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CHAPTER 1. ELECTROMAGNETISM1

1-1 Electrical forces1

1-2 Electric and magnetic fields3

1-3 Characteristics of vector fields4

1-4 The laws of electromagnetism5

1-5 What are the fields?9

1-6 Electromagnetism in science and technology10

CHAPTER 2. DIFFERENTIAL CALCULUS OF VECTOR FIELDS13

2-1 Understanding physics13

2-2 Scalar and vector fields—T and h14

2-3 Derivatives of fields—the gradient16

2-4 The operator18

2-5 Operations with19

2-6 The differential equation of heat flow20

2-7 Second derivatives of vector fields21

2-8 Pitfalls23

CHAPTER 3. VECTOR INTEGRAL CALCULUS25

3-1 Vector integrals; the line integral of25

3-2 The flux of a vector field26

3-3 The flux from a cube; Gauss' theorem28

3-4 Heat conduction; the diffusion equation30

3-5 The circulation of avector field32

3-6 The circulation around a square;Stokes' theorem33

3-7 Curl-free and divergence-free fields34

3-8 Summary35

CHAPTER 4. ELECTROSTATICS37

4-1 Statics37

4-2 Coulomb's law; superposition38

4-3 Electric potential40

4-4 E=-？φ42

4-5 The flux of E43

4-6 Gauss' law; divergence of E45

4-7 Field of a sphere of charge46

4-8 Fieldlines; equiporential surfaces47

CHAPTER 5. APPLICATION OF GAUSS' LAW49

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

5-2 Equilibrium in an electrostatic field49

5-3 Equilibrium with conductors50

5-4 Stability of atoms51

5-5 The field of a line charge51

5-6 A sheet of charge; two sheets52

5-7 A sphere of charge; a spherical shell52

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

5-9 The fields of a conductor55

5-10 The field in a cavity of a conductor56

CHAPTER 6. THE ELECTRIC FIELD IN VARIOUS CIRCUMSTANCES59

6-1 Equations of the electrostatic potential59

6-2 The electric dipole60

6-3 Remarks on vector equations62

6-4 The dipole potential as a gradient62

6-5 The dipole approximation for an arbitrary distribution64

6-6 The fields of charged conductors66

6-7 The method of images66

6-8 A point charge near a conducting plane67

6-9 A point charge near a conducting sphere68

6-10 Condensers; parallel plates69

6-11 High-voltage breakdown71

6-12 The field-emission microscope72

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

7-1 Methods for finding the electrostatic fleld73

7-2 Two-dimensional fields; functions of the complex variable74

7-3 Plasma oscillations77

7-4 Colloidal particles in an electrolyte80

7-5 The electrostatic field of a grid82

CHAPTER 8. ELECTROSTATIC ENERGY85

8-1 The electrostatic energy of charges. A uniform sphere85

8-2 The energy of a condenser. Forces on charged conductors86

8-3 The electrostatic energy of an ionic crystal88

8-4 Electrostatic energy in nuclei90

8-5 Energy in the electrostatic field93

8-6 The energy of a point charge96

CHAPTER 9. ELECTRICITY IN THE ATMOSPHERE97

9-1 The electric potential gradient of the atmosphere97

9-2 Electric currents in the atmosphere98

9-3 Origin of the atmospheric currents100

9-4 Thunderstorms101

9-5 The mechanism of charge separation103

9-6 Lightning106

CHAPTER 10. DIELECTRICS109

10-1 The dielectric constant109

10-2 The polarization vector P110

10-3 Polarization charges111

10-4 The electrostatic equations with dielectrics114

10-5 Fields and forces with dielectrics115

CHAPTER 11. INSIDE DIELECTRICS119

11-1 Molecular dipoles119

11-2 Electronic polarization119

11-3 Polar molecules; orientation polarization121

11-4 Electric fields in cavities of a dielectric123

11-5 The dielectric constant of liquids; the Clausius-Mossotti equation124

11-6 Solid dielectrics126

11-7 Ferroelectricity; BaTiO3126

CHAPTER 12. ELECTROSTATIC ANALOGS131

12-1 The same equations have the same solutions131

12-2 The flow of heat; a point source near an infinite plane boundary132

12-3 The stretched membrane135

12-4 The diffusion of neutrons; a uniform spherical source in a homogeneous medium136

12-5 Irrotational fluid flow; the flow past a sphere138

12-6 Illumination; the uniform lighting of a plane140

12-7 The “underlying unity” of nature142

CHAPTER 13. MAGNETOSTATICS145

13-1 The magnetic field145

13-2 Electric current; the conservation of charge145

13-3 The magnetic force on a current146

13-4 The magnetic field of steady currents;Ampere's law147

13-5 The magnetic field of a straight wire and of a solenoid; atomic currents149

13-6 The relativity of magnetic and electric fields150

13-7 The transformation of currents and charges155

13-8 Superposition; the right-hand rule155

CHAPTER 14. THE MAGNETIC FIELD IN VARIOUS SITUATIONS157

14-1 The vector potential157

14-2 The vector potential of known currents159

14-3 A straight wire160

14-4 A long solenoid161

14-5 The field of a small loop; the magnetic dipole163

14-6 The vector potential of a circuit164

14-7 The law of Biot and Savart165

CHAPTER 15. THE VECTOR POTENTIAL167

15-1 The forces on a current loop; energy of a dipole167

15-2 Mechanical and electrical energies169

15-3 The energy of steady currents172

15-4 B versus A173

15-5 The vector potential and quantum mechanics174

15-6 What is true for statics is false for dynamics180

CHAPTER 16. INDUCED CURRENTS183

16-1 Motors and generators183

16-2 Transformers and inductances186

16-3 Forces on induced currents187

16-4 Electrical technology190

CHAPTER 17. THE LAWS OF INDUCTION193

17-1 The physics of induction193

17-2 Exceptions to the “flux rule”194

17-3 Particle acceleration by an induced electric field;the betatron195

17-4 A paradox197

17-5 Alternating-current generator198

17-6 Mutual inductance201

17-7 Self-inductance203

17-8 Inductance and magnetic energy204

CHAPTER 18. THE MAXWELL EQUATIONS209

18-1 Maxwell's equations209

18-2 How the new term works211

18-3 All of classical physics213

18-4 A travelling field213

18-5 The speed of light216

18-6 Solving Maxwell's equations; the potentials and the wave equation217

CHAPTER 19. THE PRINCIPLE OF LEAST ACTION221

A special lecture—almost verbatim221

A note added after the lecture234

CHAPTER 20. SOLUTIONS OF MAXWELL'S EQUATIONS IN FREE SPACE235

20-1 Waves in free space; plane waves235

20-2 Three-dimensional waves242

20-3 Scientific imagination243

20-4 Spherical waves246

CHAPTER 21. SOLUTIONS OF MAXWELL'S EQUATIONS WITH CURRENTS AND CHARGES251

21-1 Light and electromagnetic waves251

21-2 Spherical waves from a point source252

21-3 The general solution of Maxwell's equations254

21-4 The fields of an oscillating dipole255

21-5 The potentials of a moving charge; the general solution of Lienard and Wiechert259

21-6 The potentials for a charge moving with constant velocity; the Lorentz formula262

CHAPTER 22. AC CIRCUITS265

22-1 Impedances265

22-2 Generators269

22-3 Networks of ideal elements; Kirchhoff's rules271

22-4 Equivalent circuits274

22-5 Energy275

22-6 A ladder network276

22-7 Filters278

22-8 Other circuit elements280

CHAPTER 23. CAvrrY RESONATORS283

23-1 Real circuit elements283

23-2 A capacitor at high frequencies284

23-3 A resonant cavity288

23-4 Cavity modes291

23-5 Cavities and resonant circuits292

CHAPTER 24. WAVEGUIDES295

24-1 The transmission line295

24-2 The rectangular waveguide298

24-3 The cutoff frequency300

24-4 The speed of the guided waves301

24-5 Observing guided waves301

24-6 Waveguide plumbing302

24-7 Waveguide modes304

24-8 Another way of looking at the guided waves304

CHAPTER 25. ELECTRODYNAMICS IN RELATIVISTIC NOTATION307

25-1 Four-vectors307

25-2 The scalar product309

25-3 The four-dimensional gradient312

25-4 Electrodynamics in four-dimensional notation314

25-5 The four-potential of a moving charge315

25-6 The invariance of the equations of electrodynamics316

CHAPTER 26. LORENTZ TRANSFORMATIONS OF THE FIELDS319

26-1 The four-potential of a moving charge319

26-2 The fields of a point charge with a constant velocity320

26-3 Relativistic transformation of the fields323

26-4 The equations of motion in relativistic notation329

CHAPTER 27. FIELD ENERGY AND FIELD MOMENTUM333

27-1 Local conservation333

27-2 Energy conservation and electromagnetism334

27-3 Energy density and energy flow in the electromagnetic field335

27-4 The ambiguity of the field energy338

27-5 Examples of energy flow338

27-6 Field momentum341

CHAPTER 28. ELECTROMAGNETIC MASS345

28-1 The field energy of a point charge345

28-2 The field momentum of a moving charge346

28-3 Electromagnetic mass347

28-4 The force of an electron on itself348

28-5 Attempts to modify the Maxwell theory350

28-6 The nuclear force field356

CHAPTER 29. THE MOTION OF CHARGES IN ELECTRIC AND MAGNETIC FIELDS359

29-1 Motion in a uniform electric or magnetic field359

29-2 Momentum analysis359

29-3 An electrostatic lens360

29-4 A magnetic lens361

29-5 The electron microscope361

29-6 Accelerator guide fields362

29-7 Alternating-gradient focusing364

29-8 Motion in crossed electric and magnetic fields366

CHAPTER 30. THE INTERNAL GEOMETRY OF CRYSTALS367

30-1 The internal geometry of crystals367

30-2 Chemical bonds in crystals368

30-3 The growth of crystals369

30-4 Crystal lattices369

30-5 Symmetries in two dimensions370

30-6 Symmetries in three dimensions373

30-7 The strength of metals 30-8374

30-8 Dislocations and crystal growth375

30-9 The Bragg-Nye crystal model375

CHAPTER 31. TENSORS393

31-1 The tensor of polarizability393

31-2 Transforming the tensor components395

31-3 The energy ellipsoid395

31-4 Other tensors; the tensor of inertia398

31-5 The cross product400

31-6 The tensor of stress401

31-7 Tensors of higher rank403

31-8 The four-tensor of electromagnetic momentum404

CHAPTER 32. REFRACTIVE INDEX OF DENSE MATERIALS407

32-1 Polarization of matter407

32-2 Maxwell's equations in a dielectric409

32-3 Waves in a dielectric411

32-4 The complex index of refraction414

32-5 The index of a mixture414

32-6 Waves in metals416

32-7 Low-frequency and high-frequency approximations;the skin depth and the plasma frequency417

CHAPTER 33. REFLECTION FROM SURFACES421

33-1 Reflection and refraction of light421

33-2 Waves in dense materials422

33-3 The boundary conditions424

33-4 The reflected and transmitted waves427

33-5 Reflection from metals431

33-6 Total internal reflection432

CHAPTER 34. THE MAGNETISM OF MATTER435

34-1 Diamagnetism and paramagnetism435

34-2 Magnetic moments and angular momentum437

34-3 The precession of atomic magnets438

34-4 Diamagnetism439

34-5 Larmor's theorem440

34-6 Classical physics gives neither diamagnetism nor paramagnetism442

34-7 Angular momentum in quantum mechanics442

34-8 The magnetic energy of atoms445

CHAPTER 35. PARAMAGNETISM AND MAGNETIC RESONANCE447

35-1 Quantized magnetic states447

35-2 The Stern-Gerlach experiment449

35-3 The Rabi molecular-beam method450

35-4 The paramagnetism of bulk materials452

35-5 Cooling by adiabatic demagnetization455

35-6 Nuclear magnetic resonance456

CHAPTER 36. FERROMAGNETISM459

36-1 Magnetization currents459

36-2 The field H463

36-3 The magnetization curve464

36-4 Iron-core inductances466

36-5 Electromagnets467

36-6 Spontaneous magnetization469

CHAPTER 37. MAGNETIC MATERIALS475

37-1 Understanding ferromagnetism475

37-2 Thermodynamic properties478

37-3 The hysteresis curve479

37-4 Ferromagnetic materials484

37-5 Extraordinary magnetic materials485

CHAPTER 38. ELASTICITY489

38-1 Hooke's law489

38-2 Uniform strains490

38-3 The torsion bar; shear waves493

38-4 The bent beam497

38-5 Buckling499

CHAPTER 39. ELASTIC MATERIALS501

39-1 The tensor of strain501

39-2 The tensor of elasticity504

39-3 The motions in an elastic body506

39-4 Nonelastic behavior508

39-5 Calculating the elastic constants510

CHAPTER 40. THE FLOW OF DRY WATER515

40-1 Hydrostatics515

40-2 The equations of motion516

40-3 Steady flow—Bernoulli's theorem520

40-4 Circulation523

40-5 Vortex lines524

CHAPTER 41. THE FLOW OF WET WATER527

41-1 Viscosity527

41-2 Viscous flow530

41-3 The Reynolds number531

41-4 Flow past a circular cylinder533

41-5 The limit of zero viscosity535

41-6 Couette flow536

CHAPTER 42. CURVED SPACE539

42-1 Curved spaces with two dimensions539

42-2 Curvature in three-dimensional space543

42-3 Our space is curved544

42-4 Geometry in space-time545

42-5 Gravity and the principle of equivalence546

42-6 The speed of clocks in a gravitational field547

42-7 The curvature of space-time549

42-8 Motion in curved space-time550

42-9 Einstein's theory of gravitation551