Understanding Physics

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Understanding Physics - Second edition is a comprehensive, yet compact, introductory physics textbook aimed at physics undergraduates and also at engineers and other scientists taking a general physics course. Written with today's students in mind, this text covers the core material required by an introductory course in a clear and refreshing way. A second colour is used throughout to enhance learning and understanding. Each topic is introduced from first principles so that the text is suitable for students without a prior background in physics. At the same time the book is designed to enable students to proceed easily to subsequent courses in physics and may be used to support such courses. Mathematical methods (in particular, calculus and vector analysis) are introduced within the text as the need arises and are presented in the context of the physical problems which they are used to analyse. Particular aims of the book are to demonstrate to students that the easiest, most concise and least ambiguous way to express and describe phenomena in physics is by using the language of mathematics and that, at this level, the total amount of mathematics required is neither large nor particularly demanding. 'Modern physics' topics (relativity and quantum mechanics) are introduced at an earlier stage than is usually found in introductory textbooks and are integrated with the more 'classical' material from which they have evolved. This book encourages students to develop an intuition for relativistic and quantum concepts at as early a stage as is practicable. The text takes a reflective approach towards the scientific method at all stages and, in keeping with the title of the text, emphasis is placed on understanding of, and insight into, the material presented.

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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

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