Preface to Second Edition xv

1 Understanding the physical universe 1

1.1 The programme of physics 1

1.2 The building blocks of matter 2

1.3 Matter in bulk 4

1.4 The fundamental interactions 5

1.5 Exploring the physical universe: the scientific method 5

1.6 The role of physics: its scope and applications 7

2 Using mathematical tools in physics 9

2.1 Applying the scientific method 9

2.2 The use of variables to represent displacement and time 9

2.3 Representation of data 10

2.4 The use of differentiation in analysis: velocity and acceleration in linear motion 12

2.5 The use of integration in analysis 16

2.6 Maximum and minimum values of physical variables: general linear motion 21

2.7 Angular motion: the radian 23

2.8 The role of mathematics in physics 25

Worked examples 26

Problems 28

3 The causes of motion: dynamics 31

3.1 The concept of force 31

3.2 The first law of dynamics (Newton’s first law) 32

3.3 The fundamental dynamical principle (Newton’s second law) 33

3.4 Systems of units: SI 36

3.5 Time dependent forces: oscillatory motion 38

3.6 Simple harmonic motion 40

3.7 Mechanical work and energy: power 44

3.8 Energy in simple harmonic motion 48

3.9 Dissipative forces: damped harmonic motion 50

3.10 Forced oscillations 54

3.11 Nonlinear dynamics: chaos 56

Worked examples 57

Problems 61

4 Motion in two and three dimensions 63

4.1 Vector physical quantities 63

4.2 Vector algebra 64

4.3 Velocity and acceleration vectors 67

4.4 Force as a vector quantity: vector form of the laws of dynamics 69

4.5 Constraint forces 70

4.6 Friction 72

4.7 Motion in a circle: centripetal force 74

4.8 Motion in a circle at constant speed 75

4.9 Tangential and radial components of acceleration 77

4.10 Hybrid motion: the simple pendulum 78

4.11 Angular quantities as vectors: the cross product 79

Worked examples 81

Problems 84

5 Force fields 87

5.1 Newton’s law of universal gravitation 87

5.2 Force fields 88

5.3 The concept of flux 89

5.4 Gauss’ law for gravitation 90

5.5 Motion in a constant uniform field: projectiles 94

5.6 Mechanical work and energy 96

5.7 Energy in a constant uniform field 102

5.8 Energy in an inverse square law field 103

5.9 Moment of a force: angular momentum 105

5.10 Planetary motion: circular orbits 107

5.11 Planetary motion: elliptical orbits and Kepler’s laws 108

Worked examples 110

Problems 114

6 Many-body interactions 117

6.1 Newton’s third law 117

6.2 The principle of conservation of momentum 120

6.3 Mechanical energy of systems of particles 121

6.4 Particle decay 122

6.5 Particle collisions 123

6.6 The centre of mass of a system of particles 127

6.7 The two-body problem: reduced mass 128

6.8 Angular momentum of a system of particles 131

6.9 Conservation principles in physics 132

Worked examples 133

Problems 137

7 Rigid body dynamics 141

7.1 Rigid bodies 141

7.2 Rigid bodies in equilibrium: statics 142

7.3 Torque 143

7.4 Dynamics of rigid bodies 144

7.5 Measurement of torque: the torsion balance 145

7.6 Rotation of a rigid body about a fixed axis: moment of inertia 146

7.7 Calculation of moments of inertia: the parallel axis theorem 147

7.8 Conservation of angular momentum of rigid bodies 149

7.9 Conservation of mechanical energy in rigid body systems 149

7.10 Work done by a torque: torsional oscillations: rotational power 152

7.11 Gyroscopic motion 154

7.12 Summary: connection between rotational and translational motions 155

Worked examples 156

Problems 158

8 Relative motion 161

8.1 Applicability of Newton’s laws of motion: inertial reference frames 161

8.2 The Galilean transformation 162

8.3 The CM (centre-of-mass) reference frame 165

8.4 Example of a noninertial frame: centrifugal force 170

8.5 Motion in a rotating frame: the Coriolis force 171

8.6 The Foucault pendulum 175

8.7 Practical criteria for inertial frames: the local view 176

Worked examples 177

Problems 181

9 Special relativity 183

9.1 The velocity of light 183

9.2 The principle of relativity 184

9.3 Consequences of the principle of relativity 184

9.4 The Lorentz transformation 187

9.5 The Fitzgerald-Lorentz contraction 190

9.6 Time dilation 191

9.7 Paradoxes in special relativity 192

9.8 Relativistic transformation of velocity 193

9.9 Momentum in relativistic mechanics 194

9.10 Four vectors: the energy-momentum 4-vector 196

9.11 Energy-momentum transformations: relativistic energy conservation 198

9.12 Relativistic energy: mass-energy equivalence 199

9.13 Units in relativistic mechanics 202

9.14 Mass-energy equivalence in practice 202

9.15 General relativity 203

9.16 Simultaneity: quantitative analysis of the twin paradox 204

Worked examples 206

Problems 209

10 Continuum mechanics: mechanical properties of materials 211

10.1 Dynamics of continuous media 211

10.2 Elastic properties of solids 212

10.3 Fluids at rest 215

10.4 Elastic properties of fluids 217

10.5 Pressure in gases 217

10.6 Archimedes’ principle 218

10.7 Fluid dynamics 220

10.8 Viscosity 223

10.9 Surface properties of liquids 224

10.10 Boyle’s law (Mariotte’s law) 226

10.11 A microscopic theory of gases 227

10.12 The mole 230

10.13 Interatomic forces: modifications to the kinetic theory of gases 230

10.14 Microscopic models of condensed matter systems 232

Worked examples 234

Problems 236

11 Thermal physics 239

11.1 Friction and heating 239

11.2 Temperature scales 240

11.3 Heat capacities of thermal systems 242

11.4 Comparison of specific heat capacities: calorimetry 243

11.5 Thermal conductivity 244

11.6 Convection 245

11.7 Thermal radiation 246

11.8 Thermal expansion 248

11.9 The first law of thermodynamics 249

11.10 Change of phase: latent heat 251

11.11 The equation of state of an ideal gas 252

11.12 Isothermal, isobaric and adiabatic processes: free expansion 252

11.13 The Carnot cycle 256

11.14 Entropy and the second law of thermodynamics 258

11.15 The Helmholtz and Gibbs functions 260

11.16 Microscopic interpretation of temperature 261

11.17 Polyatomic molecules: principle of equipartition of energy 263

11.18 Ideal gas in a gravitational field: the ‘law of atmospheres’ 265

11.19 Ensemble averages and distribution functions 266

11.20 The distribution of molecular velocities in an ideal gas 267

11.21 Distribution of molecular speeds, momenta and energies 269

11.22 Microscopic interpretation of temperature and heat capacity in solids 271

Worked examples 272

Problems 274

12 Wave motion 277

12.1 Characteristics of wave motion 277

12.2 Representation of a wave which is travelling in one dimension 279

12.3 Energy and power in a wave motion 281

12.4 Plane and spherical waves 282

12.5 Huygens’ principle: the laws of reflection and refraction 282

12.6 Interference between waves 284

12.7 Interference of waves passing through openings: diffraction 288

12.8 Standing waves 290

12.9 The Doppler effect 293

12.10 The wave equation 294

12.11 Waves along a string 295

12.12 Waves in elastic media: longitudinal waves in a solid rod 296

12.13 Waves in elastic media: sound waves in gases 297

12.14 Superposition of two waves of slightly different frequencies: wave and group velocities 298

12.15 Other wave forms: Fourier analysis 300

Worked examples 302

Problems 304

13 Introduction to quantum mechanics 307

13.1 Physics at the beginning of the twentieth century 307

13.2 The blackbody radiation problem 308

13.3 The photoelectric effect 311

13.4 The X-ray continuum 313

13.5 The Compton effect: the photon model 314

13.6 The de Broglie hypothesis: electron waves 316

13.7 Interpretation of wave-particle duality 318

13.8 The Heisenberg uncertainty principle 319

13.9 The wavefunction: expectation values 322

13.10 The Schr€odinger (wave mechanical) method 323

13.11 The free particle 324

13.12 The time-independent Shr€odinger equation: eigenfunctions and eigenvalues 327

13.13 The infinite square potential well 328

13.14 The potential step 331

13.15 Other potential wells and barriers 336

Worked examples 341

Problems 344

14 Electric currents 347

14.1 Electric currents 347

14.2 Force between currents 349

14.3 The unit of electric current 350

14.4 Heating effect revisited: electrical resistance 351

14.5 Strength of a power supply: emf 353

14.6 Resistance of a circuit 354

14.7 Potential difference 354

14.8 Effect of internal resistance 356

14.9 Comparison of emfs: the potentiometer 358

14.10 Multiloop circuits 359

14.11 Kirchhoff’s rules 360

14.12 Comparison of resistances: the Wheatstone bridge 361

14.13 Power supplies connected in parallel 362

14.14 Resistivity 363

14.15 Variation of resistance with temperature 365

Worked examples 365

Problems 368

15 Electric fields 371

15.1 The electric charge model 371

15.2 Interpretation of electric current in terms of charge 373

15.3 Electric fields: electric field strength 374

15.4 Forces between point charges: Coulomb’s law 376

15.5 Electric flux and electric flux density 376

15.6 Electric fields due to systems of point charges 378

15.7 Gauss’ law for electrostatics 381

15.8 Potential difference in electric fields: electric potential 383

15.9 Acceleration of charged particles 388

15.10 Dielectric materials 389

15.11 Capacitors 391

15.12 Capacitors in series and in parallel 395

15.13 Charge and discharge of a capacitor through a resistor 396

Worked examples 398

Problems 401

16 Magnetic fields 403

16.1 Magnetism 403

16.2 The work of Ampere, Biot and Savart 405

16.3 Magnetic pole strength 406

16.4 Magnetic field strength 407

16.5 Ampere’s law 408

16.6 The Biot-Savart law 410

16.7 Applications of the Biot-Savart law 411

16.8 Magnetic flux and magnetic flux density 413

16.9 Magnetic fields due to systems of poles 413

16.10 Forces between magnets 414

16.11 Forces between currents and magnets 415

16.12 The permeability of vacuum 416

16.13 Current loop in a magnetic field 417

16.14 Magnetic dipoles and magnetic materials 419

16.15 Moving coil meters and electric motors 423

16.16 Magnetic fields due to moving charges 425

16.17 Force on an electric charge in a magnetic field 425

16.18 Magnetic dipole moments of charged particles in closed orbits 427

16.19 Electric and magnetic fields in moving reference frames 428

Worked examples 431

Problems 433

17 Electromagnetic induction: time-varying emfs 437

17.1 The principle of electromagnetic induction 437

17.2 Simple applications of electromagnetic induction 440

17.3 Self-inductance 441

17.4 The series L-R circuit 444

17.5 Discharge of a capacitor through an inductor and a resistor 446

17.6 Time-varying emfs: mutual inductance: transformers 447

17.7 Alternating current (a.c.) 449

17.8 Alternating current transformers 453

17.9 Resistance, capacitance and inductance in a.c. circuits 454

17.10 The series L-C-R circuit: phasor diagrams 456

17.11 Power in an a.c. circuit 459

Worked examples 460

Problems 462

18 Maxwell’s equations: electromagnetic radiation 465

18.1 Reconsideration of the laws of electromagnetism: Maxwell’s equations 465

18.2 Plane electromagnetic waves 468

18.3 Experimental observation of electromagnetic radiation 470

18.4 The electromagnetic spectrum 471

18.5 Polarisation of electromagnetic waves 473

18.6 Energy, momentum and angular momentum in electromagnetic waves 476

18.7 Reflection of electromagnetic waves at an interface between nonconducting media 479

18.8 Electromagnetic waves in a conducting medium 480

18.9 The photon model revisited 483

18.10 Invariance of electromagnetism under the Lorentz transformation 484

Worked examples 485

Problems 487

19 Optics 489

19.1 Electromagnetic nature of light 489

19.2 Coherence: the laser 492

19.3 Diffraction at a single slit 493

19.4 Two slit interference and diffraction: Young’s double slit experiment 496

19.5 Multiple slit interference: the diffraction grating 498

19.6 Diffraction of X-rays: Bragg scattering 501

19.7 The ray model: geometrical optics 504

19.8 Reflection of light 505

19.9 Image formation by spherical mirrors 506

19.10 Refraction of light 508

19.11 Refraction at successive plane interfaces 512

19.12 Image formation by spherical lenses 513

19.13 Image formation of extended objects: magnification 517

19.14 Dispersion of light 520

Worked examples 521

Problems 524

20 Atomic physics 527

20.1 Atomic models 527

20.2 The spectrum of hydrogen: the Rydberg formula 529

20.3 The Bohr postulates 530

20.4 The Bohr theory of the hydrogen atom 531

20.5 The quantum mechanical (Schr€odinger) solution of the one-electron atom 534

20.6 The radial solutions of the lowest energy state of hydrogen 538

20.7 Interpretation of the one-electron atom eigenfunctions 539

20.8 Intensities of spectral lines: selection rules 543

20.9 Quantisation of angular momentum 544

20.10 Magnetic effects in one-electron atoms: the Zeeman effect 545

20.11 The Stern–Gerlach experiment: electron spin 547

20.12 The spin–orbit interaction 549

20.13 Identical particles in quantum mechanics: the Pauli exclusion principle 550

20.14 The periodic table: multielectron atoms 552

20.15 The theory of multielectron atoms 554

20.16 Further uses of the solutions of the one-electron atom 555

Worked examples 556

Problems 557

21 Electrons in solids: quantum statistics 559

21.1 Bonding in molecules and solids 559

21.2 The classical free electron model of solids 563

21.3 The quantum mechanical free electron model: the Fermi energy 565

21.4 The electron energy distribution at 0 K 568

21.5 Electron energy distributions at T > 0 K 570

21.6 Specific heat capacity and conductivity in the quantum free electron model 571

21.7 The band theory of solids 573

21.8 Semiconductors 574

21.9 Junctions in conductors and semiconductors: p-n junctions 576

21.10 Transistors 581

21.11 The Hall effect 583

21.12 Quantum statistics: systems of bosons 584

21.13 Superconductivity 585

Worked examples 586

Problems 588

22 Nuclear physics, particle physics and astrophysics 589

22.1 Properties of atomic nuclei 589

22.2 Nuclear binding energies 591

22.3 Nuclear models 592

22.4 Radioactivity 595

22.5 a-, b- and g-decay 597

22.6 Detection of radiation: units of radioactivity 600

22.7 Nuclear reactions 602

22.8 Nuclear fission and nuclear fusion 603

22.9 Fission reactors 604

22.10 Thermonuclear fusion 606

22.11 Subnuclear particles 609

22.12 The quark model 613

22.13 The physics of stars 617

22.14 The origin of the universe 622

Worked examples 625

Problems 627

Answers to problems 629

Appendix A: Mathematical rules and formulas 639

Appendix B: Some fundamental physical constants 659

Appendix C: Some astrophysical and geophysical data 661

Bibliography 663

Index 665