This book is intended as a basic text for a two-semester sequence for undergraduate students desiring a fundamental comprehension of electromagnetic fields. The text can also be used for a one-semester course as long as the topics omitted do not resu1t in any loss of continuity or of student's preparation for ensuing chapters and courses. This text may also serve as a reference for students preparing for an advanced course in electromagnetic fields.
ELECTROMAGNETIC FIELD THEORY has been and wil1 continue to be one of the most important fundamental courses of the electrical engineering curriculum. It is one of the best established general theories, providing explanations and solutions to intricate electrical engineering problems when other theories are no longer app1icable.
This book is intended as a basic text for a two-semester sequence for undergraduate students desiring a fundamental comprehension of electromagnetic fields. The text can also be used for a one-semester course as long as the topics omitted do not resu1t in any loss of continuity or of student's preparation for ensuing chapters and courses. This text may also serve as a reference for students preparing for an advanced course in electromagnetic fields.
We have developed the text from first principles and have presented sufficient information on vector analysis for a student to comprehend the presentation with a minimum of instructional help. This text also contains many numerous, carefully placed, worked examples. These examples, clearly delineated from the textual matter, not only enhance
appreciation of a concept or a physical law but also bridge the perceived gap, rea1 or otherwise, between a formal theoretical development and its applications. We believe that examples are necessary for immediate reinforcement and further clarification of a topic. We have also included exercises at the end of each section to impart motivation, nurture confidence, and heighten the understanding of the material presented. The problems at the end of each chapter also offer a wide range of challenges to the student. These problems are an important part of the text and form an integral part of the study of electromagnetic fields. We recommend that the student use basic laws and intuitive reasoning to solve them. The practice of such problem-solving techniques instills confidence, empowering the student to tackle more difficult, real-life problems. Each chapter ends with a summary and a set of review questions. The summaries also include some of the important equations for easy reference. The review questions are designed to ensure that a student has grasped the basics of the material. We have tried to make this text as studentfriendly as possible and we welcome any suggestions in this regard.
Our experience dictates that students tend to view the theoretical development as an abstraction and place emphasis on some of the equations, considering them as "formulas". Soon frustrations set in as the students find that the so-called formulas are different, not only for different media but also for different configurations. The array of equations needed to compute just one field quantity intimidates them to the extent that they lose interest in the material. It then becomes just another "difficult" course that they must pass to satisfy the requirements for a degree in electrical engineering. We believe that it is definitely the instructor's responsibility to
* Explain the aim of each development,
* Justify assumptions imperative to that development,
* Emphasize its limitations,
* Highlight the influence of the medium, and
* Illustrate the impact of geometry on an equation.
To attain these goals, instructors must use their own experiences in the subject and also emphasize other areas of applications. They must also stress any new advancements in the held while they are discussing the fundamentals. For example, while explaining the magnetic force between two current-carrying conductors, an instructor can discuss magnetically levitated vehicles. Or, an instructor can deliberate upon the design of a microwave oven while discussing a cavity resonator.
When the subject matter is explained properly and the related equations are developed from basic laws, the student then learns to
* Appreciate the theoretical development,
* Forsake intimidation,
* Regain motivation and confidence, and
* Grasp the power of reasoning to develop new ideas.
A quick glance at the table of contents revea1s that the text is basically divided into two parts. The first part introduces the students to static fields such as electrostatic fields,magnetostatic fields, and fields due to steady currents. Because most of the applications of static fields involve both electric and magnetic fields, we decided to present such applications in one chapter. We also felt that once the students understand the basics of static fields, they can study the applications with a minimum of guidance. For these reasons, we have devoted Chapter 6 to some of the well-known applications of static electric and magnetic fields.
We present the developments of Maxwell's equations in both the time domain and phasor (frequency) domain in Chapter 7, stressing the concept of average power density and the coexistence of time--varying electric and magnetic fields. This chapter also inc1udes some of the applications of time-varying fields.
The rest of the book deals with the propagation, transmission, and radiation of electromagnetic fields in a medium under various constraints. Even though the Smith chart provides a visual picture of what is happening along a transmission line, we still feel that it is basically a transmission-line calculator. We can now use pocket calculators and computers to obtain exact information on the line. For this reason, we have discussed the Smith chart in an appendix. The instructor can decide whether to highlight its applications or to omit it.
Acknowledgments
We are deeply grateful for the help we received from Dr. A. Haq Qureshi, Professor, Cleveland State University, during the development of the first--draft manuscript. His understanding of the subject and yearning for accuracy kept us on our toes during the initial stages of this immensely complex project.
We also extend our gratitude to the following reviewers:
Gijs Bosman
University of Florida
Kent Chamberlain
University of New Hampshire
Michael Cloud
Lawrence Technological University
We appreciate the following persons and companies that cooperated in providing us with photographs on various transmission lines and waveguides:
Bernard Surtz, Andrew Corporalion, Orlando Park, Illinois
Bruce Whitney, Detrou Edison, Detrou, Michigan
Ellen Modock, keithlcy Instruments, Cleveland, Ohio
We could not have written this text without the unconditional support, active encouragement, complete cooperation, and honest sacrifices by our families. To appreciate their immense contributions, this text is lovingly dedicated to them.
B.S.G
H.R.H
1 ELECTROMAGNETIC FIELD THEORY 1
1.1 Introduction 1
1.2 Field Concept 2
1.3 Vector Analysis 3
1.4 Differential and Integral Formulations 4
1.5 Static Fields 5
1.6 Time-Varying Fields 6
1.7 Applications of Time-Varying Fields 7
1.8 Numerical Solutions 9
1.9 Further Study 9
2 VECTOR ANALYSIS 11
2.1 Introduction 11
2.2 Scalar and Vector Quantities 11
2.3 Vector Operations 12
2.3.1 Vector Addition 12
2.3.2 Vector Subtraction 13
2.3.3 Multiplication of a Vector by a Scalar 13
2.3.4 Product of Two Vectors 13
2.4 The Coordinate Systems 16
2.4.1 Rectangular Coordinate System 17
2.4.2 Cylindrical Coordinate System 19
2.4.3 Spherical Coordinate System 23
2.5 Scalar and Vector Fields 27
2.6 Differential Elements of Length, Surface, and Volume 29
2.6.1 Rectangular Coordinate System 29
2.6.2 Cylindrical Coordinate System 30
2.6.3 Spherical Coordinate System 30
2.7 Line, Surface, and Volume Integrals 31
2.7.1 The Line Integral 31
2.7.2 The Surface Integral 33
2.7.3 The Volume Integral 35
2.8 The Gradient of a Scalar Function 36
2.9 Divergence of a Vector Field 39
2.9.1 The Divergence Theorem 40
2.10 The Curl of a Vector Field 43
2.10.1 Stokes' Theorem 47
2.11 The Laplacian Operator 49
2.12 Some Theorems and Field Classifications 50
2.12.1 Green's Theorem 50
2.12.2 The Uniqueness Theorem 51
2.12.3 Classification of Fields 52
2.13 Vector Identities 54
2.14 Summary 55
2.15 Review Questions 56
2.16 Problems 58
3 ELECTROSTATICS 6 1
3.1 Introduction 61
3.2 Coulomb's Law 61
3.3 Electric Field Intensity 64
3.3.1 Electric Field Intensity Due to Charge Distributions 67
3.4 Electric Flux and Electric Flux Density 71
3.4.1 Definition of Electric Flux 72
3.4.2 Gauss's Law 72
3.5 The EIectric Potential 75
3.6 Electric Dipole 79
3.7 Materials in an Electric Field 81
3.7.1 Conductors in an Electric Field 81
3.7.2 Dielectrics in an Electric Field 84
3.7.3 Semiconductors in an Electric Field 88
3.8 Energy Stored in an EIectric Field 89
3.9 Boundary Conditions 93
3.9.1 The Normal Component of D 93
3.9.2 The Tangential Component of E 94
3.10 Capacitor and Capacitance 96
3.11 Poisson's and Laplace's Equations 100
3.12 Method of Images 104
3.13 Summary 108
3.14 Review Questions 110
3.15 Problems 112
4 STEADY ELECTRIC CURRENTS 12O
4.1 Introduction 120
4.2 Nature of Current and Current Density 121
4.2.1 Conduction Current 121
4.2.2 Convection Current 122
4.2.3 Convection Current Density 122
4.2.4 Conduction Current Density 123
4.3 Resistance of a Conductor 126
4.4 The Equation Of Continuity 127
4.S Relaxation Time 132
4.6 Joule's Law 134
4.7 Steady Current in a Diode 136
4.8 Boundary Conditions for Current Density 139
4.9 Analogy Between D and J 141
4.10 The Electromotive Force 144
4.11 Summary 147
4.12 Review Questions 149
4.13 Problems 150
5 MAGNETO5TATICS 155
5.1 Introduction 155
5.2 The Biot-Savart Law 156
5.3 Ampere's Force Law 161
5.4 Magnetic Torque 165
5.5 Magnetic Flux and Gauss's Law for Magnetic Fields 168
5.6 Magnetic Vector Potential 171
5.7 Magnetic Field Intensity and Ampere's Circuital Law 174
5.8 Magnetic Materials 177
5.8.1 Ferromagnetism 181
S.9 Magnetic Scalar Potential 184
5.10 Boundary Conditions for Magnetic Fields 186
5.10.1 Boundary Conditions for Normal Components of B
Field 186
5.10.2 Boundary Conditions for Tangential Components of H Field 187
5.11 Energy in a Magnetic Field 190
5.12 Magnetic Circuits 191
5.13 Summary 199
5.14 Review Questions 201
5.15 Problems 203
6 APPLICATIONS OF STATIC FIELDS 21O
6.1 Introduction 210
6.2 Deflection of a Charged Particle 210
6.3 Cathode-Ray Oscilloscope 212
6.4 Ink-Jet Printer 215
6.5 Sorting of Minerals 216
6.6 Electrostatic Generator 218
6.7 ElectrostaticVoltmeter 220
6.8 Magnetic Separator 221
6.9 Magnetic Deflection 222
6.10 Cyclotron 224
6.11 The Velocity Selector and the Mass Spectrometer 226
6.12 The Hall Effect 228
6.13 Magnetohydrodynamic Generator 231
6.14 An Electromagnetic Pump 232
6.15 A Direct-Current Motor 232
6.16 Summary 234
6.17 Review Questions 236
6.18 Problems 237
7 TIME-VARYING ELECTROMAGNETIC FIELDS 24O
7.1 Introduction 240
7.2 Motional Electromotive Force 240
7.2.1 General Expression for Motional emf 242
7.3 Faraday's Law of Induction 245
7.3.1 Induced emf Equation 247
7.4 Maxwell's Equation (Faraday's Law) 249
7.4.1 General Equations 250
7.5 Self-Inductance 253
7.6 Mutual Inductance 257
7.7 Inductance of Coupled Coils 261
7.7.1 Series Connection 261
7.7.2 Parallel Connection 262
7.8 Energy in a Magnetic Field 263
7.8.1 Single Coil 263
7.8.2 Coupled Coils 265
7.9 Maxwell's Equation from Ampere's Law 267
7.10 Maxwell's Equations from Gauss's Laws 270
7.11 Maxwell's Equations and Boundary Conditions 270
7.11.1 Maxwell's Equations 271
7.11.2 The Constitutive Equations 272
7.11.3 Boundary Conditions 273
7.12 Poynting's Theorem 275
7.13 Time-Harmonic Fields 279
7.13.1 Maxwell's Equations in Phasor Form 281
7.13.2 Boundary Conditions in Phasor Form 281
7.13.3 Poynting Theorem in Phasor Form 282
7.14 Applications of Electromagnetic Fields 284
7.14.1 The Transformer 285
7.14.2 The Autotransformer 290
7.14.3 The Betatron 293
7.15 Summary 295
7.16 Review Questions 297
7.17 Problems 298
8 PLANE WAVE PROPAGATION 3O5
8.1 Introduction 305
8.2 General Wave Equations 305
8.3 Plane Wave in a Dielectric Medium 307
8.3.1 The Forward-Travelling Wave 309
8.3.2 The Backward-Travelling Wave 311
8.3.3 Boundless Dielectric Medium 312
8.4 Plane Wave in Free Space 315
8.5 Plane Wave in a Conducting Medium 316
8.6 Plane Wave in a Good Conductor 322
8.6.1 Surface Resistance 323
8.7 Plane Wave in a Good Dielectric 325
8.8 Polarization of a Wave 327
8.8.1 A Linearly Polarized Wave 328
8.8.2 An Elliptically Polarized Wave 329
8.8.3 A Circularly Polarized Wave 330
8.9 Normal Incidence of Uniform Plane Waves 331
8.9.1 Conductor-Conductor Interface 332
8.9.2 Dielectric-Dielectric Interface 336
8.9.3 Dielectric-Perfect Conductor Interface 338
8.9.4 DieIectric-Conductor Interface 342
8.10 Oblique Incidence on a Plane Boundary 344
8.10.1 Perpendicular Polarization 345
8.10.2 Parallel Polarization 356
8.11 Summary 360
8.12 Review Questions 362
8.13 Problems 363
9 TRANSMISSION LINES 367
9.1 Introduction 367
9.2 A Parallel-Plate Transmission Line 369
9.2.1 Parameters of a Parallel-Plate Transmission Line 372
9.2.2 Equivalent Circuit of a Parallel-Plate Transmission Line 374
9.3 Voltage and Current in Terms of the Sending-End and Receiving-End Variables 379
9.4 The Input Impedance 382
9.4.1 Quarter-Wavelength Line 384
9.4.2 Half-Wavelength Line 385
9.5 Reflections at Discontinuity Points Along Transmission Lines 389
9.6 Standing Waves in Transmission Lines 392
9.6.1 Voltage Standing-Wave Ratio 395
9.7 Impedance Matching with Shunt Stub 398
9.8 Transmission Lines with Imperfect Materials 400
9.8.1 Wave Equations 400
9.8.2 Voltage and Current Relationships 403
9.9 Transients in Transmission Lines 405
9.9.1 Transmission Line Equations in the Time Domain 406
9.9.2 Transient Response of a Lossless Transmission Line 40
9.9.3 Lattice Diagrams 412
9.10 Skin Effect and Resistance 421
9.11 Summary 425
9.12 Review Questions 427
9.13 Problems 428
1O WAVEGUIDES AND CAVITY RESONATORS 433
10.1 Introduction 433
10.2 Wave Equations in Cartesian Coordinates 435
10.3 Transverse Magnetic (TM) Mode 438
10.3.1 Operation Below Cutoff Frequency 441
10.3.2 Operation Above Cutoff Frequency 442
10.3.3 Power Flow in TM Mode 444
10.4 Transverse-Etectric (TE) Mode 448
10.4.1 Operation Below Cutoff Frequency 451
10.4.2 Operation Above Cutoff Frequency 452
10.4.3 Power Flow in TE Mode 452
10.5 Losses in a Waveguide 455
10.5.1 Perfect Dielectric Medium with Finitely Conducting Walls 456
10.5.2 Imperfect Dielectric Medium with Perfectly Conducting Watls 459
10.6 Cavity Resonators 460
10.6.1 Transverse Magnetic (TM) Mode 461
10.6.2 Transverse Electric (UE) Mode 462
10.6.3 Quality Factor 464
10.7 Summary 468
10.8 Review Questions 469
10.9 Problems 470
11 ANTENNAS 473
11.1 Introduction 473
11.2 Wave Equations in Terms of Potential Functions 474
11.3 Hertzian Dipole 477
11.3.1 Near-Zone Fields 479
11.3.2 Radiation Fields 480
11.3.3 Radiation Resistance 482
11.3.4 Directive Gain and Directivity 482
11.4 A Magnetic Dipole 483
11.5 A Short Dipole Antenna 487
11.6 A Half-Wave Dipole Antenna 488
11.7 Antenna Arrays 491
11.8 Linear Arrays 495
11.9 Efficiency of an Antenna 499
11.10 Receiving Antenna and Friis Equation 500
11.11 The Radar System 503
11.11.1 Doppler Effect 504
11.12 Summary 505
11.13 Review Questions 506
11.14 Problems 507
12 COM PUTER-Al DED ANALYSIS OF ELECTROMnGNETIC FIELDS 511
12.1 Introduction 511
12.2 Finite-Difference Method 512
12.2.1 Boundary Conditions 514
12.2.2 Iterative Solution of Finite-Difference Equations 516
12.3 Finite-Element Method 519
12.4 Method of Moments 530
12.5 Summary 534
12.6 Review Questions 534
12.7 Problems 535
APPENDIX A SMITH CHART AND ITS APPLICATIONS
A.1 Introduction 538
A.2 Smith Chart 539
A.3 Determination of VSWR Using the Smith Chart 551
A.4 Admittance of an Impedance Using the Smith Chart 555
A.5 Impedance Matching with Shunt Stub Lines 557
APPENDIX B COMPUTER PROGRAMS FOR VARIOUS
PROBLEMS 562
PPENDIX C USEFUL MATHEMATICAL TABLES 581
INDEX 589
