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CHAPTER 1. ELECTROMAGNETISM 1

1-1 Electrical forces 1

1-2 Electric and magnetic fields 3

1-3 Characteristics of vector fields 4

1-4 The laws of electromagnetism 5

1-5 What are the fields? 9

1-6 Electromagnetism in science and technology 10

CHAPTER 2. DIFFERENTIAL CALCULUS OF VECTOR FIELDS 13

2-1 Understanding physics 13

2-2 Scalar and vector fields—T and h 14

2-3 Derivatives of fields—the gradient 16

2-4 The operator 18

2-5 Operations with 19

2-6 The differential equation of heat flow 20

2-7 Second derivatives of vector fields 21

2-8 Pitfalls 23

CHAPTER 3. VECTOR INTEGRAL CALCULUS 25

3-1 Vector integrals; the line integral of 25

3-2 The flux of a vector field 26

3-3 The flux from a cube; Gauss' theorem 28

3-4 Heat conduction; the diffusion equation 30

3-5 The circulation of avector field 32

3-6 The circulation around a square;Stokes' theorem 33

3-7 Curl-free and divergence-free fields 34

3-8 Summary 35

CHAPTER 4. ELECTROSTATICS 37

4-1 Statics 37

4-2 Coulomb's law; superposition 38

4-3 Electric potential 40

4-4 E=-？φ 42

4-5 The flux of E 43

4-6 Gauss' law; divergence of E 45

4-7 Field of a sphere of charge 46

4-8 Fieldlines; equiporential surfaces 47

CHAPTER 5. APPLICATION OF GAUSS' LAW 49

5-1 Electrostatics is Gauss's law plus... 49

5-2 Equilibrium in an electrostatic field 49

5-3 Equilibrium with conductors 50

5-4 Stability of atoms 51

5-5 The field of a line charge 51

5-6 A sheet of charge; two sheets 52

5-7 A sphere of charge; a spherical shell 52

5-8 Is the field of a point charge exactly 1/ r2? 53

5-9 The fields of a conductor 55

5-10 The field in a cavity of a conductor 56

CHAPTER 6. THE ELECTRIC FIELD IN VARIOUS CIRCUMSTANCES 59

6-1 Equations of the electrostatic potential 59

6-2 The electric dipole 60

6-3 Remarks on vector equations 62

6-4 The dipole potential as a gradient 62

6-5 The dipole approximation for an arbitrary distribution 64

6-6 The fields of charged conductors 66

6-7 The method of images 66

6-8 A point charge near a conducting plane 67

6-9 A point charge near a conducting sphere 68

6-10 Condensers; parallel plates 69

6-11 High-voltage breakdown 71

6-12 The field-emission microscope 72

CHAPTER 7. THE ELECTRIC FIELD IN VARIOUS CIRCUMSTANCES （Continued） 73

7-1 Methods for finding the electrostatic fleld 73

7-2 Two-dimensional fields; functions of the complex variable 74

7-3 Plasma oscillations 77

7-4 Colloidal particles in an electrolyte 80

7-5 The electrostatic field of a grid 82

CHAPTER 8. ELECTROSTATIC ENERGY 85

8-1 The electrostatic energy of charges. A uniform sphere 85

8-2 The energy of a condenser. Forces on charged conductors 86

8-3 The electrostatic energy of an ionic crystal 88

8-4 Electrostatic energy in nuclei 90

8-5 Energy in the electrostatic field 93

8-6 The energy of a point charge 96

CHAPTER 9. ELECTRICITY IN THE ATMOSPHERE 97

9-1 The electric potential gradient of the atmosphere 97

9-2 Electric currents in the atmosphere 98

9-3 Origin of the atmospheric currents 100

9-4 Thunderstorms 101

9-5 The mechanism of charge separation 103

9-6 Lightning 106

CHAPTER 10. DIELECTRICS 109

10-1 The dielectric constant 109

10-2 The polarization vector P 110

10-3 Polarization charges 111

10-4 The electrostatic equations with dielectrics 114

10-5 Fields and forces with dielectrics 115

CHAPTER 11. INSIDE DIELECTRICS 119

11-1 Molecular dipoles 119

11-2 Electronic polarization 119

11-3 Polar molecules; orientation polarization 121

11-4 Electric fields in cavities of a dielectric 123

11-5 The dielectric constant of liquids; the Clausius-Mossotti equation 124

11-6 Solid dielectrics 126

11-7 Ferroelectricity; BaTiO3 126

CHAPTER 12. ELECTROSTATIC ANALOGS 131

12-1 The same equations have the same solutions 131

12-2 The flow of heat; a point source near an infinite plane boundary 132

12-3 The stretched membrane 135

12-4 The diffusion of neutrons; a uniform spherical source in a homogeneous medium 136

12-5 Irrotational fluid flow; the flow past a sphere 138

12-6 Illumination; the uniform lighting of a plane 140

12-7 The “underlying unity” of nature 142

CHAPTER 13. MAGNETOSTATICS 145

13-1 The magnetic field 145

13-2 Electric current; the conservation of charge 145

13-3 The magnetic force on a current 146

13-4 The magnetic field of steady currents;Ampere's law 147

13-5 The magnetic field of a straight wire and of a solenoid; atomic currents 149

13-6 The relativity of magnetic and electric fields 150

13-7 The transformation of currents and charges 155

13-8 Superposition; the right-hand rule 155

CHAPTER 14. THE MAGNETIC FIELD IN VARIOUS SITUATIONS 157

14-1 The vector potential 157

14-2 The vector potential of known currents 159

14-3 A straight wire 160

14-4 A long solenoid 161

14-5 The field of a small loop; the magnetic dipole 163

14-6 The vector potential of a circuit 164

14-7 The law of Biot and Savart 165

CHAPTER 15. THE VECTOR POTENTIAL 167

15-1 The forces on a current loop; energy of a dipole 167

15-2 Mechanical and electrical energies 169

15-3 The energy of steady currents 172

15-4 B versus A 173

15-5 The vector potential and quantum mechanics 174

15-6 What is true for statics is false for dynamics 180

CHAPTER 16. INDUCED CURRENTS 183

16-1 Motors and generators 183

16-2 Transformers and inductances 186

16-3 Forces on induced currents 187

16-4 Electrical technology 190

CHAPTER 17. THE LAWS OF INDUCTION 193

17-1 The physics of induction 193

17-2 Exceptions to the “flux rule” 194

17-3 Particle acceleration by an induced electric field;the betatron 195

17-4 A paradox 197

17-5 Alternating-current generator 198

17-6 Mutual inductance 201

17-7 Self-inductance 203

17-8 Inductance and magnetic energy 204

CHAPTER 18. THE MAXWELL EQUATIONS 209

18-1 Maxwell's equations 209

18-2 How the new term works 211

18-3 All of classical physics 213

18-4 A travelling field 213

18-5 The speed of light 216

18-6 Solving Maxwell's equations; the potentials and the wave equation 217

CHAPTER 19. THE PRINCIPLE OF LEAST ACTION 221

A special lecture—almost verbatim 221

A note added after the lecture 234

CHAPTER 20. SOLUTIONS OF MAXWELL'S EQUATIONS IN FREE SPACE 235

20-1 Waves in free space; plane waves 235

20-2 Three-dimensional waves 242

20-3 Scientific imagination 243

20-4 Spherical waves 246

CHAPTER 21. SOLUTIONS OF MAXWELL'S EQUATIONS WITH CURRENTS AND CHARGES 251

21-1 Light and electromagnetic waves 251

21-2 Spherical waves from a point source 252

21-3 The general solution of Maxwell's equations 254

21-4 The fields of an oscillating dipole 255

21-5 The potentials of a moving charge; the general solution of Lienard and Wiechert 259

21-6 The potentials for a charge moving with constant velocity; the Lorentz formula 262

CHAPTER 22. AC CIRCUITS 265

22-1 Impedances 265

22-2 Generators 269

22-3 Networks of ideal elements; Kirchhoff's rules 271

22-4 Equivalent circuits 274

22-5 Energy 275

22-6 A ladder network 276

22-7 Filters 278

22-8 Other circuit elements 280

CHAPTER 23. CAvrrY RESONATORS 283

23-1 Real circuit elements 283

23-2 A capacitor at high frequencies 284

23-3 A resonant cavity 288

23-4 Cavity modes 291

23-5 Cavities and resonant circuits 292

CHAPTER 24. WAVEGUIDES 295

24-1 The transmission line 295

24-2 The rectangular waveguide 298

24-3 The cutoff frequency 300

24-4 The speed of the guided waves 301

24-5 Observing guided waves 301

24-6 Waveguide plumbing 302

24-7 Waveguide modes 304

24-8 Another way of looking at the guided waves 304

CHAPTER 25. ELECTRODYNAMICS IN RELATIVISTIC NOTATION 307

25-1 Four-vectors 307

25-2 The scalar product 309

25-3 The four-dimensional gradient 312

25-4 Electrodynamics in four-dimensional notation 314

25-5 The four-potential of a moving charge 315

25-6 The invariance of the equations of electrodynamics 316

CHAPTER 26. LORENTZ TRANSFORMATIONS OF THE FIELDS 319

26-1 The four-potential of a moving charge 319

26-2 The fields of a point charge with a constant velocity 320

26-3 Relativistic transformation of the fields 323

26-4 The equations of motion in relativistic notation 329

CHAPTER 27. FIELD ENERGY AND FIELD MOMENTUM 333

27-1 Local conservation 333

27-2 Energy conservation and electromagnetism 334

27-3 Energy density and energy flow in the electromagnetic field 335

27-4 The ambiguity of the field energy 338

27-5 Examples of energy flow 338

27-6 Field momentum 341

CHAPTER 28. ELECTROMAGNETIC MASS 345

28-1 The field energy of a point charge 345

28-2 The field momentum of a moving charge 346

28-3 Electromagnetic mass 347

28-4 The force of an electron on itself 348

28-5 Attempts to modify the Maxwell theory 350

28-6 The nuclear force field 356

CHAPTER 29. THE MOTION OF CHARGES IN ELECTRIC AND MAGNETIC FIELDS 359

29-1 Motion in a uniform electric or magnetic field 359

29-2 Momentum analysis 359

29-3 An electrostatic lens 360

29-4 A magnetic lens 361

29-5 The electron microscope 361

29-6 Accelerator guide fields 362

29-7 Alternating-gradient focusing 364

29-8 Motion in crossed electric and magnetic fields 366

CHAPTER 30. THE INTERNAL GEOMETRY OF CRYSTALS 367

30-1 The internal geometry of crystals 367

30-2 Chemical bonds in crystals 368

30-3 The growth of crystals 369

30-4 Crystal lattices 369

30-5 Symmetries in two dimensions 370

30-6 Symmetries in three dimensions 373

30-7 The strength of metals 30-8 374

30-8 Dislocations and crystal growth 375

30-9 The Bragg-Nye crystal model 375

CHAPTER 31. TENSORS 393

31-1 The tensor of polarizability 393

31-2 Transforming the tensor components 395

31-3 The energy ellipsoid 395

31-4 Other tensors; the tensor of inertia 398

31-5 The cross product 400

31-6 The tensor of stress 401

31-7 Tensors of higher rank 403

31-8 The four-tensor of electromagnetic momentum 404

CHAPTER 32. REFRACTIVE INDEX OF DENSE MATERIALS 407

32-1 Polarization of matter 407

32-2 Maxwell's equations in a dielectric 409

32-3 Waves in a dielectric 411

32-4 The complex index of refraction 414

32-5 The index of a mixture 414

32-6 Waves in metals 416

32-7 Low-frequency and high-frequency approximations;the skin depth and the plasma frequency 417

CHAPTER 33. REFLECTION FROM SURFACES 421

33-1 Reflection and refraction of light 421

33-2 Waves in dense materials 422

33-3 The boundary conditions 424

33-4 The reflected and transmitted waves 427

33-5 Reflection from metals 431

33-6 Total internal reflection 432

CHAPTER 34. THE MAGNETISM OF MATTER 435

34-1 Diamagnetism and paramagnetism 435

34-2 Magnetic moments and angular momentum 437

34-3 The precession of atomic magnets 438

34-4 Diamagnetism 439

34-5 Larmor's theorem 440

34-6 Classical physics gives neither diamagnetism nor paramagnetism 442

34-7 Angular momentum in quantum mechanics 442

34-8 The magnetic energy of atoms 445

CHAPTER 35. PARAMAGNETISM AND MAGNETIC RESONANCE 447

35-1 Quantized magnetic states 447

35-2 The Stern-Gerlach experiment 449

35-3 The Rabi molecular-beam method 450

35-4 The paramagnetism of bulk materials 452

35-5 Cooling by adiabatic demagnetization 455

35-6 Nuclear magnetic resonance 456

CHAPTER 36. FERROMAGNETISM 459

36-1 Magnetization currents 459

36-2 The field H 463

36-3 The magnetization curve 464

36-4 Iron-core inductances 466

36-5 Electromagnets 467

36-6 Spontaneous magnetization 469

CHAPTER 37. MAGNETIC MATERIALS 475

37-1 Understanding ferromagnetism 475

37-2 Thermodynamic properties 478

37-3 The hysteresis curve 479

37-4 Ferromagnetic materials 484

37-5 Extraordinary magnetic materials 485

CHAPTER 38. ELASTICITY 489

38-1 Hooke's law 489

38-2 Uniform strains 490

38-3 The torsion bar; shear waves 493

38-4 The bent beam 497

38-5 Buckling 499

CHAPTER 39. ELASTIC MATERIALS 501

39-1 The tensor of strain 501

39-2 The tensor of elasticity 504

39-3 The motions in an elastic body 506

39-4 Nonelastic behavior 508

39-5 Calculating the elastic constants 510

CHAPTER 40. THE FLOW OF DRY WATER 515

40-1 Hydrostatics 515

40-2 The equations of motion 516

40-3 Steady flow—Bernoulli's theorem 520

40-4 Circulation 523

40-5 Vortex lines 524

CHAPTER 41. THE FLOW OF WET WATER 527

41-1 Viscosity 527

41-2 Viscous flow 530

41-3 The Reynolds number 531

41-4 Flow past a circular cylinder 533

41-5 The limit of zero viscosity 535

41-6 Couette flow 536

CHAPTER 42. CURVED SPACE 539

42-1 Curved spaces with two dimensions 539

42-2 Curvature in three-dimensional space 543

42-3 Our space is curved 544

42-4 Geometry in space-time 545

42-5 Gravity and the principle of equivalence 546

42-6 The speed of clocks in a gravitational field 547

42-7 The curvature of space-time 549

42-8 Motion in curved space-time 550

42-9 Einstein's theory of gravitation 551