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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 61

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 Electric 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 Electric Field 89

3.9 Boundary Conditions 93

3.9.1 The Normal Component of？ 93

3.9.2 The Tangential Component of？ 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 120

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

4.5 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 ？ and ？ 141

4.10 The Electromotive Force 144

4.11 Summary 147

4.12 Review Questions 149

4.13 Problems 150

5 MAGNETOSTATICS 155

5.1 Introduction 155

5.2 The Biot-Savart Law 156

5.3 Ampère'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

5.9 Magnetic Scalar Potential 184

5.10 Boundary Conditions for Magnetic Fields 186

5.10.1 Boundary Conditions for Normal Components of ？ Field 186

5.10.2 Boundary Conditions for Tangential Components of ？ 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 210

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 Electrostatic Voltmeter 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 240

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 Ampère'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 305

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 Dielectric-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 406

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

10 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-Electric (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 Walls 459

10.6 Cavity Resonators 460

10.6.1 Transverse Magnetic(TM)Mode 461

10.6.2 Transverse Electric(TE)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 COMPUTER-AIDED ANALYSIS OF ELECTROMAGNETIC 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 538

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

APPENDIX C USEFUL MATHEMATICAL TABLES 581

INDEX 589