CONTENTS

Preface xiiiA Note to the Student xvi

PART 1 : VECTOR ANALYSIS

1 Vector Algebra 3

1.1 Introduction 311.2 A Preview of the Book 4

1.3 Scalars and Vectors 41.4 Unit Vector 5

115 Vector Addition and Subtraction 61.6 Position and Distance Vectors 71.7 Vector Multiplication 111.8 Components of a Vector 16

Summary 22Review Questions 23Problems 25

2 Coordinate Systems and Transformation 28

2.1 Introduction 282.2 Cartesian Coordinates (x, y, z) 292.3 Circular Cylindrical Coordinates (p, <f>, z)2.4 Spherical Coordinates (r, d, z) 32

f2.5 Constant-Coordinate Surfaces 41Summary 46Review Questions 47Problems 49

29

VII

Contents

3 Vector Calculus 53

3.1 Introduction 533.2 Differential Length, Area, and Volume 533.3 Line, Surface, and Volume Integrals 603.4 Del Operator 633.5 Gradient of a Scalar 653.6 Divergence of a Vector and Divergence Theorem 693.7 Curl of a Vector and Stokes's Theorem 753.8 Laplacian of a Scalar 83

t3.9 Classification of Vector Fields 86Summary 89Review Questions 90Problems 93

PART 2: ELECTROSTATICS

4 Electrostatic Fields 103

4.1 Introduction 1034.2 Coulomb's Law and Field Intensity 1044.3 Electric Fields due to Continuous Charge Distributions 1114.4 Electric Flux Density 1224.5 Gauss's Law—Maxwell's Equation 1244.6 Applications of Gauss's Law 1264.7 Electric Potential 1334.8 Relationship between E and V—Maxwell's Equation 1394.9 An Electric Dipole and Flux Lines 1424.10 Energy Density in Electrostatic Fields 146

Summary 150Review Questions 153Problems 155

5 Electric Fields in Material Space 161

5.1 Introduction 1615.2 Properties of Materials 1615.3 Convection and Conduction Currents 1625.4 Conductors 1655.5 Polarization in Dielectrics 1715.6 Dielectric Constant and Strength 774

f 5.7 Linear, Isotropic, and Homogeneous Dielectrics 1755.8 Continuity Equation and Relaxation Time 180

CONTENTS IX

5.9 Boundary Conditions 182Summary 191Review Questions 192Problems 194

6 Electrostatic Boundary-Value Problems 199

6.1 Introduction 1996.2 Poisson's and Laplace's Equations 199

f 6.3 Uniqueness Theorem 2016.4 General Procedure for Solving Poisson's or Laplace's

Equation 2026.5 Resistance and Capacitance 2236.6 Method of Images 240

Summary 246Review Questions 247Problems 249

PART 3: MAGNETOSTATICS

7 Magnetostatic Fields 261

7.1 Introduction 2617.2 Biot-Savart's Law 2637.3 Ampere's Circuit Law—Maxwell's Equation 2737.4 Applications of Ampere's Law 2747.5 Magnetic Flux Density—Maxwell's Equation 2817.6 Maxwell's Equations for Static EM Fields 2837.7 Magnetic Scalar and Vector Potentials 284

f 7.8 Derivation of Biot-Savart's Law and Ampere's Law 290Summary 292Review Questions 293Problems 296

8 Magnetic Forces, Materials, and Devices 304

8.1 Introduction 3048.2 Forces due to Magnetic Fields 3048.3 Magnetic Torque and Moment 3168.4 A Magnetic Dipole 3188.5 Magnetization in Materials 323

f 8.6 Classification of Magnetic Materials 3278.7 Magnetic Boundary Conditions 3308.8 Inductors and Inductances 336

Contents

8.9 Magnetic Energy 339f8.10 Magnetic Circuits 34718.11 Force on Magnetic Materials

Summary 354Review Questions 356Problems 358

349

PART 4: WAVES AND APPLICATIONS

9 Maxwell's Equations 369

9.1 Introduction 3699.2 Faraday's Law 3709.3 Transformer and Motional EMFs 3729.4 Displacement Current 3819.5 Maxwell's Equations in Final Forms 384

t9.6 Time-Varying Potentials 3879.7 Time-Harmonic Fields 389

Summary 400Review Questions 407Problems 404

10 Electromagnetic Wave Propagation 410

10.1 Introduction 410tl0.2 Waves in General 411

10.3 Wave Propagation in Lossy Dielectrics 41710.4 Plane Waves in Lossless Dielectrics 42310.5 Plane Waves in Free Space 42310.6 Plane Waves in Good Conductors 42510.7 Power and the Poynting Vector 43510.8 Reflection of a Plane Wave at Normal Incidence 440

f 10.9 Reflection of a Plane Wave at Oblique Incidence 451Summary 462Review Questions 464Problems 466

11 Transmission Lines 473

11.1 Introduction 47311.2 Transmission Line Parameters 47411.3 Transmission Line Equations 47711.4 Input Impedance, SWR, and Power 48411.5 The Smith Chart 492

CONTENTS XI

11.6 Some Applications of Transmission Lines 505f 11.7 Transients on Transmission Lines 512111.8 Microstrip Transmission Lines 524

Summary 528Review Questions 530Problems 533

12 Waveguides 542

12.1 Introduction 54212.2 Rectangular Waveguides 54312.3 Transverse Magnetic (TM) Modes 54712A Transverse Electric (TE) Modes 55212.5 Wave Propagation in the Guide 56312.6 Power Transmission and Attenuation 565

tl2.7 Waveguide Current and Mode Excitation 56912.8 Waveguide Resonators 575

Summary 581Review Questions 582Problems 583

13 Antennas 588

13.1 Introduction 58813.2 Hertzian Dipole 59013.3 Half-Wave Dipole Antenna 59413.4 Quarter-Wave Monopole Antenna 59813.5 Small Loop Antenna 59913.6 Antenna Characteristics 60413.7 Antenna Arrays 612

113.8 Effective Area and the Friis Equation 62 /tl3.9 The Radar Equation 625

Summary 629Review Questions 630Problems 632

14 Modern Topics 638

14.1 Introduction 63814.2 Microwaves 63814.3 Electromagnetic Interference and Compatibility14.4 Optical Fiber 649

Summary 656Review Questions 656Problems 658

644

\ii • Contents

15 Numerical Methods 660

15.1tl5.2

15.315.415.5

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

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