电动力学导论【2025|PDF|Epub|mobi|kindle电子书版本百度云盘下载】

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1 Vector Analysis1

1.1 Vector Algebra1

1.1.1 Vector Operations1

1.1.2 Vector Algebra:Component Form4

1.1.3 Triple Products7

1.1.4 Position,Displacement,and Separation Vectors8

1.1.5 How Vectors Transform10

1.2 Differential Calculus13

1.2.1 "Ordinary"Derivatives13

1.2.2 Gradient13

1.2.3 The Operator16

1.2.4 The Divergence17

1.2.5 The Curl19

1.2.6 Product Rules20

1.2.7 Second Derivatives22

1.3 Integral Calculus24

1.3.1 Line,Surface,and Volume Integrals24

1.3.2 The Fundamental Theorem of Calculus28

1.3.3 The Fundamental Theorem for Gradients29

1.3.4 The Fundamental Theorem for Divergences31

1.3.5 The Fundamental Theorem for Curls34

1.3.6 Integration by Parts37

1.4 Curvilinear Coordinates38

1.4.1 Spherical Polar Coordinates38

1.4.2 Cylindrical Coordinates43

1.5 The Dirac Delta Function45

1.5.1 The Divergence of ？/r245

1.5.2 The One-Dimensional Dirac Delta Function46

1.5.3 The Three-Dimensional Delta Function50

1.6 The Theory of Vector Fields52

1.6.1 The Helmholtz Theorem52

1.6.2 Potentials53

2 Electrostatics58

2.1 The Electric Field58

2.1.1 Introduction58

2.1.2 Coulomb's Law59

2.1.3 The Electric Field60

2.1.4 Continuous Charge Distributions61

2.2 Divergence and Curl of Electrostatic Fields65

2.2.1 Field Lines,Flux,and Gauss's Law65

2.2.2 The Divergence of E69

2.2.3 Applications of Gauss's Law70

2.2.4 The Curl of E76

2.3 Electric Potential77

2.3.1 Introduction to Potential77

2.3.2 Comments on Potential79

2.3.3 Poisson's Equation and Laplace's Equation83

2.3.4 The Potential of a Localized Charge Distribution83

2.3.5 Summary;Electrostatic Boundary Conditions87

2.4 Work and Energy in Electrostatics90

2.4.1 The Work Done to Move a Charge90

2.4.2 The Energy of a Point Charge Distribution91

2.4.3 The Energy of a Continuous Charge Distribution93

2.4.4 Comments on Electrostatic Energy95

2.5 Conductors96

2.5.1 Basic Properties96

2.5.2 Induced Charges98

2.5.3 Surface Charge and the Force on a Conductor102

2.5.4 Capacitors103

3 Special Techniques110

3.1 Laplace's Equation110

3.1.1 Introduction110

3.1.2 Laplace's Equation in One Dimension111

3.1.3 Laplace's Equation in Two Dimensions112

3.1.4 Laplace's Equation in Three Dimensions114

3.1.5 Boundary Conditions and Uniqueness Theorems116

3.1.6 Conductors and the Second Uniqueness Theorem118

3.2 The Method of Images121

3.2.1 The Classic Image Problem121

3.2.2 Induced Surface Charge123

3.2.3 Force and Energy123

3.2.4 Other Image Problems124

3.3 Separation of Variables127

3.3.1 Cartesian Coordinates127

3.3.2 Spherical Coordinates137

3.4 Multipole Expansion146

3.4.1 Approximate Potentials at Large Distances146

3.4.2 The Monopole and Dipole Terms149

3.4.3 Origin of Coordinates in Multipole Expansions151

3.4.4 The Electric Field of a Dipole153

4 Electric Fields in Matter160

4.1 Polarization160

4.1.1 Dielectrics160

4.1.2 Induced Dipoles160

4.1.3 Alignment of Polar Molecules163

4.1.4 Polarization166

4.2 The Field of a Polarized Object166

4.2.1 Bound Charges166

4.2.2 Physical Interpretation of Bound Charges170

4.2.3 The Field Inside a Dielectric173

4.3 The Electric Displacement175

4.3.1 Gauss's Law in the Presence of Dielectrics175

4.3.2 A Deceptive Parallel178

4.3.3 Boundary Conditions178

4.4 Linear Dielectrics179

4.4.1 Susceptibility,Permittivity,Dielectric Constant179

4.4.2 Boundary Value Problems with Linear Dielectrics186

4.4.3 Energy in Dielectric Systems191

4.4.4 Forces on Dielectrics193

5 Magnetostatics202

5.1 The Lorentz Force Law202

5.1.1 Magnetic Fields202

5.1.2 Magnetic Forces204

5.1.3 Currents208

5.2 The Biot-Savart Law215

5.2.1 Steady Currents215

5.2.2 The Magnetic Field of a Steady Current215

5.3 The Divergence and Curl of B221

5.3.1 Straight-Line Currents221

5.3.2 The Divergence and Curl of B222

5.3.3 Applications of Ampère's Law225

5.3.4 Comparison of Magnetostatics and Electrostatics232

5.4 Magnetic Vector Potential234

5.4.1 The Vector Potential234

5.4.2 Summary;Magnetostatic Boundary Conditions240

5.4.3 Multipole Expansion of the Vector Potential242

6 Magnetic Fields in Matter255

6.1 Magnetization255

6.1.1 Diamagnets,Paramagnets,Ferromagnets255

6.1.2 Torques and Forces on Magnetic Dipoles255

6.1.3 Effect of a Magnetic Field on Atomic Orbits260

6.1.4 Magnetization262

6.2 The Field of a Magnetized Object263

6.2.1 Bound Currents263

6.2.2 Physical Interpretation of Bound Currents266

6.2.3 The Magnetic Field Inside Matter268

6.3 The Auxiliary Field H269

6.3.1 Ampère's law in Magnetized Materials269

6.3.2 A Deceptive Parallel273

6.3.3 Boundary Conditions273

6.4 Linear and Nonlinear Media274

6.4.1 Magnetic Susceptibility and Permeability274

6.4.2 Ferromagnetism278

7 Electrodynamics285

7.1 Electromotive Force285

7.1.1 Ohm's Law285

7.1.2 Electromotive Force292

7.1.3 Motional emf294

7.2 Electromagnetic Induction301

7.2.1 Faraday's Law301

7.2.2 The Induced Electric Field305

7.2.3 Inductance310

7.2.4 Energy in Magnetic Fields317

7.3 Maxwell's Equations321

7.3.1 Electrodynamics Before Maxwell321

7.3.2 How Maxwell Fixed Ampère's Law323

7.3.3 Maxwell's Equations326

7.3.4 Magnetic Charge327

7.3.5 Maxwell's Equations in Matter328

7.3.6 Boundary Conditions331

8 Conservation Laws345

8.1 Charge and Energy345

8.1.1 The Continuity Equation345

8.1.2 Poynting's Theorem346

8.2 Momentum349

8.2.1 Newton's Third Law in Electrodynamics349

8.2.2 Maxwell's Stress Tensor351

8.2.3 Conservation of Momentum355

8.2.4 Angular Momentum358

9 Electromagnetic Waves364

9.1 Waves in One Dimension364

9.1.1 The Wave Equation364

9.1.2 Sinusoidal Waves367

9.1.3 Boundary Conditions:Reflection and Transmission370

9.1.4 Polarization373

9.2 Electromagnetic Waves in Vacuum375

9.2.1 The Wave Equation for E and B375

9.2.2 Monochromatic Plane Waves376

9.2.3 Energy and Momentum in Electromagnetic Waves380

9.3 Electromagnetic Waves in Matter382

9.3.1 Propagation in Linear Media382

9.3.2 Reflection and Transmission at Normal Incidence384

9.3.3 Reflection and Transmission at Oblique Incidence386

9.4 Absorption and Dispersion392

9.4.1 Electromagnetic Waves in Conductors392

9.4.2 Reflection at a Conducting Surface396

9.4.3 The Frequency Dependence of Permittivity398

9.5 Guided Waves405

9.5.1 Wave Guides405

9.5.2 TE Waves in a Rectangular Wave Guide408

9.5.3 The Coaxial Transmission Line411

10 Potentials and Fields416

10.1 The Potential Formulation416

10.1.1 Scalar and Vector Potentials416

10.1.2 Gauge Transformations419

10.1.3 Coulomb Gauge and Lorentz Gauge421

10.2 Continuous Distributions422

10.2.1 Retarded Potentials422

10.2.2 Jefimenko's Equations427

10.3 Point Charges429

10.3.1 Liénard-Wiechert Potentials429

10.3.2 The Fields of a Moving Point Charge435

11 Radiation443

11.1 Dipole Radiation443

11.1.1 What is Radiation?443

11.1.2 Electric Dipole Radiation444

11.1.3 Magnetic Dipole Radiation451

11.1.4 Radiation from an Arbitrary Source454

11.2 Point Charges460

11.2.1 Power Radiated by a Point Charge460

11.2.2 Radiation Reaction465

11.2.3 The Physical Basis of the Radiation Reaction469

12 Electrodynamics and Relativity477

12.1 The Special Theory of Relativity477

12.1.1 Einstein's Postulates477

12.1.2 The Geometry of Relativity483

12.1.3 The Lorentz Transformations493

12.1.4 The Structure of Spacetime500

12.2 Relativistic Mechanics507

12.2.1 Proper Time and Proper Velocity507

12.2.2 Relativistic Energy and Momentum509

12.2.3 Relativistic Kinematics511

12.2.4 Relativistic Dynamics516

12.3 Relativistic Electrodynamics522

12.3.1 Magnetism as a Relativistic Phenomenon522

12.3.2 How the Fields Transform525

12.3.3 The Field Tensor535

12.3.4 Electrodynamics in Tensor Notation537

12.3.5 Relativistic Potentials541

A Vector Calculus in Curvilinear Coordinates547

A.1 Introduction547

A.2 Notation547

A.3 Gradient548

A.4 Divergence549

A.5 Curl552

A.6 Laplacian554

B The Helmholtz Theorem555

C Units558

Index562