Preface xv
1. Electrostatics I 1
1.1 Review of F = ma 1
1.2 Enter electricity 3
1.3 Coulomb's law 8
1.4 Properties of charge 10
1.4.1 Superposition principle 12
1.5 Verifying Coulomb's law 13
1.6 The ratio of gravitational to electric forces 15
1.7 Coulomb's law for continuous charge density 17
2. The Electric Field 19
2.1 Review of key ideas 19
2.2 Digression on nuclear forces 20
2.3 The electric field E 22
2.4 Visualizing the field 25
2.5 Field of a dipole 33
2.5.1 Far field of dipole: general case 36
2.6 Response to a field 38
2.6.1 Dipole in a uniform field 39
3. Gauss's Law I 42
3.1 Field of an infinite line charge 43
3.2 Field of an infinite sheet of charge 47
3.3 Spherical charge distribution: Gauss's law 52
3.4 Digression on the area vector dA 53
3.4.1 Composition of areas 55
3.4.2 An application of the area vector 57
3.5 Gauss's law through pictures 59
3.5.1 Continuous charge density 64
4. Gauss's Law II: Applications 65
4.1 Applications of Gauss's law 66
4.2 Field inside a shell 69
4.3 Field of an infinite charged wire, redux 72
4.4 Field of an infinite plane, redux 74
4.5 Conductors 75
4.5.1 Field inside a perfect conductor is zero 76
4.5.2 The net charge on a conductor will reside at the surface 77
4.5.3 A conductor with a hole inside 78
4.5.4 Field on the surface of a conductor 79
5. The Coulomb Potential 81
5.1 Conservative forces and potential energy 82
5.2 Is the electrostatic field conservative? 88
5.3 Path independence through pictures 92
5.4 Potential and field of a dipole 93
6. Conductors and Capacitors 97
6.1 Cases where computing V from E is easier 99
6.2 Visualizing V 101
6.3 Equipotentials 103
6.4 Method of images 104
6.4.1 Proof of uniqueness (optional section) 110
6.4.2 Additional properties of the potential V(r) 112
6.5 Capacitors 113
6.6 Energy stored in a capacitor 115
6.7 Energy of a charge distribution 116
7. Circuits and Currents 119
7.1 Energy in the electric field 120
7.2 Circuits and conductivity 121
7.3 Circuits 126
7.4 The battery and the EMF ε 130
7.5 The RC circuit with a battery 135
7.6 Miscellaneous circuits 138
8. Magnetism I 142
8.1 Experiments pointing to magnetism 142
8.2 Examples of the Lorentz force, the cyclotron 147
8.3 Lorentz force on current-carrying wires 151
8.4 The magnetic dipole 154
8.5 The DC motor 156
9. Magnetism II: Biot-Savart Law 158
9.1 Practice with Biot-Savart: field of a loop 160
9.2 Microscopic description of a bar magnet 162
9.3 Magnetic field of an infinite wire 164
9.4 Ampére's law 167
9.5 Maxwell's equations (static case) 172
10. Ampère II, Faraday, and Lenz 174
10.1 Field of an infinite wire, redux 175
10.2 Field of a solenoid 179
10.3 Faraday and Lenz 184
10.4 Optional digression on Faraday's law 195
11. More Faraday 200
11.1 Betatron 200
11.2 Generators 205
11.3 Inductance 208
11.4 Mutual inductance 211
11.5 Self-inductance 214
11.6 Energy in the magnetic field 217
12. AC Circuits 220
12.1 Review of inductors 226
12.2 The LC circuit 226
12.2.1 Driven LC circuit 229
12.3 The LCR circuit 231
12.3.1 Review of complex numbers 231
12.3.2 Solving the LCR equation 236
12.3.3 Visualizing Z 239
12.4 Complex form of Ohm's law 241
13. LCR Circuits and Displacement Current 244
13.1 Analysis of LCR results 246
13.1.1 Transients and the complementary solution 251
13.2 Power of the complex numbers 253
13.3 Displacement current 259
14. Electromagnetic Waves 263
14.1 The wave equation 266
14.2 Restricted Maxwell equations in vacuum 270
14.2.1 Maxwell equations involving infinitesimal cubes 270
14.2.2 Maxwell equations involving infinitesimal loops 272
14.3 The wave! 275
14.4 Sinusoidal solution to the wave equation 277
14.5 Energy in the electromagnetic wave 283
14.6 Origin of electromagnetic waves 285
14.7 Maxwell equations-the general case (optional) 286
14.7.1 Maxwell equations involving infinitesimal cubes 286
14.7.2 Maxwell equations involving infinitesimal loops 288
14.7.3 Consequences for the restricted E and B 293
14.8 From microscopic to macroscopic (optional) 294
14.8.1 Maxwell equations involving cubes 295
14.8.2 Maxwell equations involving loops 297
15. Electromagnetism and Relativity 300
15.1 Magnetism from Coulomb's law and relativity 301
15.2 Relativistic invariance of electrodynamics 305
15.3 Review of Lorentz transformations 305
15.3.1 Implications for Newtonian mechanics 307
15.4 Scalar and vector fields 309
15.5 The derivative operator 312
15.6 Lorentz scalars and vectors 315
15.7 The four-current J 317
15.7.1 Charge conservation and the four-current J 318
15.8 The four-potential A 319
15.8.1 Gauge invariance 322
15.9 Wave equation for the four-vector A 324
15.9.1 Why work with Vand A? 327
15.10 The electromagnetic tensor F 328
15.10.1 Tensors 328
15.10.2 The electromagnetic field tensor F 332
16. Optics I: Geometric Optics Revisited 336
16.1 Geometric or ray optics 336
16.2 Brief history of c 338
16.3 Some highlights of geometric optics 340
16.4 The law of reflection from Fermat's principle 343
16.5 Snell's law from Fermat's principle 344
16.6 Reflection off a curved surface by Fermat 346
16.7 Elliptical mirrors and Fermat's principle 349
16.8 Parabolic mirrors 352
17. Optics II: More Mirrors and Lenses 355
17.1 Spherical approximations to parabolic mirrors 355
17.2 Image formation: geometric optics 357
17.2.1 A midlife crisis 359
17.3 Image formation by Fermat's principle 360
17.4 Tricky cases 364
17.4.1 Fermat's principle for virtual focal points 365
17.4.2 Ray optics for virtual images 366
17.5 Lenses à la Fermat 368
17.6 Principle of least action 370
17.7 The eye 372
18. Wave Theory of Light 377
18.1 Interference of waves 381
18.2 Adding waves using real numbers 383
18.3 Adding waves with complex numbers 385
18.4 Analysis of interference 388
18.5 Diffraction grating 394
18.6 Single-slit diffraction 397
18.7 Understanding reflection and crystal diffraction 398
18.8 Light incident on an oil slick 401
18.8.1 Normal incidence 401
18.8.2 Oblique incidence 404
19. Quantum Mechanics: The Main Experiment 406
19.1 Double-slit experiment with light 407
19.2 Trouble with Maxwell 407
19.3 Digression on photons 412
19.3.1 Photoelectric effect 412
19.3.2 Compton effect 414
19.4 Matter waves 415
19.5 Photons versus electrons 420
19.6 The Heisenberg uncertainty principle 422
19.6.1 There are no states of well-defined position and momentum 423
19.6.2 Heisenberg microscope 427
19.7 Let there be light 430
19.8 The wave function Ψ 435
19.9 Collapse of the wave function 438
19.10 Summary 439
20. The Wave Function and Its Interpretation 442
20.1 Probability in classical and quantum mechanics 446
20.2 Getting to know Ψ 451
20.3 Statistical concepts: mean and uncertainty 456
21. Quantization and Measurement 460
21.1 More on momentum states 462
21.2 Single-valuedness and quantization of momentum 464
21.2.1 Quantization 467
21.2.2 The integral of Ψp(x) 468
21.3 Measurement postulate: momentum 469
21.3.1 An example solvable by inspection 476
21.3.2 Using a normalized Ψ 478
21.4 Finding A(p) by computation 480
21.5 More on Fourier's theorems 486
21.6 Measurement postulate: general 491
21.7 More than one variable 493
22. States of Definite Energy 495
22.1 Free particle on a ring 500
22.1.1 Analysis of energy levels: degeneracy 503
22.2 Thinking inside the box 507
22.2.1 Particle in a well 507
22.2.2 The box: an exact solution 516
22.3 Energy measurement in the box 521
23. Scattering and Dynamics 524
23.1 Quantum scattering 524
23.1.1 Scattering for E > V₀ 526
23.1.2 Scattering for E < V₀ 530
23.2 Tunneling 531
23.3 Quantum dynamics 533
23.3.1 A solution of the time-dependent Schrödinger equation 535
23.3.2 Derivation of the particular solution ΨE(x,t) 536
23.4 Special properties of the product solution 538
23.5 General solution for time evolution 541
23.5.1 Time evolution: a more complicated example 545
24. Summary and Outlook 550
24.1 Postulates: first pass 550
24.2 Refining the postulates 554
24.2.1 Toward a compact set of postulates 555
24.2.2 Eigenvalue problem 556
24.2.3 The Dirac delta function and the operator X 558
24.3 Postulates: final 565
24.4 Many particles, bosons, and fermions 566
24.4.1 Identical versus indistinguishable 567
24.4.2 Implications for atomic structure 574
24.5 Energy-time uncertainty principle 576
24.6 What next? 583
Constants 585
Index 587