《INTRODUCTION TO ELECTRODYNAMICS》

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ONEVECTOR ANALYSIS7

1.1VECTOR ALGEBRA7

1.1.1 Vector Operations7

1.1.2 Vector Algebra：Component Form10

1.1.3 Triple Products13

1.1.4 How Vectors Transform14

1.2DIFFERENTIAL CALCULUS16

1.2.1 “Ordinary” Derivatives16

1.2.2 Gradient17

1.2.3 The Operator ▽20

1.2.4 Divergence21

1.2.5 The Curl22

1.2.6 Product Rules24

1.2.7 Second Derivatives26

1.3INTEGRAL CALCULUS28

1.3.1 “Ordinary” Integration28

1.3.2 The Fundamental Theorem for Gradients29

1.3.3 The Fundamental Theorem for Divergences31

1.3.4 The Fundamental Theorem for Curls35

1.3.5 Relations Among the Fundamental Theorems38

1.3.6 Divergence-Less and Curl-Less Fields40

1.4 CURVILINEAR COORDINATES40

1.4.1Spherical Polar Coordinates40

1.4.2 Cylindrical Coordinates45

1.5 THE ROLE OF VECTOR CALCULUS IN ELECTRODYNAMICS46

TWOELECTROSTATICS49

2.1THE ELECTROSTATIC FIELD49

2.1.1 Introduction49

2.1.2 Coulomb’s Law50

2.1.3 The Electric Field51

2.1.4 Continuous Charge Distributions52

2.2DIVERGENCE AND CURL OF ELECTROSTATIC FIELDS56

2.2.1 Field Lines and Gauss’s Law56

2.2.2 The Divergence of E60

2.2.3 Applications of Gauss’s Law61

2.2.4 The Curl of E66

2.3 ELECTRIC POTENTIAL68

2.3.1Introduction to Potential68

2.3.2 Comments on Potential69

2.3.3 Poisson’s Equation and Laplace’s Equation73

2.3.4 Potential of a Charge Distribution74

2.3.5 Summary； Electrostatic Boundary Conditions77

2.4 WORK AND ENERGY IN ELECTROSTATICS79

2.4.1The Work Done in Moving a Charge79

2.4.2 The Energy of a Point Charge Distribution80

2.4.3 The Energy of a Continuous Charge Distribution82

2.4.4 Comme？ts on Electrostatic Energy83

2.5 CONDUCTORS85

2.5.1Basic Properties of Conductors85

2.5.2 Induced Charges87

2.5.3 The Surface Charge on a Conductor； the Force on a Surface Charge90

2.5.4 Capacitors91

THREESPECIAL TECHNIQUES FOR CALCULATING POTENTIALS96

3.1LAPLACE’S EQUATION AND UNIQUENESS THEOREMS96

3.1.1 Introduction96

3.1.2 Laplace’s Equation in One Dimension97

3.1.3 Laplace’s Equation in Two Dimensions98

3.1.4 Laplace’s Equation in Three Dimensions100

3.1.5 Boundary Conditions for Laplace’s Equation101

3.1.6 Conductors and the Second Uniqueness Theorem103

3.2 THE METHOD OF IMAGES106

3.2.1The Classic Image Problem106

3.2.2 The Induced Surface Charge108

3.2.3 Force and Energy108

3.2.4 Other Image Problems109

3.3 SEPARATION OF VARIABLES112

3.3.1Cartesian Coordinates112

3.3.2 Spherical Coordinates121

3.4 MULTIPOLE EXPANSION129

3.4.1Approximate Potential at Large Distances129

3.4.2 The Monopole and Dipole Terms131

3.4.3 Origin of Coordinates in Multipole Expansions133

3.4.4 The Electric Field of a Dipole134

FOURELECTROSTATIC FIELDS IN MATTER138

4.1POLARIZATION138

4.1.1 Dielectrics138

4.1.2 Induced Dipoles139

4.1.3 Alignment of Polar Molecules141

4.1.4 Polarization144

4.2THE FIELD OF A POLARIZED OBJECT144

4.2.1 Bound Charges144

4.2.2 Physical Interpretation of Bound Charge147

4.2.3 The Field Inside a Dielectric150

4.3 THE ELECTRIC DISPLACEMENT152

4.3.1Gauss’s Law in the Presence of Dielectrics152

4.3.2 A Deceptive Parallel155

4.4 LINEAR DIELECTRICS156

4.4.1Susceptibility，Permittivity，Dielectric Constant156

4.4.2 Special Problems Involving Linear Dielectrics161

4.4.3 Force and Energy in Dielectric Systems166

4.4.4 Polarizability and Susceptibility170

FIVEMAGNETOSTATICS174

5.1THE LORENTZ FORCE LAW174

5.1.1 Magnetic Fields174

5.1.2 Magnetic Forces176

5.1.3 Currents180

5.2 THE BIOT-SAVART LAW184

5.2.1Steady Currents184

5.2.2 The Magnetic Field of a Steady Current185

5.3 THE DIVERGENCE AND CURL OF B190

5.3.1Straight-Line Currents190

5.3.2 The Divergence of B192

5.3.3 The Curl of B193

5.3.4 Ampere’s Law194

5.3.5 Comparison of Magnetostatics and Electrostatics201

5.4 MAGNETIC VECTOR POTENTIAL203

5.4.1The Vector Potential203

5.4.2 Summary； Magnetestatic Boundary Conditions208

5.4.3 Multipole Expansion of the Vector Potential210

SIXMAGNETOSTATIC FIELDS IN MATTER218

6.1MAGNETIZATION218

6.1.1 Diamagnets，Paramagnets，Ferromagnets218

6.1.2 Torques and Forces on Magnetic Dipoles219

6.1.3 Effect of Magnetic Field on Atomic Orbits222

6.1.4 Magnetization224

6.2 THE FIELD OF A MAGNETIZED OBJECT225

6.2.1Bound Currents225

6.2.2 Physical Interpretation of Bound Currents227

6.2.3 The Magnetic Field Inside Matter229

6.3 THE AUXILIARY FIELD H230

6.3.1Ampere’s Law in Magnetized Materials230

6.3.2 A Deceptive Parallel233

6.4 LINEAR AND NONLINEAR MEDIA234

6.4.1Magnetic Susceptibility and Permeability234

6.4.2 Ferromagnetism237

SEVENELECTRODYNAMICS243

7.1ELECTROMOTIVE FORCE243

7.1.1 Ohm’s Law243

7.1.2 Electromotive Force250

7.1.3 Motional emf252

7.2FARADAY’S LAW257

7.2.1 Electromagnetic Induction257

7.2.2 Inductance263

7.2.3 Energy in Magnetic Fields268

7.3MAXWELL’S EQUATIONS273

7.3.1 Electrodynamics Before Maxwell273

7.3.2 How Maxwell Fixed Up Ampere’s Law274

7.3.3 Maxwell’s Equations and Magnetic Charge276

7.3.4 Maxwell’s Equations Inside Matter277

7.3.5 Boundary Conditions280

7.4 POTENTIAL FORMULATION OF ELECTRODYNAMICS282

7.4.1Scalar and Vector Pater？ials282

7.4.2 Gauge Transformation？283

7.4.3 Coulomb Gauge and Lorentz Gauge284

7.4.4 Lorentz Force Law in Patential Form286

7.5 ENERGY AND MOMENTUM IN ELECTRODYNAMICS287

7.5.1Newton’s Third Law in Electrodynamics287

7.5.2 Poynting’s Theorem288

7.5.3 Maxwell’s Stress Tensor291

EIGHTELECTROMAGNETIC WAVES295

8.1THE WAVE EQUATION295

8.1.1 Introduction295

8.1.2 The Wave Equation in One Dimension297

8.1.3 Sinusoidal Waves300

8.1.4 Polarization304

8.1.5 Boundary Conditions：Reflection and Transmission306

8.2 ELECTROMAGNETIC WAVES IN NONCONDUCTING MEDIA309

8.2.1Monochromatic Pl？？？Waves in Vacuum309

8.2.2 Energy and Momentum of Electromagnetic Waves313

8.2.3 Propagation Through Linear Media315

8.2.4 Reflection and Transmission at Normal Incidence316

8.2.5 Reflection and Transmission at Oblique Incidence318

8.3 ？CTROMAGNETIC WAVES IN CONDUCTORS324

8.3.1 The Modified Wave E？？？tion324

8.3.2 Monochromatic Plane Waves in Conducting Media327

8.3.3 Reflection and Trans？？？ssion at a Conducting Surface330

8.4 DISPERSION333

8.4.1The Frequency Dependence of ？，μ，and σ333

8.4.2 Dispersion in Nonconductors335

8.4.3 Free Electrons in Conductors and Plasmas340

NINEELECTROMAGNETIC RADIATION345

9.1DIPOLE RADIATION345

9.1.1 Retarded Potentials345

9.1.2 Electric Dipole Radiation350

9.1.3 Magnetic Dipole Radiation356

9.1.4 Radiation from an Arbitrary Distribution of Charges and Currents360

9.2RADIATION FROM A POINT CHARGE365

9.2.1 Lienard-Wiechert Potentials365

9.2.2 The Fields of a Point Charge in Motion370

9.2.3 Power Radiated by a Point Charge375

9.3 RADIATION REACTIQN380

9.3.1The Abraham-Lorentz Formula380

9.3.2 The Physical Origin of the Radiation Reaction384

TENELECTRODYNAMICS AND RELATIVITY388

10.1THE SPECIAL THEORY OF RELATIVITY388

10.1.1 Einstein’s Postulates388

10.1.2 The Geometry of Relativity396

10.1.3 The Lorentz Transformations406

10.1.4 The Structure of Spacetime412

10.2 RELATIVISTIC MECHANICS420

10.2.1Proper Time and Prop？r Velocity420

10.2.2 Relativistic Energy and Momentum422

10.2.3 Relativistic Kinematics426

10.2.4 Relativistic Dynamics430

10.3RELATIVISTIC ELECTRODYNAMICS435

10.3.1 Magnetism as a Relativistic Phenomenon435

10.3.2 How the Fields Transform437

10.3.3 The Field Tensor445

10.3.4 Electrodynamics in Tensor Notation448

10.3.5 Potential Formulation of Relativistic Electrodynamics451

APPENDIX AVECTOR CALCULUS IN CURVILINEAR COORDINATES454

INTRODUCTION454

NOTATION454

GRADIENT455

DIVERGENCE456

CURL458

LAPLACIAN460

APPENDIX BUNITS467

INDEX467