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