1 History and Perspective 1
1.1 Brief History of the Science of Electromagnetism 1
1.2 Electromagnetism in the Standard Model 5
2 Vector Calculus 9
2.1 Vector Algebra 10
2.1.1 Definitions 10
2.1.2 Addition and Multiplication of Vectors 13
2.1.3 Vector Product Identities 14
2.1.4 Geometric Meanings 16
2.2 Vector Differential Operators 18
2.2.1 Gradient of a Scalar Function 18
2.2.2 Divergence of a Vector Function 19
2.2.3 Curl of a Vector Function 20
2.2.4 DelIdentities 23
2.3 Integral Theorems 25
2.3.1 Gauss’s Theorem 26
2.3.2 Stokes’s Theorem 27
2.3.3 Vector Calculus in Fluid Mechanics 29
2.4 Curvilinear Coordinates 30
2.4.1 General Derivations 30
2.4.2 Cartesian, Cylindrical, and Spherical Coordinates 33
2.5 The Helmholtz Theorem 37
3 Basic Principles of Electrostatics 44
3.1 Coulomb’s Law 44
3.1.1 The Superposition Principle 46
3.2 The Electric Field 46
3.2.1 Definition 46
3.2.2 Charge as the Source of E 47
3.2.3 Field of a Charge Continuum 49
3.3 Curl and Divergence of E 54
3.3.1 Field Theory Versus Action at a Distance 56
3.3.2 Boundary Conditions of the Electrostatic Field 56
3.4 The Integral Form of Gauss’s Law 57
3.4.1 Flux and Charge 57
3.4.2 Proof of Gauss’s Law 57
3.4.3 Calculations Based on Gauss’s Law 59
3.5 Green’s Function and the Dirac delta Function 62
3.5.1 The Dirac delta Function 62
3.5.2 Another Proof of Gauss’s Law 65
3.6 The Electric Potential 65
3.6.1 Definition and Construction 65
3.6.2 Poisson’s Equation 68
3.6.3 Example Calculations of V （x） 69
3.7 Energy of the Electric Field 72
3.8 The Multipole Expansion 75
3.8.1 Two Charges 75
3.8.2 The Electric Dipole 77
3.8.3 Moments of a General Charge Distribution 78
3.8.4 Equipotentials and Field Lines 79
3.8.5 Torque and Potential Energy for a Dipole in an Electric Field 80
3.9 Applications 82
3.10 Chapter Summary 83
4 Electrostatics and Conductors 92
4.1 Electrostatic properties of conductors 93
4.2 Electrostatic Problems with Rectangular Symmetry 98
4.2.1 Charged Plates 98
4.2.2 Problems with Rectangular Symmetry and External Point Charges.The Method of Images 102
4.3 Problems with Spherical Symmetry 107
4.3.1 Charged Spheres 107
4.3.2 Problems with Spherical Symmetry and External Charges 113
4.4 Problems with Cylindrical Symmetry 116
4.4.1 Charged Lines and Cylinders 116
4.4.2 Problems with Cylindrical Symmetry and an External Line Charge 124
5 General Methods for Laplace’s Equation 133
5.1 Separation of Variables for Cartesian Coordinates 135
5.1.1 Separable Solutions for Cartesian Coordinates 136
5.1.2 Examples 138
5.2 Separation of Variables for Spherical Polar Coordinates 147
5.2.1 Separable Solutions for Spherical Coordinates 147
5.2.2 Legendre Polynomials 149
5.2.3 Examples with Spherical Boundaries 150
5.3 Separation of Variables for Cylindrical Coordinates 159
5.3.1 Separable Solutions for Cylindrical Coordinates 160
5.4 Conjugate Functions in 2 Dimensions 163
5.5 Iterative Relaxation: A Numerical Method 172
6 Electrostatics and Dielectrics 186
6.1 The Atom as an Electric Dipole 187
6.1.1 Induced Dipoles 187
6.1.2 Polar Molecules 189
6.2 Polarization and Bound Charge 191
6.3 The Displacement Field 195
6.3.1 Linear Dielectrics 197
6.3.2 The Clausius-Mossotti Formula 198
6.3.3 Poisson’s Equation in a Uniform Linear Dielectric 200
6.4 Dielectric Material in a Capacitor 201
6.4.1 Design of Capacitors 203
6.4.2 Microscopic Theory 204
6.4.3 Energy in a Capacitor 205
6.4.4 A Concrete Model of a Dielectric 207
6.5 Boundary Value Problems with Dielectrics 208
6.5.1 The Boundary Conditions 208
6.5.2 A Dielectric Sphere in an Applied Field 209
6.5.3 A Point Charge above a Dielectric with a Planar Bound-ary Surface 211
6.5.4 A Capacitor Partially Filled with Dielectric 212
7 Electric Currents 222
7.1 Electric Current in a Wire 222
7.2 Current Density and the Continuity Equation 224
7.2.1 Local Conservation of Charge 226
7.2.2 Boundary Condition on J（x, t） 226
7.3 Current and Resistance 228
7.3.1 Ohm’s Law 228
7.3.2 Fabrication of Resistors 233
7.3.3 The Surface Charge on a Current Carrying Wire 234
7.4 A Classical Model of Conductivity 236
7.5 Joule’s Law 238
7.6 Decay of a Charge Density Fluctuation 239
7.7 Ⅰ-Ⅴ Characteristic of a Vacuum-Tube Diode 241
7.8 Chapter Summary 246
8 Magnetostatics 252
8.1 The Magnetic Force and the Magnetic Field 253
8.1.1 Force on a Moving Charge 253
8.1.2 Force on a Current-Carrying Wire 255
8.2 Applications of the Magnetic Force 255
8.2.1 Helical or Circular Motion of q in Uniform B 255
8.2.2 Cycloidal Motion of q in Crossed E and B 258
8.2.3 Electric Motors 260
8.3 Electric Current as a Source of Magnetic Field 262
8.3.1 The Biot-Savart Law 262
8.3.2 Forces on Parallel Wires 266
8.3.3 General Field Equations for B（x） 267
8.4 Ampere’s Law 270
8.4.1 Ampere Law Calculations 271
8.4.2 Formal Proof of Ampere’s Law 277
8.5 The Vector Potential 280
8.5.1 General Solution for A（x） 281
8.6 The Magnetic Dipole 284
8.6.1 Asymptotic Analysis 284
8.6.2 Dipole Moment of a Planar Loop 286
8.6.3 Torque and Potential Energy of a Magnetic Dipole 287
8.6.4 The Magnetic Field of the Earth 291
8.7 The Full Field of a Current Loop 291
9 Magnetic Fields and Matter 307
9.1 The Atom as a Magnetic Dipole 307
9.1.1 Diamagnetism 310
9.1.2 Paramagnetism 313
9.2 Magnetization and Bound Currents 314
9.2.1 Examples 316
9.2.2 A Geometric Derivation of the Bound Currents 320
9.3 Ampere’s Law for Free Currents, and H 323
9.3.1 The Integral Form of Ampere’s Law 326
9.3.2 The Constitutive Equation 326
9.3.3 Magnetic Susceptibilities 326
9.3.4 Boundary Conditions for Magnetic Fields 329
9.4 Problems Involving Free Currents and Magnetic Materials 331
9.5 A Magnetic Body in an External Field: The Magnetic Scalar Potentialφm （x） 335
9.6 Ferromagnetism 342
9.6.1 Measuring Magnetization Curves: The Rowland Ring 343
9.6.2 Magnetization Curves of Ferromagnetic Materials 345
9.6.3 The Permeability of a Ferromagnetic Material 346
10 Electromagnetic Induction 355
10.1 Motional EMF 356
10.1.1 Electromotive Force 356
10.1.2 EMF from Motion in B 357
10.1.3 The Faraday Disk Generator 358
10.2 Faraday’s Law of Electromagnetic Induction 360
10.2.1 Mathematical Statement 361
10.2.2 Lenz’s Law 363
10.2.3 Eddy Currents 364
10.3 Applications of Faraday’s Law 368
10.3.1 The Electric Generator and Induction Motor 369
10.3.2 The Betatron 371
10.3.3 Self-Inductance 372
10.3.4 Classical Model of Diamagnetism 375
10.4 Mutual Inductance 376
10.5 Magnetic Field Energy 382
10.5.1 Energy in a Ferromagnet 386
11 The Maxwell Equations 397
11.1 The Maxwell Equations in Vacuum and the Displacement Current 398
11.1.1 The Displacement Current 399
11.2 Scalar and Vector Potentials 405
11.2.1 Gauge Transformations and Gauge Invariance 406
11.2.2 Gauge Choices and Equations for A（x,t） and V（x,t） 407
11.3 The Maxwell Equations in Matter 410
11.3.1 Free and Bound Charge and Current 410
11.3.2 Boundary Conditions of Fields 413
11.4 Energy and Momentum of Electromagnetic Fields 415
11.4.1 Poynting’s Theorem 416
11.4.2 Field Momentum 421
11.5 Electromagnetic Waves in Vacuum 423
11.5.1 Derivation of the Wave Equation 424
11.5.2 An Example of a Plane Wave Solution 425
11.5.3 Derivation of the General Plane Wave Solution 431
11.5.4 A Spherical Harmonic Wave 434
11.5.5 The Theory of Light 437
12 Electromagnetism and Relativity 445
12.1 Coordinate Transformations 446
12.1.1 The Galilean Transformation 446
12.1.2 The Lorentz Transformation 448
12.1.3 Examples Involving the Lorentz Transformation 450
12.2 Minkowski Space 452
12.2.1 4-vectors, Scalars, and Tensors 452
12.2.2 Kinematics of a Point Particle 455
12.2.3 Relativistic Dynamics 457
12.3 Electromagnetism in Covariant Form 458
12.3.1 The Lorentz Force and the Field Tensor 458
12.3.2 Maxwell’s Equations in Covariant Form 460
12.3.3 The 4-vector Potential 462
12.4 Field Transformations 463
12.5 Fields Due to a Point Charge in Uniform Motion 468
12.6 Magnetism from Relativity 474
12.7 The Energy-Momentum Flux Tensor 477
13 Electromagnetism and Optics 485
13.1 Electromagnetic Waves in a Dielectric 485
13.2 Reflection and Refraction at a Dielectric Interface 488
13.2.1 Wave Vectors 490
13.2.2 Reflectivity for Normal Incidence 494
13.2.3 Reflection for Incidence at Arbitrary Angles: Fresnel’s Equations 498
13.3 Electromagnetic Waves in a Conductor 505
13.3.1 Reflectivity of a Good Conductor 509
13.4 A Classical Model of Dispersion: The Frequency Dependence of Material Properties 511
13.4.1 Dispersion in a Dielectric 512
13.4.2 Dispersion in a Plasma 514
14 Wave Guides and Transmission Lines 523
14.1 Electromagnetic Waves Between Parallel Conducting Planes 524
14.1.1 The TEM Solution 526
14.1.2 TE Waves 528
14.1.3 TM Waves 537
14.1.4 Summary 540
14.2 The Rectangular Wave Guide 540
14.2.1 Transverse Electric Modes TE（m, n） 541
14.2.2 Transverse Magnetic Modes TM（m, n） 547
14.3 Wave Guide of Arbitrary Shape 549
14.4 The TEM Mode of a Coaxial Cable 551
14.5 Cavity Resonance 555
15 Radiation of Electromagnetic Waves 560
15.1 The Retarded Potentials 561
15.1.1 Green’s Functions 561
15.2 Radiation from an Electric Dipole 567
15.2.1 The Hertzian Dipole 571
15.2.2 Atomic Transitions 574
15.2.3 Magnetic Dipole Radiation 575
15.2.4 Complete Fields of a Hertzian Dipole 577
15.3 The Half-Wave Linear Antenna 579
15.4 The Larmor Formula: Radiation from a Point Charge 584
15.5 Classical Electron Theory of Light Scattering 589
15.6 Complete Fields of a Point Charge: The Lienard-Wiechert Potentials 593
15.6.1 A Charge with Constant Velocity 596
15.6.2 The Complete Fields 598
15.6.3 Generalization of the Larmor Formula 599
A Electric and Magnetic Units 607
B The Helmholtz Theorem 610
Index 613