《CLASSICAL ELECTRICITY AND MAGNETISM》

CHAPTER 1.THE ELECTROSTATIC FIELD IN VACUUM1

1-1Vector fields1

1-2 The electric field7

1-3 Coulomb’s law8

1-4 The electrostatic potential10

1-5 The potential in terms of charge distribution11

1-6 Field singularities13

1-7 Clusters of point charges13

1-8 Dipole interactions19

1-9 Surface singularities20

1-10 Volume distributions of dipole moment23

CHAPTER 2.BOUNDARY CONDITIONS AND RELATION OF MICROSCOPIC TO MACROSCOPIC FIELDS28

2-1The displacement vector28

2-2 Boundary conditions31

2-3 The electric field in a material medium33

2-4 Polarizability38

CHAPTER 3.GENERAL METHODS FOR THE SOLUTION OF POTENTIAL PROBLEMS42

3-1Uniqueness theorem42

3-2 Green’s reciprocation theorem43

3-3 Solution by Green’s function44

3-4 Solution by inversion47

3-5 Solution by electrical images49

3-6 Solution of Laplace’s equation by the separation of variables53

CHAPTER 4.TWO-DIMENSIONAL POTENTIAL PROBLEMS61

4-1Conjugate complex functions61

4-2 Capacity and field strength63

4-3 The potential of a uniform field64

4-4 The potential of a line charge64

4-5 Complex transformations66

4-6 General Schwarz transformation67

4-7 Single-angle transformations70

4-8 Multiple-angle transformations71

4-9 Direct solution of Laplace’s equation by the method of harmonics73

4-10 Illustration:Line charge and dielectric cylinder74

4-11 Line charge in an angle between two conductors77

CHAPTER 5.THREE-DIMENSIONAL POTENTIAL PROBLEMS81

5-1The solution of Laplace’s equation in spherical coordinates81

5-2 The potential of a point charge82

5-3 The potential of a dielectric sphere and a point charge83

5-4 The potential of a dielectric sphere in a uniform field84

5-5 The potential of an arbitrary axially-symmetric spherical potential distribution86

5-6 The potential of a charged ring87

5-7 Problems not having axial symmetry88

5-8 The solution of Laplace’s equation in cylindrical coordinates88

5-9 Application of cylindrical solutions to potential problems91

CHAPTER 6.ENERGY RELATIONS AND FORCES IN THE ELECTRO-STATIC FIELD95

6-1Field energy in free space95

6-2 Energy density within a dielectric98

6-3 Thermodynamic interpretation of U100

6-4 Thomson’s theorem101

6-5 Maxwell stress tensor103

6-6 Volume forces in the electrostatic field in the presence of dielectrics107

6-7 The behavior of dielectric liquids in an electrostatic field111

CHAPTER 7.STEADY CURRENTS AND THEIR INTERACTION118

7-1Ohm’s law118

7-2 Electromotive force119

7-3 The solution of stationary current problems120

7-4 Time of relaxation in a homogeneous medium122

7-5 The magnetic interaction of steady line currents123

7-6 The magnetic induction field125

7-7 The magnetic scalar potential125

7-8 The magnetic vector potential127

7-9 Types of currents129

7-10 Polarization currents129

7-11 Magnetic moments130

7-12 Magnetization and magnetization currents134

7-13 Vacuum displacement current135

CHAPTER 8.MAGNETIC MATERIALS AND BOUNDARY VALUE PROBLEMS139

8-1Magnetic field intensity139

8-2 Magnetic sources140

8-3 Permeable media:magnetic susceptibility and boundary conditions144

8-4 Magnetic circuits145

8-5 Solution of boundary value problems by magnetic scalar potentials146

8-6 Uniqueness theorem for the vector potential147

8-7 The use of the vector potential in the solution of problems148

8-8 The vector potential in two dimensions151

8-9 The vector potential in cylindrical coordinates153

CHAPTER 9.MAXWELL’S EQUATIONS158

9-1Faraday’s law of induction158

9-2 Maxwell’s equations for stationary media159

9-3 Faraday’s law for moving media160

9-4 Maxwell’s equations for moving media163

9-5 Motion of a conductor in a magnetic field165

CHAPTER 10.ENERGY,FORCE,AND MOMENTUM RELATIONS IN THE ELECTROMAGNETIC FIELD170

10-1Energy relations in quasi-stationary current systems170

10-2 Forces on current systems172

10-3 Inductance174

10-4 Magnetic volume force177

10-5 General expressions for electromagnetic energy178

10-6 Momentum balance181

CHAPTER 11.THE WAVE EQUATION AND PLANE WAVES185

11-1The wave equation185

11-2 Plane waves187

11-3 Radiation pressure191

11-4 Plane waves in a moving medium193

11-5 Reflection and refraction at a plane boundary195

11-6 Waves in conducting media and metallic reflection200

11-7 Group velocity202

CHAPTER 12.CONDUCTING FLUIDS IN A MAGNETIC FIELD(MAGNETOHYDRODYNAMICS)205

12-1"Frozen-in"lines of force205

12-2 Magnetohydrodynamic waves207

CHAPTER 13.WAVES IN THE PRESENCE OF METALLIC BOUNDARIES212

13-1The nature of metallic boundary conditions212

13-2 Eigenfunctions and eigenvalues of the wave equation214

13-3 Cavities with rectangular boundaries218

13-4 Cylindrical cavities219

13-5 Circular cylindrical cavities222

13-6 Wave guides223

13-7 Scattering by a circular cylinder226

13-8 Spherical waves229

13-9 Scattering by a sphere233

CHAPTER 14.THE INHOMOGENEOUS WAVE EQUATION240

14-1The wave equation for the potentials240

14-2 Solution by Fourier analysis242

14-3 The radiation fields245

14-4 Radiated energy248

14-5 The Hertz potential254

14-6 Computation of radiation fields by the Hertz method255

14-7 Electric dipole radiation257

14-8 Multipole radiation260

14-9 Derivation of multipole radiation from scalar superpotentials264

14-10 Energy and angular momentum radiated by multipoles267

CHAPTER 15.THE EXPERIMENTAL BASIS FOR THE THEORY OF SPECIAL RELATIVITY272

15-1Galilean relativity and electrodynamics272

15-2 The search for an absolute ether frame274

15-3 The Lorentz-Fitzgerald contraction hypothesis278

15-4 "Ether drag"279

15-5 Emission theories280

15-6 Summary283

CHAPTER 16.RELATIVISTIC KINEMATICS AND THE LORENTZ TRANSFORMATION286

16-1The velocity of light and simultaneity286

16-2 Kinematic relations in special relativity288

16-3 The Lorentz transformation293

16-4 Geometric interpretations of the Lorentz transformation297

16-5 Transformation equations for velocity301

CHAPTER 17.COVARIANCE AND RELATIVISTIC MECHANICS305

17-1The Lorentz transformation of a four-vector305

17-2 Some tensor relations useful in special relativity307

17-3 The conservation of momentum311

17-4 Relation of energy to momentum and to mass313

17-5 The Minkowski force316

17-6 The collision of two similar particles318

17-7 The use of four-vectors in calculating kinematic relations for collisions320

CHAPTER 18.COVARIANT FORMULATION OF ELECTRODYNAMICS324

18-1The four-vector potential324

18-2 The electromagnetic field tensor327

18-3 The Lorentz force in vacuum331

18-4 Covariant description of sources in material media332

18-5 The field equations in a material medium334

18-6 Transformation properties of the partial fields336

CHAPTER 19.THE LIENARD-WIECHERT POTENTIALS AND THE FIELD OF A UNIFORMLY MOVING ELECTRON341

19-1The Liénard-Wiechert potentials341

19-2 The fields of a charge in uniform motion344

19-3 Direct solution of the wave equation347

19-4 The"convection potential"348

19-5 The virtual photon concept350

CHAPTER 20.RADIATION FROM AN ACCELERATED CHARGE354

20-1Fields of an accelerated charge354

20-2 Radiation at low velocity358

20-3 The case of ？ parallel to u359

20-4 Radiation when the acceleration is perpendicular to the velocity(radiation from circular orbits)363

20-5 Radiation with no restrictions on the acceleration or velocity370

20-6 Classical cross section for bremsstrahlung in a Coulomb field371

20-7 ？erenkov radiation373

CHAPTER 21.RADIATION REACTION AND COVARIANT FORMULATION OF THE CONSERVATION LAWS OF ELECTRODYNAMICS377

21-1Covariant formulation of the conservation laws of vacuum electrodynamics377

21-2 Transformation properties of the"free" radiation field379

21-3 The electromagnetic energy momentum tensor in material media380

21-4 Electromagnetic mass381

21-5 Electromagnetic mass—qualitative considerations383

21-6 The reaction necessary to conserve radiated energy386

21-7 Direct computation of the radiation reaction from the retarded fields387

21-8 Properties of the equation of motion389

21-9 Covariant description of the mechanical properties of the electromagnetic field of a charge390

21-10 The relativistic equations of motion392

21-11 The integration of the relativistic equation of motion394

21-12 Modification of the theory of radiation to eliminate divergent mass integrals.Advanced potentials394

21-13 Direct calculation of the relativistic radiation reaction398

CHAPTER 22.RADIATION,SCATTERING,AND DISPERSION401

22-1Radiative damping of a charged harmonic oscillator401

22-2 Forced vibrations403

22-3 Scattering by an individual free electron404

22-4 Scattering by a bound electron407

22-5 Absorption of radiation by an oscillator407

22-6 Equilibrium between an oscillator and a radiation field409

22-7 Effect of a volume distribution of scatterers411

22-8 Scattering from a volume distribution.Rayleigh scattering414

22-9 The dispersion relation416

22-10 A general theorem on scattering and absorption419

CHAPTER 23.THE MOTION OF CHARGED PARTICLES IN ELECTRO-MAGNETIC FIELDS425

23-1World-line description425

23-2 Hamiltonian formulation and the transition to three-dimensional formalism427

23-3 Equations for the trajectories430

23-4 Applications433

23-5 The motion of a particle with magnetic moment in an electromagnetic field437

CHAPTER 24.HAMILTONIAN FORMULATION OF MAXWELL’S EQUATIONS446

24-1Transition to a one-dimensional continuous system446

24-2 Generalization to a three-dimensional continuum448

24-3 The electromagnetic field451

24-4 Periodic solutions in a box.Plane wave representation454

APPENDIX Ⅰ.UNITS AND DIMENSIONS IN ELECTROMAGNETIC THEORY459

Tables:Ⅰ-1.Conversion Factors465

Ⅰ-2.Fundamental Electromagnetic Relations Valid in vacuo as They Appear in the Various Systems of Units466

Ⅰ-3.Definition of Fields from Sources(mks system)468

Ⅰ-4.Useful Numerical Relations469

APPENDIX Ⅱ.USEFUL VECTOR RELATIONS470

Table Ⅱ-1.Vector Formulas470

APPENDIX Ⅲ.VECTOR RELATIONS IN CURVILINEAR COORDINATES473

Table Ⅲ-1.Coordinate Systems475

BIBLIOGRAPHY479

INDEX485