Electromagnetic fieldsPDF电子书下载

Chapter One: Introduction to Fields and Field Theory 1

1.1.Types of Fields 2

1.2.Typical Field Behavior 2

1.2.1.The Field Approach -A Temperature Field Example 3

1.3.Electromagnetic Fields, Energy, and Waves- A Preview 7

Chapter Two: Electromagnetic Field Laws in Free Space 10

2.1.Basic Postulates and Definitions 11

2.2.Charge Density and Current Density 14

2.3.Postulate Ⅳ-The Field Equations in Free Space 16

2.3.1.Line, Surface, and Volume Integrals 19

2.3.2.The Physical Significance of the Field Equations 24

2.4.Applications of the Integral Field Laws 28

2.4.1.The Point-Charge Field 28

2.4.2.A Line of Charge 30

2.4.3.A Line of Current 32

2.5.Summary and Conclusions 34

2.6.Selected References 35

Problems 36

Chapter Three: Vector Analysis 41

3.1.Scalars and Vectors 41

3.2.Vector Addition and Subtraction 42

3.3.Orthogonal Coordinate Systems 43

3.3.1.Cartesian Coordinates 45

3.3.2.Circular-Cylindrical Coordinates 46

3.3.3.Spherical Coordinates 49

3.4.The Scalar or Dot Product 52

3.5.The Vector or Cross Product 55

3.6.Line, Surface, and Volume Integration 59

3.6.1.Differential Lengths, Surfaces, and Volumes 60

3.6.2.Evaluation of Line Integrals 65

3.6.3.Evaluation of Surface Integrals 71

3.6.4.Evaluation of Volume Integrals 74

3.7.The Gradient and the Directional Derivative of a Scalar Field 76

3.7.1.Definition of the Gradient 76

3.7.2.Examples and Properties of the Gradient 79

3.7.3.Evaluation of the Gradient 82

3.8.The Divergence and Gauss' Theorem 85

3.8.1.Definition and Evaluation 85

3.8.2.Properties and Examples of the Divergence 92

3.8.3.Gauss' Theorem 93

3.9.The Curl and Stokes' Theorem 95

3.9.1.Definition and Evaluation 95

3.9.2.Physical Properties of the Curl-The Curl Meter 102

3.9.3.Mathematical Properties of the Curl-Stokes' Theorem 106

3.10.Summary and Conclusions 109

3.11.Selected References 111

Problems 111

Chapter Four: The Differential Field Laws 115

4.1.The Differential Field Laws in Free Space 115

4.1.1.The Divergence Relations 116

4.1.2.The Curl Relations- Maxwell's Equations 117

4.1.3.The Significance of the Differential Field Laws 118

4.2.Surface Charge Density and Surface Current Density 119

4.3.Boundary Conditions 122

4.3.1.Discontinuities in the Normal Components 123

4.3.2.Tangential Field Components 126

4.3.3.The Signifi cance of the Boundary Conditions 127

4.4.Some Direct Applications of the Differential Laws 128

4.4.1.A Spherical Cloud of Charge 128

4.4.2.Shell of Charge 131

4.4.3.Cylinder of Current 134

4.4.4.Shell of Current 137

4.5.Electromagnetic Fields in Conductors 140

4.5.1.The Macroscopic Model of Conducting Material 140

4.5.2.The Differential Laws in Conductors 141

4.6.Preview of the “Field Approach”-Some Mathematically Acceptable Static Fields 142

4.6.1.The Point-Charge Field 143

4.6.2.A Uniform E Field 145

4.6.3.A Uniform H Field 146

4.7.Summary and Conclusions 147

Problems 148

Chapter Five: Static Fields Ⅰ 153

5.1.The Static Field Laws 154

5.2.Electrostatic Fields 155

5.2.1.The Coulomb Field of Known Stationary Charges 155

5.2.2.Examples of Static E Fields 159

5.2.2.1.An Electric Dipole 159

5.2.2.2.A Ring of Charge 162

5.2.2.3.A Semicircular Ring of Charge 165

5.3.The Differential Equations for the Scalar Potential 167

5.3.1.Poisson's Equation and Laplace's Equation 167

5.3.2.The Particular Solution of Poisson's Equation 169

5.3.3.The Need for a Homogeneous Solution 170

5.4.Physical Properties of Laplace's Equation 172

5.4.1.A Wire Grid Analog 172

5.4.2.An Elastic Membrane Analog 175

5.5.Mathematical Properties of Laplace's Equation 179

5.5.1.A Maximum-Minimum Theorem 179

5.5.2.The Uniqueness Theorem 179

5.6.Solutions of Laplace's Equation in Rectangular Coordinates 182

5.6.1.Trivial Solutions 183

5.6.2.General Solutions 184

5.6.3.Two-Dimensional Solutions 187

5.7.Examples of Electrostatic Fields in Cartesian Coordinates 187

5.7.1.A Parallel-Plate Capacitor 188

5.7.2.A Rectangular Model of a Resistor 192

5.7.3.A Rectangular Conducting Sheet 196

5.7.4.A Rectangular Air Slot 202

5.7.4.1.Sinusoidal Excitation 205

5.7.4.2.Uniform Excitation 208

5.7.4.3.Arbitrary Excitation 213

5.8.Summary and Conclusions 213

Problems 215

Chapter Six: Static Fields Ⅱ 223

6.1.Two-Dimensional Solutions of Laplace's Equation in Cylindrical Coordinates 223

6.1.1.Trivial Solutions 224

6.1.2.General Solutions 226

6.2.Solutions of Laplace's Equation in Spherical Coordinates 231

6.2.1.Trivial Solutions 232

6.2.2.General Solutions 233

6.3.Summary of the Solutions of Laplace's Equation 236

6.4.Electrostatic Field Examples 237

6.4.1.Electric Dipole Within a Conducting Sphere 237

6.4.1.1.Uncharged Shell 238

6.4.1.2.Charged Shell 243

6.4.1.3.Arbitrary Charge Distribution Within the Shell 246

6.4.2.A Conducting Sphere in a Uniform Field 249

6.4.3.A Conducting Cylinder in a Uniform Current 254

6.4.3.1.Case A: σ1 = σ2 257

6.4.3.2.Case B: σ2 = 0 =σ（σ，1>0） 257

6.4.3.3.Case C: σ2 = ∞ （0 < σ1 <∞） 260

6.4.3.4.Case D: General Values of v1 and σ2 263

6.4.4.A Circular Resistor with Fringing 264

6.4.4.1.The Field in the Conductor and the Source 264

6.4.4.2.The Outside （Fringing） Field 266

6.5.Static Magnetic Fields 270

6.5.1.The Magnetic Vector Potential 271

6.5.2.The Magnetic Field of Known Fixed Currents 272

6.6.The Scalar Magnetic Potential 275

6.6.1.Currents Within V'-the Particular Solution 276

6.6.2.The Homogeneous Solution and the Scalar Magnetic Potential 276

6.6.3.Boundary Conditions and Uniqueness 277

6.7.Examples of Static H Fields 278

6.7.1.A Single-Turn Inductor 278

6.7.2.A Spherical Coil 280

6.8.Dipole Layer Analog of Static Current Loops 287

6.8.1.A Single-Turn Current Loop 288

6.8.2.The Dipole Layer Analog 291

6.8.3.A Current Loop Dipole Field 294

6.8.4.A Closely Wound Solenoid 297

6.9.Far-Field Potentials and the Multipole Expansion 303

6.9.1.The Zero-Order Approximation 304

6.9.2.Higher Order Approximations 305

6.9.3.The Multipole Expansion 308

6.10.Summary and Conclusions 314

6.11.Selected References 316

Problems 317

Chapter Seven: Macroscopic Fields in Matter 326

7.1.Microscopic and Macroscopic Fields in Matter 326

7.2.The Macroscopic Model of Polarized Matter 327

7.2.1.The Mechanics of Polarization 328

7.2.2.Polarization Density 330

7.2.3.Polarization Charge Density and Current Density （Volume Effects） 331

7.2.4.Polarization Surface Effects 334

7.3.The Electromagnetic Field Laws in Dielectric Material 336

7.3.1.The E-P Form of the Field Laws in Polarized Matter 336

7.3.2.The E-D Form of the Field Laws in Matter 338

7.4.Examples of Permanently Polarized Bodies 340

7.4.1.A Permanently Polarized Slab 340

7.4.1.1.Case 1: Uniform Polarization 340

7.4.1.2.Case 2: Nonuniform Polarization 343

7.4.2.A Permanently Polarized Block 346

7.4.3.A Uniformly Polarized Sphere 349

7.5.Examples of Systems With Specified Permittivity ？ 355

7.5.1.A Sphere of Uniform Permittivity in a Uniform Field 355

7.5.2.A Parallel-Plate Capacitor Filled with a Uniform ？ Material 360

7.5.3.A Parallel-Plate Capacitor Filled with Nonuni-form ？ Material 364

7.5.4.A Parallel-Plate Capacitor with Layers of Dielectric Slabs 368

7.6.The Macroscopic Model of Magnetized Matter 370

7.6.1.The Physical Basis of Magnetism 370

7.6.2.The Magnetization Vector 372

7.7.The Amperian-Current Model 372

7.7.1.The Amperian-Current Density 373

7.7.2.The Amperian-Current Form of the Field Laws in Matter 376

7.8.The Magnetic-Charge Model 377

7.8.1.The Concept of Magnetic Charge 377

7.8.2.Magnetic Charge and Magnetic-Charge Density 378

7.9.The B-D Form of the Field Laws in Matter 382

7.10.An Example of the Fields in Magnetic Material 385

7.10.1.A Permanently Magnetized Cylinder 385

7.10.1.1.Use of Amperian-Current Model 385

7.10.1.2.Use of Magnetic-Charge Model 388

7.11.The Constituent Relations 392

7.12.Summary and Conclusions 396

7.13.Selected References 398

Problems 398

Chapter Eight: Electromagnetic Energy and Power 404

8.1.Electromagnetic Force on Moving Charges 404

8.2.Power Supplied to Moving Charges 405

8.3.Conservation of Energy- Poynting's Theorem 407

8.3.1.Differential Form of Poynting's Theorem 407

8.3.2.Integral Form of Poynting's Theorem 410

8.3.3.Some Difficulties in the Identification of S and w 411

8.4.The Energy Stored in Electric and Magnetic Fields 412

8.4.1.Electric Energy Stored in an Air-Filled Capacitor 413

8.4.2.Magnetic Energy Stored in an Air-Filled Inductor 414

8.5.Power Absorbed by Matter 416

8.5.1.Polarization, Magnetization, and Conduction Power Densities 416

8.5.2.Poynting's Theorem in Matter 418

8.6.Static Power Flow and Dissipation 421

8.6.1.Static Power Flow in a Resistor 422

8.6.1.1.The Static E and H Fields 423

8.6.1.2.Poynting's Vector and Power Flow 426

8.6.2.The Static Power Flow in a Rectangular Resistor 428

8.6.2.1.Resistor with Battery at Infinity 428

8.6.2.2.Resistor with Battery Distributed Along One Edge 431

8.6.3.The Static Power Flow in an Electron Beam 434

8.6.3.1.Dynamics of the Electron Beam 434

8.6.3.2.The Static E and H Fields 437

8.6.3.3.Poynting's Vector and the Static Power 439

8.7.Polarization Energy and Electric Energy 441

8.7.1.The Polarization Energy Density 441

8.7.2.The Electric Energy Density 444

8.7.3.Total Electric Energy 445

8.7.4.Examples of Stored Electric Energy-an ？ Filled Capacitor 446

8.8.Magnetization Energy and Magnetic Energy 448

8.8.1.The Magnetization Energy Density 448

8.8.2.The Magnetic Energy Density 449

8.8.3.Total Magnetic Energy 450

8.8.4.Examples of Stored Magnetic Energy 451

8.8.4.1.A Single-Turn Inductor 451

8.8.4.2.A General n-Turn Inductor Coil 453

8.9.Summary and Conclusions 455

8.10.Selected References 457

Problems 458

Chapter Nine: Time-Varying Fields-Low-Frequency Behavior 462

9.1.The Basic Field Laws 462

9.2.Static Versus Time-Varying Fields 464

9.2.1.E and H Field Coupling 464

9.2.2.The Physical Significance of Low-Frequency Fields 465

9.3.An Exact Wave Solution 467

9.3.1.A Simple Wave System 467

9.3.2.One-Dimensional Wave Equations 468

9.3.3.Sinusoidal Steady-State Solutions 470

9.3.4.The Time-Varying Capacitor Field 472

9.3.5.The Low-Frequency Response 474

9.4.A Power Series Approach to Time-Varying Fields 480

9.4.1.General Field Dependence on Frequency 481

9.4.2.The Power Series in ω 482

9.4.3.The Power Series Without ω 488

9.5.Examples of Quasi-Static Fields-The Low-Frequency Response of a Capacitor 490

9.5.1.A Parallel-Plate Capacitor 490

9.5.1.1.Reference Choice 490

9.5.1.2.The Zero-Order Field 492

9.5.1.3.The First-Order Field 495

9.5.1.4.The Quasi-Static Solution 498

9.5.1.5.Second-Order Fields and the Validity of Quasi-Statics 500

9.5.1.6.Third-Order Fields and Beyond 505

9.6.The Low-Frequency Response of Inductors 506

9.6.1.A Single-Turn Inductor 507

9.6.1.1.The Zero-Order Field 507

9.6.1.2.The First-Order Field 508

9.6.1.3.The Quasi-Static Response 509

9.6.1.4.EMF and Lenz's Law 512

9.6.1.5.Second-Order Fields and Beyond 515

9.6.2.An N-Turn Coil 517

9.6.2.1.The Quasi-Static Field Without the Coil 518

9.6.2.2.The Quasi-Static Field with the Coil 519

9.6.2.3.The Physical Significance of the Conserva-tive E'（t） Field 525

9.6.2.4.A Self-Excited N-Turn Coil 528

9.7.The Frequency Response of a Resistor 529

9.7.1.The Zero-Order Fields 530

9.7.2.The First-Order Fields 532

9.7.3.The Quasi-Static Response 532

9.8.Circuit Theory as a Quasi-Static Approximation 536

9.8.1.Kirchhoff's Circuit Laws from Field Theory 537

9.8.2.The Circuit Concept of Power 540

9.9.Summary and Conclusions 543

Problems 544

Chapter Ten: TEM Fields and Waves （Lossless Transmission Line Theory） 548

10.1.Transverse Electromagnetic （TEM） Fields 548

10.1.1.TEM Field Laws 549

10.1.2.TEM Structures- Perfectly Conducting Transmission Lines 550

10.1.3.TEM Boundary Conditions on Perfectly Conducting Lines 551

10.2.The Transmission Line Model 552

10.2.1.Voltage and Current Definitions 553

10.2.2.Normalized Transverse Fields 554

10.2.3.The Transmission Line Equations 556

10.2.4.Transmission Line Parameters 557

10.2.4.1.Capacitance per Unit Length 557

10.2.4.2.Inductance per Unit Length 558

10.2.4.3.Shunt Conductance per Unit Length 559

10.3.The Transmission Line as a Distributed Circuit 559

10.3.1.Transmission Line Equations from the Distributed Circuit Model 561

10.3.2.Power and Energy- Poynting's Theorem 562

10.4.Scalar Wave Motion on Lossless Transmission Lines （Time Domain Analysis） 563

10.4.1.Time-Domain Solution 563

10.4.2.Forward and Backward Traveling Waves 566

10.5.Sinusoidal Waves on Lossless Transmission Lines（Frequency Domain Analysis） 569

10.5.1.Frequency-Domain Solution 570

10.5.2.Forward and Backward Traveling Waves 571

10.5.2.1.Wave Motion and Phase Velocity 571

10.5.2.2.Energy and Power 573

10.5.2.3.Input Impedance and Source Conditions 575

10.5.2.4.Load and Source Boundary Conditions 576

10.5.3.Complete Standing Waves 578

10.5.3.1.A Short-Circuited Line 578

10.5.3.2.Energy and Power 579

10.5.3.3.Input Impedance and Source Conditions 581

10.5.3.4.Other Standing-Wave Systems 582

10.6.Complex Power （On Transmission Lines） 585

10.6.1.Complex Power in Circuit Theory 585

10.6.2.Complex Power in Transmission Line Theory 587

10.6.3.The Complex Poynting Theorem （for Trans-mission Lines） 588

10.6.4.Examples of Complex Power Flow 590

10.7.General Impedance Termination 591

10.7.1.Load Conditions and the Reflection Coefficient 592

10.7.2.Input Impedance and Source Conditions 594

10.7.3.Generalized Reflection Coefficient 595

10.7.4.Standing-Wave Measurements and the Γ-Plane 596

10.7.5.The Smith Chart 600

10.7.5.1.Usefulness of the Smith Chart 601

10.8.Summary and Conclusions 604

Problems 605

Chapter Eleven: Plane Waves in Lossless Media 612

11.1.Uniform Plane Waves-Time-Domain Solution 612

11.1.1.Nature of Uniform Plane Wave （UPW） Solutions 612

11.1.2.z-Directed Uniform Plane Waves （In Time Domain） 613

11.1.3.Fields and Power in Uniform Plane Waves 615

11.2.Fields and Power in the Frequency Domain 620

11.2.1.Use of Complex Vectors 620

11.2.2.Elliptical, Circular, and Linear Polarization 621

11.2.3.The Complex Poynting Theorem 625

11.3.Uniform Plane Waves in the Frequency Domain 628

11.3.1.X- Polarized Waves 628

11.3.2.Nature of the Solutions 629

11.3.3.Role of Uniform Plane Waves 632

11.4.Normal Incidence of a Uniform Plane Wave 632

11.4.1.Normal Incidence on a Perfect Conductor 632

11.4.2.Normal Incidence on a Lossless Dielectric 636

11.4.3.Normal Incidence on Multiple Dielectrics 640

11.5.Oblique Incidence of a Uniform Plane Wave 642

11.5.1.Components of Uniform Plane-Wave Motion 643

11.5.2.Phase, Wavelength, and Wave Velocity 646

11.5.3.Geometry of Oblique Incidence 650

11.5.4.Oblique Incidence on a Perfect Conductor 651

11.5.4.1.Incident and Reflected Wave Solutions 651

11.5.4.2.Transmission Line Analogy 656

11.5.5.Oblique Incidence on an Interface Between Lossless Dielectrics 659

11.5.5.1.Polarization Parallel to the Boundary 659

11.5.5.2.Polarization in the Plane of Incidence 663

11.5.5.3.Brewster's （Polarizing） Angle 665

11.5.5.4.Critical Reflection 667

11.6.Nonuniform Plane Waves 672

11.6.1.Nature of the Solution 672

11.6.2.Phase Delay and Attenuation 674

11.6.3.TE and TM Plane Waves 675

11.6.4.Relationship Between Uniform and Nonuniform Plane Waves 678

11.7.Guided Waves -Lossless Rectangular Waveguides 679

11.7.1.Basic Equations 681

11.7.2.TE and TM Modes 682

11.7.3.TEm,n Modes 683

11.7.3.1.General Solution 683

11.7.3.2.Waveguide Boundary Conditions 685

11.7.3.3.TEm,n Waves 685

11.7.4.TMm,n Modes 687

11.7.5.Properties of Waves in Guides 688

11.7.6.Resonant Cavities 693

11.8.Summary and Conclusions 694

Problems 696

Chapter Twelve: Radiation 702

12.1.Definition of the Problem 702

12.2.Basic Field Laws and Potentials 703

12.2.1.Scalar and Vector Potentials 704

12.2.2.Wave Equations 705

12.2.3.General Wave Solutions-Use of Retarded Potentials 705

12.3.Elemental Dipole Radiation 708

12.3.1.Point-Source Fields 708

12.3.2.The Electric-Dipole （TM） Solution 710

12.3.3.Properties of the Dipole Field 713

12.3.3.1.Wave Motion 713

12.3.3.2.Wave Impedances 714

12.3.3.3.Complex Poynting Vector and Radiated Power 715

12.3.4.The Magnetic-Dipole （TE） Solution 717

12.4.Physical Antennas 722

12.4.1.Nature of the Problem 722

12.4.2.The Physical Electric Dipole 723

12.4.2.1.Details of the Solution 723

12.4.2.2.Impedance Characteristics 727

12.4.2.3.Radiation Characteristics 732

12.4.3.A Half-Wave Antenna 734

12.4.3.1.Details of the Solution 734

12.4.3.2.Radiation Characteristics 736

12.5.The Receiving Properties of a Dipole 739

12.6.Dipole Arrays 743

12.6.1.Element Factor and Array Factor 743

12.6.2.A Two-Dipole Array 746

12.6.3.An N-Dipole Array 750

12.7.Summary and Conclusions 753

Problems 754

Appendix 1: Differential Operators in Orthogonal Coordinates 758

Appendix 2: Summary of Mathematical Formulas 760

Appendix 3: Solutions of Laplace's Equation in Cartesian, Cylindrical, and Spherical Coordinates 762

Appendix 4: Uniform Plane Waves in Lossy Media 763

Index 775