You've reached the end of your free preview.
Want to read all 1240 pages?
Unformatted text preview: Engineering
Electromagnetics Springer Science+Business Media, LLC Nathan Ida Engineering
EI ectro magnetics
With 821 Illustrations Springer Nathan Ida
Department of Electrical Engineering
The University of Akron
Akron, OH 44325-3904 USA
[email protected] Library of Congress Cataloging-in-Publication Data
Engineering electromagnetics / Nathan Ida.
Includes bibliographical references and index.
ISBN 978-1-4757-3289-4 ISBN 978-1-4757-3287-0 (eBook) DOI 10.1007/978-1-4757-3287-0 1. Electromagnetic devices-Design. 2. ElectromagnetismMathematics. 1. Title.
Printed on acid-free paper. © 2000 Springer Science+Business Media New York
Origina11y published by Springer-Verlag New York, Inc. in 2000
Softcover reprint ofthe hardcover Ist edition 2000
AU rights reserved. This work may not be translated or copied in whole or in part without the written
permission of the publisher Springer Science+Business Media, LLC.
except for brief excerpts in connection with reviews or scholarly analysis. Use in connection with
any form of information storage and retrieval, electronic adaptation, computer software, or by similar or
dissimilar methodology now known or hereafter developed is forbidden.
The use of general descriptive names, trade names, trademarks, etc., in this publication, even if the former are not especially identified, is not to be taken as a sign that such names, as understood by the Trade
Marks and Merchandise Marks Act, may accordingly be used freely by anyone.
Production coordinated by Robert Wexler and managed by Francine McNeill; manufacturing supervised by Jerome Basma.
Typeset by The Bartlett Press, !nc., Marietta, GA 9 8 7 6 5 432 1
ISBN 978-1-4757-3289-4 SPIN 10696780 This book is lovingly dedicated to Vera, my wife and partner in life. Preface You can because you ought.
One of the main difficulties in teaching electromagnetic fields is the perception on
the part of many students that electromagnetics is essentially a supportive topic. They
are told that they need to study electromagnetics early in the curriculum because they
will need it later to understand other topics in the electrical engineering curriculum,
such as electric machines, microwaves, or communication. This, with the prevailing
perception of the topic being difficult, esoteric, or boring, creates a heavy atmosphere
around the subject. More often than not, this leads to self-fulfilling prophecies, and
as a result, even those students who perform well do not get the full benefit of
the experience such an exciting topic can impart. This is particularly sad, because
electromagnetics motivates many students to enter electrical engineering. They are
familiar with electromagnetic waves, electric motors, magnetic recording, and data
storage, and have been exposed to hundreds of electromagnetic devices. Yet few
make the connection between these and the electromagnetics they are taught.
The answer is to study electromagnetics for what it is rather than in preparation
for something that will happen in the future. The study of electromagnetic fields is
not more difficult than any other topic in the electrical engineering curriculum and,
in many ways, is more interesting and more applied. The number of applications
is so vast that any attempt to summarize will easily fill a good-sized book. One can
only guess the total share of electromagnetics to the industrial output. Huge turbogenerators for generation of electricity, power transmission lines, electric motors,
actuators, relays, radio, TV and microwave transmission and reception, magnetic
storage, and even the mundane little magnet used to hold a paper note on the refrigerator are all electromagnetic in nature. One would be hard pressed to find a device
that works without relying on any electromagnetic principle or effect. One only has
to ask oneself who is going to design these systems and what are the tools necessary to do so, and the answer to why one should study electromagnetics becomes
self-evident. vii viii PREFACE This text attempts to present electromagnetics as a topic in itself with specific
objectives and specific applications. The fact that it is used as a prerequisite for other
subjects is merely a consequence that those other topics are based on electromagnetics. A good theoretical understanding of the electromagnetic field equations is
required for electromagnetic design. The text fulfills this need by a rigorous treatment of the theoretical aspects of electromagnetics. In addition, it treats a large
number of electromagnetic applications that the student will find interesting and
The text assumes the student has the necessary background in calculus. Other
required topics, including vector algebra and vector calculus, are fully covered in the
text. In addition, all mathematical relations (such as integrals, derivatives, series, and
others) are listed as needed in the text. In this sense, the book is fully self-contained.
An effort has been made to use only quantities that have been defined previously,
even if this requires, for example, change of units in mid-chapter. There will be a
few exceptions to this rule, and when this happens, the reasons for doing so are also
given. The reasons for this purist approach are many, but the most important is the
fact that the book assumes no prior knowledge of any field quantity.
In style, the text relies on simple physical explanations, in plain language and
based on known phenomena, to simplify understanding. There are many detailed
examples, exercising every significant relation and topic in the book. Many of the
examples rely on important applications and contain complete step-by-step solutions
and derivations as necessary. There is almost no use of acronyms. These are only
used when an acronym is better known than what it represents, such as TV and
FM. The presentation often relies on repetition of relations and explanations. This
serves to reinforce understanding and avoids convoluted referencing to equations
and text. In most cases, referencing is only done for completeness purposes, and the
required equation is repeated when needed. Important or often-used relations are
boxed and are always accompanied by their associated units. The notation used in the
book is standard and should be familiar to students from physics and mathematics.
The most important change in this respect is the use of unit vectors. Unit vectors
always precede the scalar component. For example, A = XAx +yAx +ZAx is a vector
with scalar components Ax in the x direction, Ay in the y direction, and Az in the z
direction. X, y, and are the corresponding unit vectors.
The structure of the book is unique in another way; most topics are discussed in
two or three separate chapters. The first chapter introduces the subject and discusses
the basic quantities and relations. The second chapter complements and expands on
the first and introduces additional topics related to the main subject. In certain cases,
a third chapter discusses additional topics or a new topic related to the first two.
For example, Chapter 3 introduces the electric field and the postulates governing
it; Chapter 4 continues with Gauss' law, effects of and on materials, capacitance,
and other quantities associated with the electric field; Chapter 5 then continues
with analytical methods of solution of electrostatic problems. This pairing includes
Chapters 1 and 2 (vector algebra followed by vector calculus), Chapters 3,4, and
5 (electric field, electric potential, and boundary value problems), Chapters 8 and
9 (the static magnetic field and magnetic materials and properties), Chapters 12
and 13 (electromagnetic waves and propagation and reflection and transmission z PREFACE ix of plane waves), and Chapters 14, 15, and 16 (theory of transmission lines, the
Smith chart and transmission line circuits, and transients on transmission lines). The
purpose of this grouping of chapters is twofold. First, it divides the material into more
coherent, easier to follow, shorter units. Second, it provides intermediate breaking
points at which both students and teachers can assess the situation and decide on the
next steps. It also allows selection of topics without the need for skipping sections
within chapters. For example, while a chapter on time-dependent fields normally
includes all material associated with Faraday's law, Maxwell's equations, and wave
propagation, I have chosen to divide this material into three chapters. One is on
Faraday's law and includes all phenomena associated with induction (Chapter 10).
The second discusses Maxwell's equations with associated material, including the
continuity equation and interface conditions (Chapter 11). The third discusses wave
propagation as a consequence of displacement currents (Chapter 12). The three
chapters discuss different aspects, using various approaches.
Chapters 1 and 2 discuss vector algebra and vector calculus, and are rather
different from the rest of the book in that the student will find no reference to
electromagnetics in these chapters. This serves two purposes. First, it indicates that
at this stage the student has little formal knowledge of electromagnetic field quantities but, paradoxically, he or she is aware of the properties of electromagnetic fields
through knowledge acquired in other areas of physics or everyday experience. Second, it shows that the same methods and the same mathematical tools are used in
other disciplines and for other applications. This approach should alleviate some
of the anxiety associated with the study of electromagnetics while still acquiring all
vector algebra and calculus tools needed for the study of electromagnetics. More
importantly, the approach lends itself to self-study. If the student or the instructor
feels that Chapters 1 and 2 are not necessary, they may be skipped without affecting
The method of presentation of the material distinguishes between basic field
relations and mathematical tools. The latter are introduced in Chapters 1 and 2,
but wherever they are needed, they are repeated to reinforce understanding of the
tools and to avoid having to refer back to Chapters 1 or 2. Similarly, other relations,
like trigonometric functions, derivatives, and integrals, are given as needed, and as
close as possible to where they are used. This should help students with reviewing
material they learned previously, but do not recall or are not certain of. These notes
are given as "reminders" either as footnotes or, more often, in the text.
Each chapter contains a set of review questions and a set of problems. The review
questions are designed to review important topics and to emphasize specific points.
The problems are of two types. Some are exercises, used to ensure that the student
has a chance to review the field relations and to use them in the way they were
intended to be used. The second type is more involved and often based on a physical
application or, in some cases, on a simplified version of a physical structure. These
problems are designed to present some of the many applications in electromagnetics,
in addition to their value as exercise problems. It is hoped that this will bring the
student closer to the idea of design than exercise problems can.
Most chapters contain a section on applications and a section on experiments.
The section on applications is intended to expand on material in the chapter and X PREFACE to expose the student to some of the myriad applications in electromagnetics or,
in some cases, to physical phenomena that depend on electromagnetism. Naturally,
only a selection of applications is given. The description is short but complete.
The section on experiments presents a few simple experiments that can be used to
demonstrate the principles discussed in the chapter. These experiments are designed
to be short and simple, and to require a minimum of materials and equipment. They
are qualitative experiments: no measurements are taken, and no exact relations are
expected to be satisfied. The instructor may choose to use these as an introduction
to a particular topic or as a means to stimulate interest. The student may view the
experiments as demonstrations of possible applications. Many of the experiments
can be repeated by students if they wish to do so. However, none of the experiments
require laboratory facilities. The main purpose is to take electromagnetic fields off
the pedestal and down to earth. I found these simple experiments particularly useful as a way of introducing a new subject. It wakes the students up, gets them to
ask questions, and creates an anticipation toward the subject. The simplicity of the
principles involved intrigues them, and they are more inclined to look at the mathematics involved as a means rather than the goal. Invariably, in student evaluations,
the experiments are mentioned in very positive terms. I would even venture to say
that the students tend to exaggerate their importance. Either way, there is value in
showing the students that a discarded magnet and an old coil can demonstrate the
principle of the ac generator. Even if no demonstrations are performed, it is recommended to read them as part of the study of the chapter-the student will find
some of the explanations useful. Both the applications and experiments sections are
excellent candidates for self-study.
This textbook was written specifically for a two-semester sequence of courses but
can be used equally well for a one-semester course. In a two-semester sequence,
the topics in Chapters 3 to 10 are expected to be covered in the first semester.
If necessary, Chapters 1 and 2 may be reviewed at the beginning of the semester,
or if the students' background in vector algebra and calculus is sufficiently strong,
these two chapters may be skipped or assigned for self-study. Chapter 6 is selfstanding and, depending on the instructor's preference, mayor may not be covered.
The second semester should ideally cover Chapters 11 to 18, or at least Chapters
11 to 16. Chapters 17 and 18 are rather extensive discussions on waveguides and
antennas, respectively, and as such introduce mostly new applications and derived
relations rather than fundamental, new ideas. These may form the basis of more
advanced elective courses on these subjects. In a one-semester course, there are
two approaches that may be followed. In the first, Chapters 3 to 5 and 7 to 12
are covered. This should give students a solid basis in electromagnetic fields and
a short introduction to electromagnetic waves. The second approach is to include
topics from Chapters 3 to 5 and 7 to 16. It is also possible to define a program that
emphasizes wave propagation by utilizing Chapters 11 to 18 and excluding all topics
in static electric and magnetic fields.
There is a variety of methods for the solution of boundary value problems. The
classical methods of separation of variables or the image methods are presented
as methods of solving particular problems. However, one of the most frustrating
aspects of fields is that there are no systematic, simple ways of solving problems PREFACE xi with any degree of generality. Too often, we rely on a canned solution to idealized
geometries, such as infinite structures. The introduction of numerical methods at
this stage is intended to reassure students that solutions indeed exist and that the
numerical methods needed to do so are not necessarily complicated. Some methods can be introduced very early in the course of study. Finite differences and the
method of moments are of this type. Finite-element methods are equally simple,
at least at their basic levels. These methods are introduced in Chapter 6 and are
applied to simple yet useful electrostatic configurations. The computer programs
necessary, plus additional material and resources, are available on the internet at
The history associated with electromagnetics is long and rich. Many of the people
involved in its development had unique personalities. While information on history
of the science is not in itself necessary for understanding of the material, I feel it has a
value in its own right. It creates a more intimate association with the subject and often
places things in perspective. A student can appreciate the fact that the great people
in electromagnetics had to struggle with the concepts the students try to understand
or that Maxwell's equations, the way we know them today, were not written by
Maxwell but by Heaviside, almost twenty years after Maxwell's death. Or perhaps
it is of some interest to realize that Lord Kelvin did not believe Maxwell's theory
well after it was proved experimentally by Hertz. Many will enjoy the eccentric
characters of Heaviside and Tesla, or the unlikely background of Coulomb. Still
others were involved in extracurricular activities that had nothing to do with the
sciences. Benjamin Franklin was what we might call a special envoy to England
and France, and Gilbert was personal physician to Queen Victoria. All these people
contributed in their own way to the development of the theory of fields, and their
story is the story of electromagnetics. Historical notes are given throughout the
book, primarily as footnotes.
Finally, I wish to thank those who were associated with the writing of this text.
In particular, Frank Lewis (class of '96), Dana Adkins (class of '97), Shi Ming (class
of '94), and Paul Stager (class of '94) have solved the examples and end-of-chapter
problems and provided valuable input into the writing of the text. Professor J,P.A.
Bastos contributed a number of examples and problems.
The University of Akron
February 2000 Contents Preface vii 1 Vector Algebra
1.2 Scalars and Vectors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.3 Products of Vectors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.4 Definition of Fields . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.5 Systems of Coordinates . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.6 Position Vectors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
47 2 Vector Calculus
2.2 Integration of Scalar and Vector Functions . . . . . . . . . . . . . . . . . . .
2.3 Differentiation of Scalar and Vector Functions. . . . . . . . . . . . . . . . .
2.4 Conservative and Nonconservative Fields . . . . . . . . . . . . . . . . . . .
2.5 Null Vector Identities and Classification of Vector Fields. . . . . . . . . .. 57
108 3 Coulomb's Law and the Electric Field
3.2 Charge and Charge Density. . . . . . . . . . . . . . . . . . . . . . . . . ..
3.3 Coulomb's Law. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ..
3.4 The Electric Field Intensity . . . . . . . . . . . . . . . . . . . . . . . . . ..
3.5 The Electric Flux Density: An Initial Definition. . . . . . . . . . . . . . ..
3.7 Experiments.................................... 121
163 4 Gauss's Law and the Electric Potential
4.2 The Electrostatic Field: Postulates . . . . . . . . . . . . . . . . . . . . . . ,
4.3 Gauss's Law. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ..
4.4 The Electric Potential . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 173
190 106 xiii xiv
4.10 CONTENTS Materials in the Electric Field . . . . . . . . . . . . . . . . . . . . . . . . ..
Interface Conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ..
Energy in the Electrostatic Field: Point and Distributed Charges ....
View Full Document