Problems in General Physics

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Problems in General Physics

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This book of problems is intended as a textbook for students at higher educational institutions studying advanced course in physics. Besides, because of the great number of simple problems it may be used by students studying a general course in physics. The book contains about 1900 problems with hints for solving the most complicated ones.

For students' convenience each chapter opens with a time-saving summary of the principal formulas for the relevant area of physics. As a rule the formulas are given without detailed explanations since a student, starting solving a problem, is assumed to know the meaning of the quantities appearing in the formulas. Explanatory notes are only given in those cases when misunderstanding may arise.

All the formulas in the text and answers are in SI system, except in Part Six, where the Gaussian system is used. Quantitative data and answers are presented in accordance with the rules of approximation and numerical accuracy.

The main physical constants and tables are summarised at the end of the book.

The Periodic System of Elements is printed at the front end sheet and the Table of Elementary Particles at the back sheet of the book. In the present edition, some misprints are corrected, and a number of problems are substituted by new ones, or the quantitative data in them are changed or refined (1.273, 1.361, 2.189, 3.249, 3.97, 4.194 and 5.78). In conclusion, the author wants to express his deep gratitude to colleagues from MIPhI and to readers who sent their remarks on some problems, helping thereby to improve the book.

Preface 5
A Few Hints for Solving the Problems 9
Notation 10

PART ONE. PHYSICAL FUNDAMENTALS OF MECHANICS 11
1.1. Kinematics 11
1.2. The Fundamental Equation of Dynamics 20
1.3. Laws of Conservation of Energy, Momentum, and Angular Momentum 30
1.4. Universal Gravitation 43
1.5. Dynamics of a Solid Body 47
1.6. Elastic Deformations of a Solid Body 58
1.7. Hydrodynamics 62
1.8. Relativistic Mechanics 67

PART TWO. THERMODYNAMICS AND MOLECULAR PHYSICS . 75
2.1. Equation of the Gas State. Processes 75
2.2. The First Law of Thermodynamics. Heat Capacity 78
2.3. Kinetic Theory of Gases. Boltzmann's Law and Maxwell's Distribution 82
2.4. The Second Law of Thermodynamics. Entropy 88
2.5. Liquids. Capillary Effects 93
2.6. Phase Transformations 96
2.7. Transport Phenomena 100

PART THREE. ELECTRODYNAMICS 105
3.1. Constant Electric Field in Vacuum 105
3.2. Conductors and Dielectrics in an Electric Field 111
3.3. Electric Capacitance. Energy of an Electric Field 118
3.4. Electric Current 125
3.5. Constant Magnetic Field. Magnetics 136
3.6. Electromagnetic Induction. Maxwell's Equations 147
3.7. Motion of Charged Particles in Electric and Magnetic Fields 160

PART FOUR. OSCILLATIONS AND WAVES 166
4.1. Mechanical Oscillations 166
4.2. Electric Oscillations 180
4.3. Elastic Waves. Acoustics 188
4.4. Electromagnetic Waves. Radiation 193

PART FIVE. OPTICS 199
5.1. Photometry and Geometrical Optics 199
5.2. Interference of Light 210
5.3. Diffraction of Light 216
5.4. Polarization of Light 226
5.5. Dispersion and Absorption of Light 234
5.6. Optics of Moving Sources 237
5.7. Thermal Radiation. Quantum Nature of Light 240

PART SIX. ATOMIC AND NUCLEAR PHYSICS 246
6.1. Scattering of Particles. Rutherford-Bohr Atom 246
6.2. Wave Properties of Particles. Schrodinger Equation 251
6.3. Properties of Atoms. Spectra 257
6.4. Molecules and Crystals 264
6.5. Radioactivity 270
6.6. Nuclear Reactions 274
6.7. Elementary Particles 278
ANSWERS AND SOLUTIONS 281

APPENDICES 365
1. Basic Trigonometrical Formulas 365
2. Sine Function Values 366
3. Tangent Function Values 367
4. Common Logarithms 368
5. Exponential Functions 370
6. Greek Alphabet 372
7. Numerical Constants and Approximations 372
8. Some Data on Vectors 372
9. Derivatives and Integrals 373
10. Astronomical Data 374
11. Density of Substances 374
12. Thermal Expansion Coefficients 375
13. Elastic Constants. Tensile Strength 375
14. Saturated Vapour Pressure 375
15. Gas Constants 376
16. Some Parameters of Liquids and Solids 376
17. Permittivities 377
18. Resistivities of Conductors 377
19. Magnetic Susceptibilities of Para- and Diamagnetics 377
20. Refractive Indices 378
21. Rotation of the Plane of Polarization 378
22. Work Function of Various Metals 379
23. K Band Absorption. Edge 379
24. Mass Absorption Coefficients 379
25. Ionization Potentials of Atoms 380
26. Mass of Light Atoms 380
27. Half-life Values of Radionuclides 380
28. Units of Physical Quantities 381
29. The Basic Formulas of Electrodynamics in the SI and Gaussian Systems 383
30. Fundamental Constants 386