Introduction and Survey 1
I.1 Maxwell Equations in Vacuum，Fields，and Sources 2
I.2 The Inverse Square Law or the Mass of the Photon 5
I.3 Linear Superposition 10
I.4 The Maxwell Equations in Macroscopic Media 13
I.5 Boundary Conditions at Interfaces between Different Media 17
I.6 Some Remarks on Idealizations in Electromagnetism 22
References and Suggested Reading 25
Chapter 1. Introduction to Electrostatics 27
1.1 Coulomb’s Law 27
1.2 Electric Field 28
1.3 Gauss’s Law 30
1.4 Differential Form of Gauss’s Law 32
1.5 Another Equation of Electrostatics and the Scalar Potential 33
1.6 Surface Distributions of Charges and Dipoles and Discontinuities in the Electric Field and Potential 35
1.7 Poisson and Laplace Equations 38
1.8 Green’s Theorem 40
1.9 Uniqueness of the Solution with Dirichlet or Neumann Boundary Condi-tions 42
1.10 Formal Solution of Electrostatic Boundary-Value Problem with Green Function 43
1.11 Electrostatic Potential Energy and Energy Density，Capacitance 45
References and Suggested Reading 49
Problems 49
Chapter 2. Boundary-Value Problems in Electrostatics：Ⅰ 54
2.1 Method of Images 54
2.2 Point Charge in the Presence of a Grounded Conducting Sphere 55
2.3 Point Charge in the Presence of a Charged，Insulated，Conducting Sphere 58
2.4 Point Charge Near a Conducting Sphere at Fixed Potential 60
2.5 Conducting Sphere in a Uniform Electric Field by the Method of Images 60
2.6 Green Function for the Sphere，General Solution for the Potential 62
2.7 Conducting Sphere with Hemispheres at Different Potentials 63
2.8 Orthogonal Functions and Expansions 65
2.9 Separation of Variables，Laplace Equation in Rectangular Coordinates 68
2.10 A Two-dimensional Potential Problem，Summation of a Fourier Series 71
2.11 Fields and Charge Densities in Two-dimensional Comers and Along Edges 75
References and Suggested Reading 78
Problems 79
Chapter 3. Boundary-Value Problems in Electrostatics：Ⅱ 84
3.1 Laplace Equation in Spherical Coordinates 84
3.2 Legendre Equation and Legendre Polynomials 85
3.3 Boundary-Value Problems with Azimuthal Symmetry 90
3.4 Behavior of Fields in a Conical Hole or near a Sharp Point 94
3.5 Associated Legendre Functions and the Spherical Harmonics Y tm（θ，φ） 98
3.6 Addition Theorem for Spherical Harmonics 100
3.7 Laplace Equation in Cylindrical Coordinates，Bessel Functions 102
3.8 Boundary-Value Problems in Cylindrical Coordinates 108
3.9 Expansion of Green Functions in Spherical Coordinates 110
3.10 Solution of Potential Problems with Spherical Green Function Expansion 113
3.11 Expansion of Green Functions in Cylindrical Coordinates 116
3.12 Eigenfunction Expansions for Green Functions 119
3.13 Mixed Boundary Conditions，Conducting Plane with a Circular Hole 121
References and Suggested Reading 127
Problems 128
Chapter 4. Multipoles，Electrostatics of Macroscopic Media，Dielectrics 136
4.1 Multipole Expansion 136
4.2 Multipole Expansion of the Energy of a Charge Distribution in an External Field 142
4.3 Elementary Treatment of Electrostatics with Ponderable Media 143
4.4 Boundary-Value Problems with Dielectrics 147
4.5 Molecular Polarizability and Electric Susceptibility 152
4.6 Models for the Molecular Polarizability 155
4.7 Electrostatic Energy in Dielectric Media 158
References and Suggested Reading 163
Problems 163
Chapter 5. Magnetostatics 168
5.1 Introduction and Definitions 168
5.2 Biot and Savart Law 169
5.3 The Differential Equations of Magnetostatics and Ampere’s Law 173
5.4 Vector Potential 175
5.5 Vector Potential and Magnetic Induction for a Circular Current Loop 177
5.6 Magnetic Fields of a Localized Current Distribution，Magnetic Moment 180
5.7 Force and Torque on and Energy of a Localized Current Distribution in an External Magnetic Induction 184
5.8 Macroscopic Equations，Boundary Conditions on B and H 187
5.9 Methods of Solving Boundary-Value Problems in Magnetostatics 191
5.10 Uniformly Magnetized Sphere 194
5.11 Magnetized Sphere in an External Field，Permanent Magnets 197
5.12 Magnetic Shielding，Spherical Shell of Permeable Material in a Uniform Field 199
5.13 Effect of a Circular Hole in a Perfectly Conducting Plane with an Asymptotically Uniform Tangential Magnetic Field on One Side 201
References and Suggested Reading 204
Problems 205
Chapter 6. Time-Varying Fields，Maxwell Equations，Conservation Laws 209
6.1 Faraday’s Law of Induction 210
6.2 Energy in the Magnetic Field 213
6.3 Maxwell’s Displacement Current，Maxwell Equations 217
6.4 Vector and Scalar Potentials 219
6.5 Gauge Transformations，Lorentz Gauge，Coulomb Gauge 220
6.6 Green Functions for the Wave Equation 223
6.7 Derivation of the Equations of Macroscopic Electromagnetism 226
6.8 Poynting’s Theorem and Conservation of Energy and Momentum for a System of Charged Particles and Electromagnetic Fields 236
6.9 Conservation Laws for Macroscopic Media 240
6.10 Poynting’s Theorem for Harmonic Fields，Field Definitions of Impedance and Admittance 241
6.11 Transformation Properties of Electromagnetic Fields and Sources under Rotations，Spatial Reflections，and Time Reversal 245
6.12 On the Question of Magnetic Monopoles 251
6.13 Discussion of the Dirac Quantization Condition 254
References and Suggested Reading 260
Problems 261
Chapter 7. Plane Electromagnetic Waves and Wave Propagation 269
7.1 Plane Waves in a Nonconducting Medium 269
7.2 Linear and Circular Polarization，Stokes Parameters 273
7.3 Reflection and Refraction of Electromagnetic Waves at a Plane Interface between Dielectrics 278
7.4 Polarization by Reflection and Total Internal Reflection 282
7.5 Frequency Dispersion Characteristics of Dielectrics，Conductors，and Plasmas 284
7.6 Simplified Model of Propagation in the Ionosphere and Magnetosphere 292
7.7 Waves in a Conducting or Dissipative Medium 296
7.8 Superposition of Waves in One Dimension，Group Velocity 299
7.9 Illustration of the Spreading of a Pulse as It Propagates in a Dispersive Medium 303
7.10 Causality in the Connection between D and E，Kramers-Kronig Relations 306
7.11 Arrival of a Signal After Propagation Through a Dispersive Medium 313
References and Suggested Reading 326
Problems 327
Chapter 8. Wave Guides and Resonant Cavities 334
8.1 Fields at the Surface of and within a Conductor 335
8.2 Cylindrical Cavities and Wave Guides 339
8.3 Wave Guides 343
8.4 Modes in a Rectangular Wave Guide 345
8.5 Energy Flow and Attenuation in Wave Guides 346
8.6 Perturbation of Boundary Conditions 350
8.7 Resonant Cavities 353
8.8 Power Losses in a Cavity，Q of a Cavity 356
8.9 Earth and Ionosphere as a Resonant Cavity，Schumann Resonances 360
8.10 Dielectric Wave Guides 364
8.11 Expansion in Normal Modes，Fields Generated by a Localized Source in Guide 369
8.12 Reflection and Transn by Plane Diaphragms，Variational Approxi-mation 375
8.13 Impedance of a Flat Strip Parallel to the Electric Field in a Rectangular Wave Guide 380
References and Suggested Reading 384
Problems 385
Chapter 9. Simple Radiating Systems，Scattering，and Diffraction 391
9.1 Fields and Radiation of a Localized Oscillating Source 391
9.2 Electric Dipole Fields and Radiation 394
9.3 Magnetic Dipole and Electric Quadrupole Fields 397
9.4 Center-fed Linear Antenna 401
9.5 Multipole Expansion for Localized Source or Aperture in Wave Guide 405
9.6 Scattering at Long Wavelengths 411
9.7 Perturbation Theory of Scattering，Rayleigh’s Explanation of the Blue Sky，Scattering by Games and Liquids 418
9.8 Scalar Diffraction Theory 427
9.9 Vector Equivalents of Kirc Integral 432
9.10 Vectorial Diffraction Theory 435
9.11 Babinet’s Principle of Complementary Screens 438
9.12 Diffraction by a Circular Aperture，Remarks on Small Apertures 441
9.13 Scattering in the Short-Wavelength Limit 447
9.14 Optical Theorem and Related Matters 453
References and Suggested Reading 459
Problems 460
Chapter 10. Magnetohydrodynamics and Plasma Physics 469
10.1 Introduction and Definitions 469
10.2 Magnetohydrodynamic Equations 471
10.3 Magnetic Diffusion，Viscosity，and Pressure 472
10.4 Magnetohydrodynamic Flow between Boundaries with Crossed Electric and Magnetic Fields 475
10.5 Pinch Effect 479
10.6 Instabilities in a Pinched Plasma Column 482
10.7 Magnetohydrodynamic Waves 485
10.8 Plasma Oscillations 490
10.9 Short-wavelength Limit on Plasma Oscillations and the Debye Screening Distance 494
References and Suggested Reading 497
Problems 498
Chapter 11. Special Theory of Relativity 503
11.1 The Situation before 1900，Einstein’s Two Postulates 504
11.2 Some Recent Experiments 507
11.3 Lorentz Transformations and Basic Kinematic Results of Special Relativity 515
11.4 Addition of Velocities，Four-Velocity 522
11.5 Relativistic Momentum and Energy of a Particle 525
11.6 Mathematical Properties of the Space-Time of Special Relativity 532
11.7 Matrix Representation of Lorentz Transformations，Infinitesimal Generators 536
11.8 Thomas Precession 541
11.9 Invariance of Electric Charge，Covariance of Electrodynamics 547
11.10 Transformation of Electromagnetic Fields 552
11.11 Relativistic Equation of Motion for Spin in Uniform or Slowly Varying Extemal Fields 556
11.12 Note on Notation and Units in Relativistic Kinematics 560
References and Suggested Reading 561
Problems 562
Chapter 12. Dynamics of Relativistic Particles and Electromagnetic Fields 571
12.1 Lagrangian and Hamiltonian for a Relativistic Charged Particle in External Electromagnetic Fields 572
12.2 On the Question of Obtaining the Magnetic Field，Magnetic Force，and the Maxwell Equations from Coulomb’s law and Special Relativity 578
12.3 Motion in a Uniform，Static，Magnetic Field 581
12.4 Motion in Combined Uniform，Static，Electric and Magnetic Fields 582
12.5 Particle Drifts in Nonuniform，Static Magnetic Fields 584
12.6 Adiabatic Invariance of Flux through Orbit of Particle 588
12.7 Lowest-Order Relativistic Corrections to the Lagrangian for Interacting Charged Particles，the Darwin Lagrangian 593
12.8 Lagrangian for the Electromagnetic Field 595
12.9 Proca Lagrangian，Photon Mass Effects 597
12.10 Canonical and Symmetric Stress Tensors，Conservation Laws 601
12.11 Solution of the Wave Equation in Covariant Form，Invariant Green Functions 608
References and Suggested Reading 612
Problems 613
Chapter 13. Collisions between Charged Particles，Energy Loss，and Scattering 618
13.1 Energy Transfer in a Coulomb Collision 619
13.2 Energy Transfer to a Harmonically Bound Charge 623
13.3 Classical and Quantum-Mechanical Energy-loss Formulas 626
13.4 Density Effect in Collision Energy Loss 632
13.5 Cherenkov Radiation 638
13.6 Energy Loss in an Electronic Plasma 641
13.7 Elastic Scattering of Fast Particles by Atoms 643
13.8 Mean Square Angle of Scattering and the Angular Distribution of Multiple Scattering 647
References and Suggested Reading 651
Problems 651
Chapter 14. Radiation by Moving Charges 654
14.1 Lienard-Wiechert Potentials and Fields for a Point Charge 654
14.2 Total Power Radiated by an Accelerated Charge：Larmor’s Formula and its Relativistic Generalization 658
14.3 Angular Distribution of Radiation Emitted by an Accelerated Charge 662
14.4 Radiation Emitted by a Charge in Arbitrary，Extremely Relativistic Motion 665
14.5 Distribution in Frequency and Angle of Energy Radiated by Accelerated Charges 668
14.6 Frequency Spectrum of Radiation Emitted by a Relativist ic Charged Particle in Instantaneously Circular Motion 672
14.7 Thomson Scattering of Radiation 679
14.8 Scattering of Radiation by Quasi-Free Charges，Coherent and Incoherent Scattering 683
14.9 Transition Radiation 685
References and Suggested Reading 693
Problems 694
Chapter 15. Bremsstrahlung，Method of Virtual Quanta，Radiative Beta Processes 701
15.1 Radiation Emitted during Collisions 702
15.2 Bremsstrahlung in Coulomb Collisions 708
15.3 Screening Effects，Relativistic Radiative Energy Loss 715
15.4 Weizsacker-Williams Method of Virtual Quanta 719
15.5 Bremsstrahlung as the Scattering of Virtual Quanta 724
15.6 Radiation Emitted During Beta Decay 725
15.7 Radiation Emitted During Orbital-Electron Capture—Disappearance of Charge and Magnetic Moment 727
References and Suggested Reading 733
Problems 733
Chapter 16. Multipole Fields 739
16.1 Basic Spherical Wave Solutions of the Scalar Wave Equation 739
16.2 Multipole Expansion of the Electromagnetic Fields 744
16.3 Properties of Multipole Fields，Energy and Angular Momentum of Mul-tipole Radiation 747
16.4 Angular Distribution of Multipole Radiation 752
16.5 Sources of Multipole Radiation，Multipole Moments 755
16.6 Multipole Radiation in Atomic and Nuclear Systems 758
16.7 Radiation from a Linear，Center-Fed Antenna 763
16.8 Spherical Wave Expansion of a Vector Plane Wave 767
16.9 Scattering of Electromagnetic Waves by a Sphere 769
16.10 Boundary-Value Problems with Multipole Fields 775
References and Suggested Reading 776
Problems 776
Chapter 17. Radiation Damping，Self-Fields of a Particle，Scattering and Absorption of Radiation by a Bound System 780
17.1 Introductory Considerations 780
17.2 Radiative Reaction Force from Conservation of Energy 783
17.3 Abraham-Lorentz Evaluation of the Self-Force 786
17.4 Difficulties with the Abraham-Lorentz Model 790
17.5 Covariant Definitions of Electromagnetic Energy and Momentum 791
17.6 Integrodifferential Equation of Motion，Including Radiation Damping 796
17.7 Line Breadth and Level Shift of an Oscillator 798
17.8 Scattering and Absorption of Radiation by an Oscillator 801
References and Suggested Reading 806
Problems 807
Appendix on Units and Dimensions 811
1 Units and Dimensions，Basic Units and Derived Units 811
2 Electromagnetic Units and Equations 813
3 Various Systems of Electromagnetic Units 816
4 Conversion of Equations and Amounts between Gaussian Units and MKSA Units 817
Bibliography 822
Index 822