Mechanics 3
1.1. Falling Chain (MIT, Stanford)
3
Cat and Mouse Tug of War (Moscow Phys-Tech, MIT)
3
1.2.
Cube Bouncing off Wall (Moscow Phys-Tech)
4
1.3.
Cue-Struck Billiard Ball (Rutgers, Moscow Phys-Tech, Wisconsin-
1.4.
Madison (a))
4
Stability on Rotating Rollers (Princeton) 5
1.5.
Swan and Crawfish (Moscow Phys-Tech)
6
1.6.
Mud from Tire (Stony Brook)
7
1.7.
Car down Ramp up Loop (Stony Brook)
7
1.8.
Pulling Strings (MIT) 8
1.9.
Thru-Earth Train (Stony Brook, Boston (a), Wisconsin-
1.10.
Madison (a))
8
String Oscillations (Moscow Phys-Tech)
1.11. 9
Hovering Helicopter (Moscow Phys-Tech)
1.12.
9
Astronaut Tether (Moscow Phys-Tech, Michigan)
9
1.13.
Spiral Orbit (MIT)
1.14.
10
Central Force with Origin on Circle (MIT, Michigan State)
1.15.
10
Central Force Orbit (Princeton)
1.16.
10
Dumbbell Satellite (Maryland, MIT, Michigan State)
11
1.17.
Yukawa Force Orbit (Stony Brook)
11
1.18.
Particle Colliding with Reflecting Walls (Stanford)
12
1.19.
Earth–Comet Encounter (Princeton)
1.20. 12
xiii
CONTENTS xiv
1.21. 13
Neutron Scattering (Moscow Phys-Tech)
1.22.
Collision of Mass–Spring System (MIT)
13
1.23. Double Collision of Mass–Spring System (MoscowPhys-Tech)
13
1.24.
Small Particle in Bowl (Stony Brook) 14
1.25.
Fast Particle in Bowl (Boston)
14
1.26.
Mass Orbiting on Table (Stony Brook, Princeton, Maryland,
Michigan)
15
1.27. Falling Chimney (Boston, Chicago)
16
1.28. Sliding Ladder (Princeton, Rutgers, Boston)
16
Unwinding String (MIT, Maryland (a,b), Chicago (a,b))
1.29.
17
1.30.
Six Uniform Rods (Stony Brook)
18
Period as Function of Energy (MIT)
1.31.
19
1.32.
Rotating Pendulum (Princeton, Moscow Phys-Tech)
19
19
Flyball Governor (Boston, Princeton, MIT)
1.33.
1.34.
Double Pendulum (Stony Brook, Princeton, MIT)
20
1.35.
Triple Pendulum (Princeton) 21
1.36.
Three Masses and Three Springs on Hoop (Columbia, Stony Brook,
MIT)
21
1.37. Nonlinear Oscillator (Princeton)
22
1.38.
Swing (MIT, Moscow Phys-Tech)
22
1.39.
Rotating Door (Boston)
22
1.40.
Bug on Globe (Boston)
23
1.41.
Rolling Coin (Princeton, Stony Brook)
24
1.42.
Unstable Top (Stony Brook)
24
1.43.
Pendulum Clock in NoninertialFrame (Maryland)
25
1.44.
Beer Can (Princeton, Moscow Phys-Tech)
26
1.45.
Space Habitat Baseball (Princeton)
27
1.46.
Vibrating String with Mass (Stony Brook)
27
1.47.
Shallow Water Waves (Princeton (a,b))
28
1.48.
Suspension Bridge (Stony Brook)
29
1.49.
Catenary (Stony Brook, MIT)
29
1.50.
Rotating Hollow Hoop (Boston)
30
1.51.
Particle in Magnetic Field (Stony Brook)
31
1.52.
Adiabatic Invariants (Boston (a)) and Dissolving Spring (Princeton,
MIT (b))
31
1.53.
Superball in Weakening Gravitational Field (Michigan State)
32
2.
Relativity
33
2.1.
Marking Sticks (Stony Brook)
33
2.2.
Rockets in Collision (Stony Brook)
34
CONTENTS
xv
Photon Box (Stony Brook) 34
2.3.
35
2.4.
Cube’s Apparent Rotation (Stanford, Moscow Phys-Tech)
36
Relativistic Rocket (Rutgers)
2.5.
36
Rapidity (MoscowPhys-Tech)
2.6.
Charge in Uniform Electric Field (Stony Brook, Maryland,
2.7.
37
Colorado)
37
Charge in Electric Field and Flashing Satellites (Maryland)
2.8.
38
Uniformly Accelerated Motion (Stony Brook)
2.9.
38
Compton Scattering (Stony Brook, Michigan State)
2.10.
39
Mossbauer Effect (Moscow Phys-Tech, MIT, Colorado)
2.11.
39
Positronium and Relativistic Doppler Effect (Stony Brook)
2.12.
39
Transverse Relativistic Doppler Effect (Moscow Phys-Tech)
2.13.
40
Particle Creation (MIT)
2.14.
40
Electron–Electron Collision (Stony Brook)
2.15.
40
Inverse Compton Scattering (MIT, Maryland)
2.16.
40
Proton–Proton Collision (MIT)
2.17.
41
Pion Creation and Neutron Decay (Stony Brook)
2.18.
41
Elastic Collision and Rotation Angle (MIT)
2.19.
43
3. Electrodynamics
43
Charge Distribution (Wisconsin-Madison)
3.1.
43
Electrostatic Forces and Scaling (Moscow Phys-Tech)
3.2.
44
Dipole Energy (MIT, Moscow Phys-Tech)
3.3.
Charged Conducting Sphere in Constant Electric Field (Stony
3.4.
44
Brook, MIT)
45
Charge and Conducting Sphere I (MIT)
3.5.
45Charge and Conducting Sphere II (Boston)
3.6.
Conducting Cylinder and Line Charge (Stony Brook, Michigan
3.7.
46State)
46Spherical Void in Dielectric (Princeton)
3.8.
47
Charge and Dielectric (Boston)
3.9.
47
Dielectric Cylinder in Uniform Electric Field (Princeton)
3.10.
48Powder of Dielectric Spheres (Stony Brook)
3.11.
48Concentric Spherical Capacitor (Stony Brook)
3.12.
49
Not-so-concentric Spherical Capacitor (Michigan Tech)
3.13.
Parallel Plate Capacitor with Solid Dielectric (Stony Brook,
3.14.
Michigan Tech, Michigan)
49
50Parallel Plate Capacitor in Dielectric Bath (MIT)
3.15.
51
Not-so-parallel Plate Capacitor (Princeton (a), Rutgers (b))
3.16.
51
Cylindrical Capacitor in Dielectric Bath (Boston, Maryland)
3.17.
xvi
CONTENTS
52
Iterated Capacitance (Stony Brook)
3.18.
52
Resistance vs. Capacitance (Boston, Rutgers (a))
3.19.
53
Charge Distribution in Inhomogeneous Medium (Boston)
3.20.
54
Green’s Reciprocation Theorem (Stony Brook)
3.21.
54
Coaxial Cable and Surface Charge (Princeton)
3.22.
55
Potential of Charged Rod (Stony Brook)
3.23.
56
Principle of Conformal Mapping (Boston)
3.24.
56
Potential above Half Planes (Princeton)
3.25.
56
Potential of Halved Cylinder (Boston, Princeton, Chicago)
3.26.
57
Resistance of a Washer (MIT)
3.27.
57
Spherical Resistor (Michigan State)
3.28.
58
3.29.
Infinite Resistor Ladder (Moscow Phys-Tech)
59
3.30.
Semi-infinite Plate (Moscow Phys-Tech)
Magnetic Field in Center of Cube (Moscow Phys-Tech) 59
3.31.
Magnetic Dipole and Permeable Medium (Princeton)
3.32.
60
Magnetic Shielding (Princeton)
3.33.
60
Electromotive Force in Spiral (Moscow Phys-Tech) 60
3.34.
3.35.
Sliding Copper Rod (Stony Brook, Moscow Phys-Tech)
61
3.36.
Loop in Magnetic Field (Moscow Phys-Tech, MIT)
61
3.37.
Conducting Sphere in Constant Magnetic Field (Boston) 62
3.38.
Mutual Inductance of Line and Circle (Michigan) 62
3.39.
62
Faraday’s Homopolar Generator (Stony Brook, Michigan)
63
Current in Wire and Poynting Vector (Stony Brook, MIT)
3.40.
63
Box and Impulsive Magnetic Field (Boston)
3.41.
3.42. 64
Coaxial Cable and Poynting Vector (Rutgers)
65
3.43. Angular Momentum of Electromagnetic Field (Princeton)
3.44. Plane Wave in Dielectric (Stony Brook, Michigan) 65
3.45.
X-Ray Mirror (Princeton)
66
3.46.
Plane Wave in Metal (Colorado, MIT)
67
3.47.
Wave Attenuation (Stony Brook)
67
3.48.
Electrons and Circularly Polarized Waves (Boston)
67
3.49.
Classical Atomic Spectral Line (Princeton, Wisconsin-Madison)
68
3.50.
Lifetime of Classical Atom (MIT, Princeton, Stony Brook)
69
3.51.
Lorentz Transformation of Fields (Stony Brook)
69
3.52.
Field of a Moving Charge (Stony Brook)
70
3.53.
Retarded Potential of Moving Line Charge (MIT)
70
3.54.
Orbiting Charges and Multipole Radiation (Princeton, Michigan
State, Maryland)
71
3.55.
Electron and Radiation Reaction (Boston)
72
3.56.
Radiation of Accelerating Positron (Princeton, Colorado)
72
3.57.
Half-Wave Antenna (Boston)
73
3.58.
Radiation (Stony Brook)
73
xvii
CONTENTS
3.59. Stability of Plasma (Boston)
74
3.60.
Charged Particle in Uniform MagneticField (Princeton)
74
3.61.
Lowest Mode of RectangularWaveGuide (Princeton, MIT,
Michigan State)
74
3.62.
TM Modes in Rectangular Wave Guide (Princeton)
75
3.63.
Betatron (Princeton, Moscow Phys-Tech, Colorado, Stony
Brook (a))
75
3.64.
SuperconductingFrameinMagneticField (Mascow Phys-Tech)
76
3.65.
Superconducting Sphere in Magnetic Field (Michigan State,
Moscow Phys- Tech)
77
3.66. London Penetration Depth (Moscow Phys-Tech)
77
3.67.
Thin Superconducting Plate in MagneticField (Stony Brook)
78
PART II: SOLUTIONS
l. Mechanics
81
1.1.
Falling Chain (MIT, Stanford)
81
1.2.
Cat and Mouse Tug of War (Moscow Phys-Tech, MIT)
81
1.3.
Cube Bouncing off Wall (Moscow Phys-Tech)
82
1.4.
Cue-struck Billiard Ball (Rutgers, Moscow Phys-Tech, Wisconsin-
Madison (a))
84
1.5. Stability on RotatingRollers (Princeton)
86
1.6.
Swan and Crawfish (Moscow Phys-Tech)
88
1.7.
Mud from Tire (Stony Brook)
90
1.8.
Car down Ramp up Loop (Stony Brook)
92
1.9.
Pulling Strings (MIT)
94
1.10.
Thru-Earth Train (Stony Brook, Boston (a), Wisconsin-Madison (a))
95
1.11.
StringOscillations (Moscow Phys-Tech)
97
1.12.
Hovering Helicopter (Moscow Phys-Tech)
98
1.13.
Astronaut Tether (Moscow Phys-Tech, Michigan)
99
1.14.
Spiral Orbit (MIT)
100
1.15.
CentralForce with Origin on Circle (MIT, Michigan State)
101
1.16.
CentralForce Orbit (Princeton)
102
1.17.
DumbbellSatellite (Maryland, MIT, Michigan State)
104
Yukawa Force Orbit (Stony Brook)
1.18.
106
1.19.
Particle Colliding with Reflecting Walls (Stanford)
107
1.20.
Earth–Comet Encounter (Princeton)
109
1.21.
Neutron Scattering (Moscow Phys-Tech) 110
CONTENTS xviii
111
1.22. Collision of Mass–Spring System (MIT)
112
Double Collision of Mass–Spring System (Moscow Phys-Tech)
1.23.
114
1.24. Small Particle in Bowl (Stony Brook)
117
Fast Particle in Bowl (Boston)
1.25.
Mass Orbiting on Table (Stony Brook, Princeton, Maryland,
1.26.
118
Michigan)
119
Falling Chimney (Boston, Chicago)
1.27.
120
Sliding Ladder (Princeton, Rutgers, Boston)
1.28.
122
Unwinding String (MIT, Maryland (a,b), Chicago (a,b))
1.29.
125
Six Uniform Rods (Stony Brook)
1.30.
128
Period as Function of Energy (MIT)
1.31.
129
Rotating Pendulum (Princeton, Moscow Phys-Tech)
1.32.
131
Flyball Governor (Boston, Princeton, MIT)
1.33.
Double Pendulum (Stony Brook, Princeton, MIT) 133
1.34.
135
Triple Pendulum (Princeton)
1.35.
Three Masses and Three Springs on Hoop (Columbia, Stony Brook,
1.36.
137
MIT)
139
1.37. Nonlinear Oscillator (Princeton)
141
Swing (MIT, Moscow Phys-Tech)
1.38.
142
1.39.
Rotating Door (Boston)
Bug on Globe (Boston) 143
1.40.
1.41.
Rolling Coin (Princeton, Stony Brook) 145
1.42.
Unstable Top (Stony Brook)
147
Pendulum Clock in Noninertial Frame (Maryland)
1.43.
148
1.44.
Beer Can (Princeton, Moscow Phys-Tech) 149
1.45.
153
Space Habitat Baseball (Princeton)
Vibrating String with Mass (Stony Brook)
1.46.
154
1.47.
Shallow Water Waves (Princeton (a,b))
157
Suspension Bridge (Stony Brook)
1.48.
160
1.49.
Catenary (Stony Brook, MIT)
161
Rotating Hollow Hoop (Boston)
1.50. 163
1.51.
Particle in Magnetic Field (Stony Brook)
165
1.52.
Adiabatic Invariants (Boston (a))
and Dissolving Spring (Princeton,
MIT(b))
168
1.53.
Superball in Weakening Gravitational Field (Michigan State)
169
2.
Relativity
171
2.1. Marking Sticks (Stony Brook)
171
2.2.
Rockets in Collision (Stony Brook)
172
2.3.
Photon Box (Stony Brook)
173
xix C
ONTENTS
2.4. Cube’s Apparent Rotation (Stanford, Moscow Phys-Tech)
175
Relativistic Rocket (Rutgers)
2.5. 176
2.6. Rapidity (Moscow Phys-Tech) 177
2.7. Charge in Uniform Electric Field (Stony Brook, Maryland,
Colorado)
178
2.8. Charge in Electric Field and Flashing Satellites (Maryland) 181
2.9. Uniformly Accelerated Motion (Stony Brook) 184
2.10. Compton Scattering (Stony Brook, Michigan State)
186
Mossbauer Effect (Moscow Phys-Tech, MIT, Colorado) 187
2.11.
Positronium and Relativistic Doppler Effect (Stony Brook)
2.12. 188
Transverse Relativistic Doppler Effect (Moscow Phys-Tech)
2.13. 189
Particle Creation (MIT)
2.14. 190
Electron–Electron Collision (Stony Brook)
190
2.15.
Inverse Compton Scattering (MIT, Maryland)
192
2.16.
193
Proton–Proton Collision (MIT)
2.17.
194
2.18. Pion Creation and Neutron Decay (Stony Brook)
Elastic Collision and Rotation Angle (MIT) 197
2.19.
Electrodynamics
3. 201
Charge Distribution (Wisconsin-Madison) 201
3.1.
Electrostatic Forces and Scaling (Moscow Phys-Tech)
201
3.2.
Dipole Energy (MIT, Moscow Phys-Tech) 202
3.3.
Charged ConductingSphere in Constant Electric Field (Stony
3.4.
203
Brook, MIT)
204
Charge and Conducting Sphere I (MIT)
3.5.
206
Charge and Conducting Sphere II (Boston)
3.6.
Conducting Cylinder and Line Charge (Stony Brook, Michigan
3.7.
207
State)
Spherical Void in Dielectric (Princeton)
208
3.8.
Charge and Dielectric (Boston)
210
3.9.
3.10. 211
Dielectric Cylinder in Uniform Electric Field (Princeton)
Powder of Dielectric Spheres (Stony Brook) 214
3.11.
216
ConcentricSpherical Capacitor (Stony Brook)
3.12.
Not-so-concentric Spherical Capacitor (Michigan Tech)
218
3.13.
Parallel Plate Capacitor with Solid Dielectric (Stony Brook,
3.14.
220
Michigan Tech, Michigan)
Parallel Plate Capacitor in Dielectric Bath (MIT)
222
3.15.
Not-so-parallel Plate Capacitor (Princeton (a), Rutgers (b))
225
3.16.
Cylindrical Capacitor in Dielectric Bath (Boston, Maryland)
226
3.17.
Iterated Capacitance (Stony Brook)
228
3.18.
CONTENTS xx
231
Resistance vs. Capacitance (Boston, Rutgers (a))
3.19.
233
Charge Distribution in Inhomogeneous Medium (Boston)
3.20.
234
Green’s Reciprocation Theorem (Stony Brook)
3.21.
235
Coaxial Cable and Surface Charge (Princeton)
3.22.
237
Potential of Charged Rod (Stony Brook)
3.23.
238
Principle of Conformal Mapping (Boston)
3.24.
240
Potential above Half Planes (Princeton)
3.25.
241
Potential of Halved Cylinder (Boston, Princeton, Chicago)
3.26.
243
Resistance of a Washer (MIT)
3.27.
244
Spherical Resistor (Michigan State)
3.28.
245
Infinite Resistor Ladder (Moscow Phys-Tech)
3.29.
246
Semi-infinite Plate (Moscow Phys-Tech)
3.30.
247
Magnetic Field in Center of Cube (Moscow Phys-Tech)
3.31.
248
MagneticDipole and Permeable Medium (Princeton)
3.32.
250
Magnetic Shielding (Princeton)
3.33.
252
Electromotive Force in Spiral (Moscow Phys-Tech)
3.34.
252
Sliding Copper Rod (Stony Brook, Moscow Phys-Tech)
3.35.
254
Loop in Magnetic Field (Moscow Phys-Tech, MIT)
3.36.
255
Conducting Sphere in Constant Magnetic Field (Boston)
3.37.
Mutual Inductance of Line and Circle (Michigan)
256
3.38.
257
Faraday’s Homopolar Generator (Stony Brook, Michigan)
3.39.
258
Current in Wire and Poynting Vector (Stony Brook, MIT)
3.40.
259
Box and Impulsive Magnetic Field (Boston)
3.41.
260
Coaxial Cable and Poynting Vector (Rutgers)
3.42.
263
Angular Momentum of Electromagnetic Field (Princeton)
3.43.
265
Plane Wave in Dielectric (Stony Brook, Michigan)
3.44.
267
X-Ray Mirror (Princeton)
3.45.
268
Plane Wave in Metal (Colorado, MIT)
3.46.
Wave Attenuation (Stony Brook)
271
3.47.
Electrons and Circularly Polarized Waves (Boston)
273
3.48.
Classical Atomic Spectral Line (Princeton, Wisconsin-Madison)
274
3.49.
Lifetime of Classical Atom (MIT, Princeton, Stony Brook)
277
3.50.
Lorentz Transformation of Fields (Stony Brook)
278
3.51.
Field of a Moving Charge (Stony Brook)
3.52. 280
Retarded Potential of Moving Line Charge (MIT)
3.53. 281
Orbiting Charges and Multipole Radiation (Princeton, Michigan
3.54.
State,Maryland)
283
Electron and Radiation Reaction (Boston)
285
3.55.
Radiation of Accelerating Positron (Princeton, Colorado)
287
3.56.
Half-Wave Antenna (Boston)
288
3.57.
Cerenkov Radiation (Stony Brook)
290
3.58.
Stability of Plasma (Boston)
3.59. 292
CONTENTS
xxi
Charged Particle in Uniform MagneticField (Princeton) 293
3.60.
Lowest Mode of Rectangular Wave Guide (Princeton, MIT,
3.61.
Michigan State) 294
3.62. TM Modes in Rectangular Wave Guide (Princeton) 297
Betatron (Princeton, Moscow Phys-Tech, Colorado, Stony
3.63.
Brook (a))
299
3.64. Superconducting Frame in Magnetic Field (Moscow Phys-Tech) 303
3.65. Superconducting Sphere in Magnetic Field (Michigan State,
Moscow Phys-Tech)
305
3.66. London Penetration Depth (Moscow Phys-Tech)
306
Thin Superconducting Plate in Magnetic Field (Stony Brook)
3.67. 308
PART III: APPENDIXES
Approximate Values of Physical Constants
313
Some Astronomical Data
314
Other Commonly Used Units
314
Conversion Table from Rationalized MKSA to Gaussian Units
315
Vector Identities
316
Vector Formulas in Spherical and Cylindrical Coordinates
317
Legendre Polynomials
320
Rodrieues’ Formula
321
Spherical Harmonics
321
BIBLIOGRAPHY
323
我的内容管理
收起
我的收益 登录查看自己的收益
我的积分
登录查看自己的积分
我的C币
登录后查看C币余额
我的收藏 
我的下载 
下载帮助 
