400 diagrams, graphs, and illustrations appear throughout the book.

**Numerous End-of-Chapter Problems**

Each chapter is concluded with a variety of homework problems to allow the students to test their understanding of the material covered in the chapter, with a total of over 300 exercise problems spread over seven chapters. The topical content of each problem is clearly identified in an abbreviated title (e.g., "Digital IC interconnects" or "Inductance of a toroid"). Many problems explore interesting applications, and most chapters include several practical "real-life" problems to motivate students.

**Historical Notes and Abbreviated Biographies**

The history of the development of electromagnetics is laden with outstanding examples of pioneering scientists and development of scientific thought. Throughout our text, we maintain a constant link with the pioneering giants and their work, to bring about a better appreciation of the complex physical concepts as well as to keep the reader interested. We provide abbreviated biographies of the pioneers, emphasizing their scientific work in electromagnetics as well as in other fields such as optics, heat, chemistry, and astronomy. We illustrate the apparatus used by discoverers such as Coulomb and Faraday so that the reader can have a feel for how one would carry out such an experiment.

**Emphasis on Clarity without Sacrificing Rigor and Completeness**

This textbook presents the material at a simple enough level to be readable by undergraduate students, but it is also rigorous in providing references and footnotes for in-depth analyses of selected concepts and applications. We provide the students with a taste of rigor and completeness at the level of classical reference texts--combined with a level of physical insight that was so well exemplified in some very old texts--while still maintaining the necessary level of organization and presentation clarity required for a modem textbook. We also provide not just a superficial but a rigorous and in-depth exposure to a diverse range of applications of electromagnetics, in the body of the text, in examples, and in end-of-chapter problems.

**Hundreds of Footnotes**

In view of its fundamental physical nature and its broad generality, electromagnetics lends itself particularly well to alternative ways of thinking about physical and engineering problems and also is particularly rich in terms of available scientific literature and many outstanding textbooks. Almost every new concept encountered can be thought of in different ways, and the interested reader can explore its implications further. We encourage such scholarly pursuit of enhanced knowledge and understanding by providing many footnotes in each chapter that provide further comments, qualifications of statements made in the text, and references for in-depth analyses of selected concepts and applications. A total of 450 footnotes are spread over eight chapters. These footnotes do not interrupt the flow of ideas and the development of the main topics, but they provide an unusual degree of completeness for a textbook at this level, with interesting and sometimes thought-provoking content to make the subject more appealing.

**ELECTROMAGNETICS IN ENGINEERING**

The particular organization of this textbook, as well as its experimentally and physically based philosophy, are motivated by our view of the current status of electromagnetics in engineering curricula. Understanding electromagnetics and appreciating its applications require a generally higher level of abstraction than most other topics encountered by electrical engineering students. Beginning electrical engineers learn to deal with voltages and currents, which appear across or flow through circuit elements or paths. The relationships between these voltages and currents are determined by the characteristics of the circuit elements and by Kirchhoff's current and voltage laws. Voltages and cur-rents in lumped electrical circuits are scalar quantities that vary only as a function of time, and are readily measurable, and the students can relate to them via their previous experiences. The relationships between the quantities (i.e., Kirchhoff's laws) are relatively simple algebraic or ordinary differential equations. On the contrary, electric and magnetic fields are **three-dimensional** and **vector** quantities that in general **vary in both space and time** and are related to one another through relatively complicated vector **partial differential** or vector **integral equations**. Even if the physical nature of electric and magnetic fields were understood, visualization of the fields and their effects on one another and on matter requires a generally high level of abstract thinking.

Most students are exposed to electromagnetics first at the freshman physics level, where electricity and magnetism are discussed in terms of their experimental bases by citing physical laws (e.g., Coulomb's law) and applying them to relatively simple and symmetrical configurations where the field quantities behave as scalars, and the governing equations are reduced to either algebraic equations of first-order integral or differential relationships. Freshman physics provides the students with their first experiences with fields and waves as well as and some of their measurable manifestations, such as electric and magnetic forces, electromagnetic induction (Faraday's law), and refraction of light by prisms.

The first course in electromagnetics, which most students take after having had vector calculus, aims at the development and understanding of Maxwell's equations, requiring the utilization of the full three-dimensional vector form of the fields and their relationships. It is this very step that makes the subject of electromagnetics appear insurmountable to many students and turns off their interest, especially when coupled with a lack of presentation and discussion of important applications and the physical (and experimental) bases of the fundamental laws of physics. Many authors and teachers have attempted to overcome this difficulty by a variety of topical organizations, ranging from those that start with Maxwell's equations as axioms to those that first develop them from their experimental basis.

Since electromagnetics is a mature basic science, and the topics covered in introductory texts are well established, the various texts primarily differ in their organization as well as range and depth of coverage. Teaching electromagnetics was the subject of a special issue of *IEEE Transactions on Education* vol. 33, February, 1990. Many of the challenges and opportunities that lie ahead in this connection were summarized well in an invited article by J. R. Whinnery. 1 Challenges include (1) the need to return to fundamentals (rather than relying on derived concepts), especially in view of the many emerging new applications that exploit unusual properties of materials and that rely on unconventional device concepts 2 , submillimeter transmission lines, 3 and optoelectronic waveguides, 4 and (2) the need to maintain student interest in spite of the decreasing popularity of the subject of electromagnetics and its reputation as a difficult and abstract subject. 5 Opportunities are abundant, especially as engineers working in electronics and computer science discover that as devices get smaller and faster, circuit theory is insufficient in describing system performance or facilitating design. It is now clear, for example, that transmission line concepts are not only important in microwave and millimeter-wave applications but also necessary in high-speed digital electronics, n-microelectronics, integrated circuits, interconnects, 6 and packaging applications. 7 The need for a basic understanding of electromagnetic waves and their guided propagation is underscored by the explosive expansion of the use of optical fibers, the use of extremely high data rates, ranging to 10 Gbits/s, 8 and the emerging use of high-performance, high-density cables for communication within systems that will soon be required to carry digital signals at Gb/s rates over distances of a few meters. 9 In addition, issues of electromagnetic interference (EMI) and electromagnetic compatibility (EMC) are beginning to limit the performance of system-, board-, and chip-level designs, and electrostatic discharge phenomena have significant impacts on the design and performance of integrated circuits. 10 Other important applications that require better understanding of electromagnetic fields are emerging in biology 11 and medicine. 12

In organizing the material for our text, we benefited greatly from a review of the electromagnetic curriculum at Stanford University that one of us conducted during the spring quarter of 1990. A detailed analysis was made of both undergraduate and graduate offerings, both at Stanford and selected other schools. Inquiries were also made with selected industry, especially in the Aerospace sector. Based on the responses we received from many of our colleagues, and based on our experience with the teaching of the two-quarter sequence at Stanford, it was decided that an emphasis on fundamentals and physical insight and a traditional order of topics would be most appropriate. It was also determined that transmission line theory and applications can naturally be studied before fields and waves, so as to provide a smooth transition from the previous circuits and systems experiences of the typical electrical engineering students and also to emphasize the newly emerging importance of these concepts in high-speed electronics and computer applications.

**RECOMMENDED COURSE CONTENT**

This book is specifically designed for a one-term first course in electromagnetics, nowadays typically the only required fields and waves course in most electrical engineering curricula. The recommended course content for a regular three-unit one semester course (42 contact hours) is provided in Table 1. The sections marked under "Cover" are recommended for complete coverage, including illustrative examples, whereas those marked "Skim" are recommended to be covered lightly, although the material provided is complete in case individual students want to go into more detail. The sections marked with a superscript asterisk are intende...

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