Table of Contents

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

About the Author

Michael Mansfield is a professor in the Department of Physics at University College Cork (Ireland). Professor Mansfield was awarded a BSc and a PhD by Imperial College London (UK) and a DSc by the National University of Ireland. He has held research and teaching appointments at universities and research institutes in Italy, Germany, UK, and Ireland. At University College Cork, he heads an atomic and molecular / plasma physics diagnostics research programme. He has published more than 60 research and review papers in this area. He is a member of the Institute of Physics and the Irish Fusion Association.
Colm O'Sullivan is Associate Professor (Emeritus) in the Physics Department, University College Cork, Ireland. He was educated at the National University of Ireland and received his PhD at the Catholic University of America, Washington DC (USA). His research interests include cosmic ray astrophysics and physics Education. Professor O'Sullivan is also involved in the EU Leonardo da Vinci 2 (Community Vocational Training Action Programme). The main objective of the ComLab project is to integrate different tools in science and technology teaching. He is co-author with Michael Mansfield of the textbook Understanding Physics published by Wiley / Praxis (January 1998).