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