Elements Of Electromagnetics - Sadiku PDF

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Summary

DUPL PHYSICAL CONSTANTS Approximate Best Experimental Value for Problem Quantity (Units) Symbol Value Work 12 Permittivity of free space (F/m) eu 8.854 x 10 Permeability of free space (H/m) /j,o 4i7 x 10" 7 12.6 x 10" 7 Intrinsic impedance of free rj o 376.6 120ir space (fl) Speed of light...

Description

DUPL

PHYSICAL CONSTANTS Best Experimental Value

Approximate Value for Problem Work

Quantity (Units)

Symbol

Permittivity of free space (F/m)

eu

8.854 x 10

Permeability of free space (H/m)

/j,o

4i7 x 10" 7

12.6 x 10" 7

Intrinsic impedance of free space (fl)

rj o

376.6

120ir

Speed of light in vacuum (m/s)

c

2.998 x 108

3 X 108

Electron charge (C)

e

Electron mass (Kg)

12

-1.6030 x 10" l 9

-1.6 x 10" 1 9

mQ

9.1066 x 10" 31

9.1 x 10" 31

Proton mass (kg)

mp

1.67248 x 10" 27

1.67 x 10" 27

Neutron mass (Kg)

ma

1.6749 x 10" 27

1.67 x 10

Boltzmann constant (J/K)

K

1.38047 x 10" 23

1.38 x 10" 23

Avogadro's number (/Kg-mole)

N

6.0228 x 1026

6 x 1026

Planck's constant (J • s)

h

6.624 x 10" 34

6.62 x 10" 3 4

Acceleration due to gravity (m/s2)

g

9.81

9.8

Universal contant of gravitation (m2/Kg • s2)

G

6.658 x 1 0 - "

6.66 x 10" 11

Electron-volt (J)

eV

1.6030 x 10" 19

1.6 x 10" 1 9

27

CONTENTS

Preface xiii A Note to the Student

xvi

PART 1 : VECTOR ANALYSIS 1

Vector Algebra 1.1 11.2 1.3 1.4 115 1.6 1.7 1.8

2

3

Introduction 3 A Preview of the Book 4 Scalars and Vectors 4 Unit Vector 5 Vector Addition and Subtraction 6 Position and Distance Vectors 7 Vector Multiplication 11 Components of a Vector 16 Summary 22 Review Questions 23 Problems 25

Coordinate Systems and Transformation 2.1 2.2 2.3 2.4 f2.5

28

Introduction 28 Cartesian Coordinates (x, y, z) 29 Circular Cylindrical Coordinates (p, , z)29 Spherical Coordinates (r, d, z) 32 Constant-Coordinate Surfaces 41 Summary 46 Review Questions 47 Problems 49

VII

Contents

3

Vector Calculus 3.1 3.2 3.3 3.4 3.5 3.6 3.7 3.8 t3.9

53

Introduction 53 Differential Length, Area, and Volume 53 Line, Surface, and Volume Integrals 60 Del Operator 63 Gradient of a Scalar 65 Divergence of a Vector and Divergence Theorem Curl of a Vector and Stokes's Theorem 75 Laplacian of a Scalar 83 Classification of Vector Fields 86 Summary 89 Review Questions 90 Problems 93

69

PART 2 : ELECTROSTATICS 4

Electrostatic Fields 4.1 4.2 4.3 4.4 4.5 4.6 4.7 4.8 4.9 4.10

5

103

Introduction 103 Coulomb's Law and Field Intensity 104 Electric Fields due to Continuous Charge Distributions 111 Electric Flux Density 122 Gauss's Law—Maxwell's Equation 124 Applications of Gauss's Law 126 Electric Potential 133 Relationship between E and V—Maxwell's Equation 139 An Electric Dipole and Flux Lines 142 Energy Density in Electrostatic Fields 146 Summary 150 Review Questions 153 Problems 155

Electric Fields in Material Space 5.1 5.2 5.3 5.4 5.5 5.6 f 5.7 5.8

161

Introduction 161 Properties of Materials 161 Convection and Conduction Currents 162 Conductors 165 Polarization in Dielectrics 171 Dielectric Constant and Strength 774 Linear, Isotropic, and Homogeneous Dielectrics 175 Continuity Equation and Relaxation Time 180

CONTENTS

5.9

6

Boundary Conditions 182 Summary 191 Review Questions 192 Problems 194

Electrostatic Boundary-Value Problems 6.1 6.2 f 6.3 6.4 6.5 6.6

199

Introduction 199 Poisson's and Laplace's Equations 199 Uniqueness Theorem 201 General Procedure for Solving Poisson's or Laplace's Equation 202 Resistance and Capacitance 223 Method of Images 240 Summary 246 Review Questions 247 Problems 249

PART 3: MAGNETOSTATICS 7

Magnetostatic Fields 7.1 7.2 7.3 7.4 7.5 7.6 7.7 f 7.8

8

261

Introduction 261 Biot-Savart's Law 263 Ampere's Circuit Law—Maxwell's Equation 273 Applications of Ampere's Law 274 Magnetic Flux Density—Maxwell's Equation 281 Maxwell's Equations for Static EM Fields 283 Magnetic Scalar and Vector Potentials 284 Derivation of Biot-Savart's Law and Ampere's Law Summary 292 Review Questions 293 Problems 296

Magnetic Forces, Materials, and Devices 8.1 8.2 8.3 8.4 8.5 f 8.6 8.7 8.8

304

Introduction 304 Forces due to Magnetic Fields 304 Magnetic Torque and Moment 316 A Magnetic Dipole 318 Magnetization in Materials 323 Classification of Magnetic Materials 327 Magnetic Boundary Conditions 330 Inductors and Inductances 336

290

IX

Contents 8.9 f8.10 18.11

Magnetic Energy Magnetic Circuits Force on Magnetic Summary 354 Review Questions Problems 358

339 347 Materials

349

356

PART 4: WAVES AND APPLICATIONS 9

Maxwell's Equations 369 9.1 9.2 9.3 9.4 9.5 t9.6 9.7

10

Electromagnetic Wave Propagation 10.1 tl0.2 10.3 10.4 10.5 10.6 10.7 10.8 f 10.9

11

Introduction 369 Faraday's Law 370 Transformer and Motional EMFs 372 Displacement Current 381 Maxwell's Equations in Final Forms 384 Time-Varying Potentials 387 Time-Harmonic Fields 389 Summary 400 Review Questions 407 Problems 404

Introduction 410 Waves in General 411 Wave Propagation in Lossy Dielectrics 417 Plane Waves in Lossless Dielectrics 423 Plane Waves in Free Space 423 Plane Waves in Good Conductors 425 Power and the Poynting Vector 435 Reflection of a Plane Wave at Normal Incidence Reflection of a Plane Wave at Oblique Incidence Summary 462 Review Questions 464 Problems 466

Transmission Lines 11.1 11.2 11.3 11.4 11.5

410

473

Introduction 473 Transmission Line Parameters 474 Transmission Line Equations 477 Input Impedance, SWR, and Power 484 The Smith Chart 492

440 451

CONTENTS

11.6 f 11.7 111.8

Some Applications of Transmission Lines Transients on Transmission Lines 512 Microstrip Transmission Lines 524 Summary 528 Review Questions 530 Problems 533

12 Waveguides 12.1 12.2 12.3 12A 12.5 12.6 tl2.7 12.8

13 Antennas 13.1 13.2 13.3 13.4 13.5 13.6 13.7 113.8 tl3.9

14

542

Introduction 542 Rectangular Waveguides 543 Transverse Magnetic (TM) Modes 547 Transverse Electric (TE) Modes 552 Wave Propagation in the Guide 563 Power Transmission and Attenuation 565 Waveguide Current and Mode Excitation 569 Waveguide Resonators 575 Summary 581 Review Questions 582 Problems 583

588 Introduction 588 Hertzian Dipole 590 Half-Wave Dipole Antenna 594 Quarter-Wave Monopole Antenna 598 Small Loop Antenna 599 Antenna Characteristics 604 Antenna Arrays 612 Effective Area and the Friis Equation 62 / The Radar Equation 625 Summary 629 Review Questions 630 Problems 632

Modern Topics 14.1 14.2 14.3 14.4

505

638

Introduction 638 Microwaves 638 Electromagnetic Interference and Compatibility Optical Fiber 649 Summary 656 Review Questions 656 Problems 658

644

XI

\ii

•

Contents

15

Numerical Methods 15.1 tl5.2 15.3 15.4 15.5

660

Introduction 660 Field Plotting 667 The Finite Difference Method 669 The Moment Method 683 The Finite Element Method 694 Summary 713 Review Questions 714 Problems 7 / 6

Appendix A Mathematical Formulas 727 Appendix B Material Constants 737 Appendix C Answers to Odd-Numbered Problems 740 Index 763

PREFACE

The fundamental objectives of the book remains the same as in the first edition—to present electromagnetic (EM) concepts in a clearer and more interesting manner than earlier texts. This objective is achieved in the following ways: 1. To avoid complicating matters by covering EM and mathematical concepts simultaneously, vector analysis is covered at the beginning of the text and applied gradually. This approach avoids breaking in repeatedly with more background on vector analysis, thereby creating discontinuity in the flow of thought. It also separates mathematical theorems from physical concepts and makes it easier for the student to grasp the generality of those theorems. 2. Each chapter starts with a brief introduction that serves as a guide to the whole chapter and also links the chapter to the rest of the book. The introduction helps students see the need for the chapter and how the chapter relates to the previous chapter. Key points are emphasized to draw the reader's attention to them. A brief summary of the major concepts is provided toward the end of the chapter. 3. To ensure that students clearly understand important points, key terms are defined and highlighted. Essential formulas are boxed to help students identify them. 4. Each chapter includes a reasonable amount of examples with solutions. Since the examples are part of the text, they are clearly explained without asking the reader to fill in missing steps. Thoroughly worked-out examples give students confidence to solve problems themselves and to learn to apply concepts, which is an integral part of engineering education. Each illustrative example is followed by a problem in the form of a Practice Exercise, with the answer provided. 5. At the end of each chapter are ten review questions in the form of multiple-choice objective items. It has been found that open-ended questions, although intended to be thought provoking, are ignored by most students. Objective review questions with answers immediately following them provide encouragement for students to do the problems and gain immediate feedback. A large number of problems are provided are presented in the same order as the material in the main text. Problems of intermediate difficulty are identified by a single asterisk; the most difficult problems are marked with a double asterisk. Enough problems are pro-

XIII

\iv

•

Preface vided to allow the instructor to choose some as examples and assign some as homework problems. Answers to odd-numbered problems are provided in Appendix C. 6. Since most practical applications involve time-varying fields, six chapters are devoted to such fields. However, static fields are given proper emphasis because they are special cases of dynamic fields. Ignorance of electrostatics is no longer acceptable because there are large industries, such as copier and computer peripheral manufacturing, that rely on a clear understanding of electrostatics. 7. The last chapter covers numerical methods with practical applications and computer programs. This chapter is of paramount importance because most practical problems are solvable only by using numerical techniques. 8. Over 130 illustrative examples and 400 figures are given in the text. Some additional learning aids, such as basic mathematical formulas and identities, are included in the Appendix. Another guide is a special note to students, which follows this preface. In this edition, a new chapter on modern topics, such as microwaves, electromagnetic interference and compatibility, and fiber optics, has been added. Also, the Fortran codes in previous editions have been converted to Matlab codes because it was felt that students are more familiar with Matlab than with Fortran. Although this book is intended to be self-explanatory and useful for self-instruction the personal contact that is always needed in teaching is not forgotten. The actual choice o1 course topics, as well as emphasis, depends on the preference of the individual instructor For example, the instructor who feels that too much space is devoted to vector analysis o: static fields may skip some of the materials; however, the students may use them as refer ence. Also, having covered Chapters 1 to 3, it is possible to explore Chapters 9 to 15. In structors who disagree with the vector-calculus-first approach may proceed with Chapter; 1 and 2, then skip to Chapter 4 and refer to Chapter 3 as needed. Enough material i covered for two-semester courses. If the text is to be covered in one semester, some sec tions may be skipped, explained briefly, or assigned as homework. Sections marked wit! the dagger sign (t) may be in this category. A suggested schedule for a four-hour semester coverage is on page xv. Acknowledgments I would like to thank Peter Gordon and the editorial and production staff of Oxford Un versity Press for a job well done. This edition has benefited from the insightful commeni of the following reviewers: Leo C. Kempel, Michigan State University; Andrew Diene University of California, Davis; George W. Hanson, University of Wisconsin-Milwaukei Samir El-Ghazaly, Arizona State University; and Sadasiva M. Rao, Auburn University, am greatly indebted to Raymond Garcia, Jerry Sagliocca, and Dr. Oladega Soriyan f< helping with the solutions manual and to Dr. Saroj Biswas for helping with Matlab. I a: grateful to Temple University for granting me a leave in Fall 1998, during which I was ab to work on the revision of this book. I owe special thanks to Dr. Keya Sadeghipour, de; of the College of Engineering, and Dr. John Helferty, chairman of the Department of Ele trical and Computer Engineering for their constant support. As always, particular than]

PREFACE

xv

Suggested Schedule Chapter 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

Title Vector Algebra Coordinate Systems and Transformation Vector Calculus Electrostatic Fields Electric Fields in Material Space Electrostatic Boundary-Value Problems Magnetostatic Fields Magnetic Forces, Materials, and Devices Maxwell's Equations Electromagnetic Wave Propagation Transmission Lines Waveguides Antennas Modern Topics Numerical Methods Exams TOTAL

Approximate Number of Hours 2 2 4 6 4 5 4 6 4 5 5 4 5 (3)

(6) 4 60

go to my wife, Chris, and our daughters, Ann and Joyce, for the patience, prayers, and full support. As usual, I welcome your comments, suggestions, and corrections. Matthew N. O. Sadiku

A NOTE TO THE STUDENT

Electromagnetic theory is generally regarded by most students as one of the most difficult courses in physics or the electrical engineering curriculum. But this misconception may be proved wrong if you take some precautions. From experience, the following ideas are provided to help you perform to the best of your ability with the aid of this textbook: 1. Pay particular attention to Part I on Vector Analysis, the mathematical tool for this course. Without a clear understanding of this section, you may have problems with the rest of the book. 2. Do not attempt to memorize too many formulas. Memorize only the basic ones, which are usually boxed, and try to derive others from these. Try to understand how formulas are related. Obviously, there is nothing like a general formula for solving all problems. Each formula has some limitations due to the assumptions made in obtaining it. Be aware of those assumptions and use the formula accordingly. 3. Try to identify the key words or terms in a given definition or law. Knowing the meaning of these key words is essential for proper application of the definition or law. 4. Attempt to solve as many problems as you can. Practice is the best way to gain skill. The best way to understand the formulas and assimilate the material is by solving problems. It is recommended that you solve at least the problems in the Practice Exercise immediately following each illustrative example. Sketch a diagram illustrating the problem before attempting to solve it mathematically. Sketching the diagram not only makes the problem easier to solve, it also helps you understand the problem by simplifying and organizing your thinking process. Note that unless otherwise stated, all distances are in meters. For example (2, - 1 , 5) actually means (2 m, - 1 m, 5 m). A list of the powers of ten and Greek letters commonly used throughout this text is provided in the tables located on the inside cover. Important formulas in calculus, vectors, and complex analysis are provided in Appendix A. Answers to odd-numbered problems are in Appendix C.

XVI

INDEX

Acceptance angle, 653 Ac resistance, 427 Ampere's law, 262, 273, 290 applications of, 274-278 Amperian path, 274 Amplitude, 412 Angle of incidence, 451 Angular frequency, 412 Antenna pattern. See Radiation pattern Antenna arrays, 612-618 binomial type, 621 broadside type, 615 end-fire type, 615 Antennas, 588-618 types of, 589 Array factor, 613 Attenuation, 649, 654 Attenuation constant, 421, 479 Azimuthal angle, 30 Bac-cab rule, 16 Band matrix method, 672, 702 Bandwidth, 638, 649 Bessel differential equation, 223 Biot-Savart's law, 262-266, 290, 307 Bonding, 647 Bonding effectiveness, 648 Bounce diagram, 514 Boundary conditions, 182-187, 330-332, 385 Boundary-value problems, 199 Brewster angle, 455 Capacitance, 224-230 Capacitor, 224-230 Cartesian coordinates, 29, 53 Characteristic admittance, 480 Characteristic impedance, 479, 525 Charge conservation, 180 Charged ring, 118 Charged sphere, 128 Circular cylindrical coordinates, 29, 55 Circulation, 60

Closed form solution, 660 Coaxial capacitor, 227 Coaxial line, 276 Colatitude, 33 Complex permittivity, 422 Complex variables, 728-729 Components of a vector, 6 Conductivity, 162, 164 values of, 737 Conductors, 161, 164-167 Conservation of magnetic flux, 283 Conservative field, 87 Constant-coordinates surfaces, 41^14 Constitutive relations, 385 Continuity equation, 180, 385 Coulomb's law, 104-107, 305 Critical angle, 653 Cross product, 13 Curie temperature, 328 Curl, 75-80 definition of, 76 properties of, 78 Current, 162-164 conduction type, 164 convection type, 163 definition of, 162 displacement type, 382 Current density, definition of, 163 Current reflection coefficient, 487 Cutoff, 549 Cutoff frequency, 542, 550 Cutoff wavelength, 550 Dc resistance, 427, 647 Definite integrals, 734 Degenerate modes, 576 Del operator, 63 Derivatives, 731 Diamagnetism, 327 Dielectric breakdown, 175 Dielectric constant, 175 values of, 738

Dielectric strength, 175 Dielectrics, 161 Difference equations, 669 Differential displacement, 53, 55, 56, 89 Differential normal area, 54, 55, 57, 89 Differential solid angle, 606 Differential volume, 54, 55, 57, 89 Dipole antenna, 589 Dipole moment, 143 Directional derivative, 67 Directive gain, 606 Directivity, 606 Dispersion, 654 Displacement current density, 381 Distance vector, 8 Distortionless line, 481 Divergence, 69-73 definition of, 69 properties of, 72 Divergence theorem, 72, 125 Dominant mode, 554, 578 Dot product, 12 Effective area, 621 Effective relative permittivity, 525 Electric dipole, 142 Electric displacement, 123 Electric field intensity, 106 Electric flux, 123 Electric flux density, 122, 123 Electric flux lines, 144 Electric susceptibility, 174 Electrical length, 486 Electrohydrodynamic pump. 203 Electromagnetic compatibility (EMC). 644 Electromagnetic interference (EMI). 644 Electromagnetics (EM), 3 Electrometer, 179 Electromotive force (emf), 370 Electrostatic field, 103, 592 Electrostatic shielding, 186 Electrostatics, 103 Element coefficient matrix, 698

763

764

Index

Emf. See Electromotive force Energy, 146, 339-341 Equipotential line, 144 Equipotential surface, 144 Evanescent mode, 549 Exponential identities, 730 External inductance, 338

Far field, 592 Faraday's law, 370 Ferromagnetism, 328 Field, classification of, 86-88 definition of, 5 harmon...