Contents

Cover

Title Page

Copyright

Preface to Second Edition Goals and Objectives Supplementary Resources A Message for Students Acknowledgements

Chapter 1: Understanding the physical universe 1.1 The Programme of Physics 1.2 The Building Blocks of Matter 1.3 Matter in Bulk 1.4 The Fundamental Interactions 1.5 Exploring the Physical Universe: The Scientific Method 1.6 The Role of Physics: Its Scope and Applications

Chapter 2: Using mathematical tools in physics 2.1 Applying the Scientific Method 2.2 The use of Variables to Represent Displacement and Time 2.3 Representation of Data 2.4 The Use of Differentiation in Analysis: Velocity and Acceleration in Linear

Motion 2.5 The use of Integration in Analysis 2.6 Maximum and minimum Values of Physical Variables: General Linear Motion 2.7 Angular Motion: the Radian 2.8 The Role of Mathematics in Physics Worked Examples

Problems

Chapter 3: The causes of motion: dynamics 3.1 The Concept of Force 3.2 The First Law of Dynamics (Newton's First Law) 3.3 The fundamental dynamical principle (Newton's second law) 3.4 Systems of Units: SI 3.5 Time Dependent Forces: Oscillatory Motion 3.6 Simple Harmonic Motion 3.7 Mechanical Work and Energy: Power 3.8 Energy in Simple Harmonic Motion 3.9 Dissipative Forces: Damped Harmonic Motion 3.10 Forced Oscillations 3.11 Nonlinear Dynamics: Chaos Worked Examples Problems

Chapter 4: Motion in two and three dimensions 4.1 Vector Physical Quantities 4.2 Vector Algebra 4.3 Velocity and Acceleration Vectors 4.4 Force as a Vector Quantity: Vector form of the Laws of Dynamics 4.5 Constraint Forces 4.6 Friction 4.7 Motion in a Circle: Centripetal Force 4.8 Motion in a Circle at Constant Speed 4.9 Tangential and Radial Components of Acceleration 4.10 Hybrid Motion: the Simple Pendulum 4.11 Angular Quantities as Vectors: the Cross Product Worked Examples Problems

Chapter 5: Force fields

5.1 Newton's Law of Universal Gravitation 5.2 Force Fields 5.3 The Concept of Flux 5.4 Gauss' Law for Gravitation Surface Integrals 5.5 Motion in a Constant Uniform Field: Projectiles 5.6 Mechanical Work and Energy 5.7 Energy in a Constant Uniform Field 5.8 Energy in an Inverse Square Law Field 5.9 Moment of a Force: Angular Momentum 5.10 Planetary Motion: Circular Orbits 5.11 Planetary Motion: Elliptical Orbits and Kepler's Laws Worked Examples Problems

Chapter 6: Many-body interactions 6.1 Newton's Third Law 6.2 The Principle of Conservation of Momentum 6.3 Mechanical Energy of Systems of Particles 6.4 Particle Decay 6.5 Particle Collisions 6.6 The Centre of Mass of a System of Particles 6.7 The Two-Body Problem: Reduced Mass 6.8 Angular Momentum of a System of Particles 6.9 Conservation Principles in Physics Worked Examples Problems

Chapter 7: Rigid body dynamics 7.1 Rigid Bodies 7.2 Rigid Bodies in Equilibrium: Statics 7.3 Torque 7.4 Dynamics of Rigid Bodies

7.5 Measurement of Torque: The Torsion Balance 7.6 Rotation of a Rigid Body About a Fixed Axis: Moment of Inertia 7.7 Calculation of Moments of Inertia: The Parallel Axis Theorem 7.8 Conservation of Angular Momentum of Rigid Bodies 7.9 Conservation of Mechanical Energy in Rigid Body Systems 7.10 Work Done by a Torque: Torsional Oscillations: Rotational Power 7.11 Gyroscopic Motion 7.12 Summary: Connection between Rotational and Translational Motions Worked Examples Problems

Chapter 8: Relative motion 8.1 Applicability of Newton's Laws of Motion: Inertial Reference Frames 8.2 The Galilean Transformation 8.3 The CM (Centre-of-Mass) Reference Frame 8.4 Example of a Noninertial Frame: Centrifugal Force 8.5 Motion in a Rotating Frame: the Coriolis Force 8.6 The Foucault Pendulum 8.7 Practical Criteria for Inertial Frames: The Local View Worked Examples Problems

Chapter 9: Special relativity 9.1 The Velocity of Light 9.2 The Principle of Relativity 9.3 Consequences of the Principle of Relativity 9.4 The Lorentz Transformation 9.5 The Fitzgerald-Lorentz contraction 9.6 Time Dilation 9.7 Paradoxes in Special Relativity 9.8 Relativistic Transformation of Velocity 9.9 Momentum in Relativistic Mechanics 9.10 Four Vectors: The Energy-Momentum 4-Vector

9.11 Energy-Momentum Transformations: Relativistic Energy Conservation 9.12 Relativistic Energy: Mass-Energy Equivalence 9.13 Units in Relativistic Mechanics 9.14 Mass-Energy Equivalence in Practice 9.15 General Relativity 9.16 Simultaneity: Quantitative Analysis of the Twin Paradox Worked Examples Problems

Chapter 10: Continuum mechanics: mechanical properties of materials 10.1 Dynamics of Continuous Media 10.2 Elastic Properties of Solids 10.3 Fluids at Rest 10.4 Elastic Properties of Fluids 10.5 Pressure in Gases 10.6 Archimedes' Principle 10.7 Fluid Dynamics 10.8 Viscosity 10.9 Surface Properties of Liquids 10.10 Boyle's law (Mariotte's law) 10.11 A Microscopic Theory of Gases 10.12 The Mole 10.13 Interatomic Forces: Modifications to the Kinetic Theory of Gases 10.14 Microscopic Models of Condensed Matter Systems Worked Examples Problems

Chapter 11: Thermal physics 11.1 Friction and Heating 11.2 Temperature Scales 11.3 Heat Capacities of Thermal Systems 11.4 Comparison of Specific Heat Capacities: Calorimetry 11.5 Thermal Conductivity

11.6 Convection 11.7 Thermal Radiation 11.8 Thermal Expansion 11.9 The First Law of Thermodynamics 11.10 Change of Phase: Latent Heat 11.11 The Equation of State of an Ideal Gas 11.12 Isothermal, Isobaric and Adiabatic Processes: Free Expansion 11.13 The Carnot Cycle 11.14 Entropy and the Second Law of Thermodynamics 11.15 The Helmholtz and Gibbs functions 11.16 Microscopic Interpretation of Temperature 11.17 Polyatomic Molecules: Principle of Equipartition of Energy 11.18 Ideal Gas in a Gravitational Field: the ‘Law of Atmospheres’ 11.19 Ensemble Averages and Distribution Functions 11.20 The Distribution of Molecular Velocities in an Ideal Gas 11.21 Distribution of Molecular Speeds, Momenta and Energies 11.22 Microscopic Interpretation of Temperature and Heat Capacity in Solids Worked Examples Problems

Chapter 12: Wave motion 12.1 Characteristics of Wave Motion 12.2 Representation of a Wave which is Travelling in one Dimension 12.3 Energy and Power in a Wave Motion 12.4 Plane and Spherical Waves 12.5 Huygens' Principle: the Laws of Reflection and Refraction 12.6 Interference Between Waves 12.7 Interference of Waves Passing Through Openings: Diffraction 12.8 Standing Waves 12.9 The Doppler Effect 12.10 The Wave Equation 12.11 Waves Along a String 12.12 Waves in Elastic Media: Longitudinal Waves in a Solid Rod

12.13 Waves in Elastic Media: Sound Waves in Gases 12.14 Superposition of Two Waves of Slightly Different Frequencies: Wave and

Group Velocities 12.15 Other Wave Forms: Fourier Analysis Worked Examples Problems

Chapter 13: Introduction to quantum mechanics 13.1 Physics at the Beginning of the Twentieth Century 13.2 The Blackbody Radiation Problem 13.3 The Photoelectric Effect 13.4 The X-ray Continuum 13.5 The Compton Effect: The Photon Model 13.6 The de Broglie Hypothesis: Electron Waves 13.7 Interpretation of Wave-Particle Duality 13.8 The Heisenberg Uncertainty Principle 13.9 The Wavefunction: Expectation Values 13.10 The Schrödinger (Wave Mechanical) Method 13.11 The Free Particle 13.12 The Time-Independent Schrödinger Equation: Eigenfunctions and

Eigenvalues 13.13 The Infinite Square Potential Well 13.14 The Potential Step 13.15 Other Potential Wells and Barriers 13.17 Further Implications of Quantum Mechanics Worked Examples Problems

Chapter 14: Electric currents 14.1 Electric Currents 14.2 Force between Currents 14.3 The Unit of Electric Current 14.4 Heating Effect Revisited: Electrical Resistance

14.5 Strength of a Power Supply: emf 14.6 Resistance of a Circuit 14.7 Potential Difference 14.8 Effect of Internal Resistance 14.10 Comparison of Emfs: the Potentiometer 14.10 Multiloop Circuits 14.11 Kirchhoff's Rules 14.12 Comparison of Resistances: the Wheatstone bridge 14.13 Power Supplies Connected in Parallel 14.14 Resistivity 14.15 Variation of Resistance with Temperature Worked Examples Problems

Chapter 15: Electric fields 15.1 The Electric Charge Model 15.2 Interpretation of Electric Current in Terms of Charge 15.3 Electric Fields: Electric Field Strength 15.4 Forces Between Point Charges: Coulomb's Law 15.5 Electric Flux and Electric Flux Density 15.6 Electric Fields Due to Systems of Point Charges 15.7 Gauss' Law for Electrostatics 15.8 Potential Difference in Electric Fields: Electric Potential 15.9 Acceleration of Charged Particles 15.10 Dielectric Materials 15.11 Capacitors 15.12 Capacitors in Series and in Parallel 15.13 Charge and Discharge of a Capacitor Through a Resistor Worked Examples Problems

Chapter 16: Magnetic fields 16.1 Magnetism

16.2 The work of Ampère, Biot and Savart 16.3 Magnetic Pole Strength 16.4 Magnetic Field Strength 16.5 Ampère's Law 16.6 The Biot-Savart Law 16.7 Applications of the Biot-Savart Law 16.8 Magnetic Flux and Magnetic Flux Density 16.9 Magnetic Fields Due to Systems of Poles 16.10 Forces between magnets 16.11 Forces Between Currents and Magnets 16.12 The Permeability of Vacuum 16.13 Current Loop in a Magnetic Field 16.14 Magnetic Dipoles and Magnetic Materials 16.15 Moving Coil Meters and Electric Motors 16.16 Magnetic Fields Due to Moving Charges 16.17 Force on an Electric Charge in a Magnetic Field 16.18 Magnetic Dipole Moments of Charged Particles in Closed Orbits 16.19 Electric and Magnetic Fields in Moving Reference Frames Worked Examples Problems

Chapter 17: Electromagnetic induction: time-varying emfs 17.1 The Principle of Electromagnetic Induction 17.2 Simple Applications of Electromagnetic Induction 17.3 Self-Inductance 17.4 The Series L-R Circuit 17.5 Discharge of a Capacitor through an Inductor and a Resistor 17.6 Time-Varying emfs: Mutual Inductance: Transformers 17.7 Alternating Current (a.c.) 17.8 Alternating Current Transformers 17.9 Resistance, Capacitance and Inductance in a.c. Circuits 17.10 The Series L-C-R Circuit: Phasor Diagrams 17.11 Power in an a.c. Circuit

Worked Examples Problems

Chapter 18: Maxwell's equations: electromagnetic radiation 18.1 Reconsideration of the Laws of Electromagnetism: Maxwell's Equations 18.2 Plane Electromagnetic Waves 18.3 Experimental Observation of Electromagnetic Radiation 18.4 The Electromagnetic Spectrum 18.5 Polarisation of Electromagnetic Waves 18.6 Energy, Momentum and Angular Momentum in Electromagnetic Waves 18.7 Reflection of Electromagnetic Waves at an Interface Between Nonconducting

Media 18.8 Electromagnetic Waves in a Conducting Medium 18.9 The Photon Model Revisited 18.10 Invariance of Electromagnetism Under the Lorentz Transformation Worked Examples Problems

Chapter 19: Optics 19.1 Electromagnetic Nature of Light 19.2 Coherence: The Laser 19.3 Diffraction at a Single Slit 19.4 Two Slit Interference and Diffraction: Young's Double Slit Experiment 19.5 Multiple Slit Interference: The Diffraction Grating 19.6 Diffraction of X-Rays: Bragg Scattering 19.7 The Ray Model: Geometrical Optics 19.8 Reflection of Light 19.9 Image Formation by Spherical Mirrors 19.10 Refraction of Light 19.11 Refraction at Successive Plane Interfaces 19.12 Image Formation by Spherical Lenses 19.13 Image Formation of Extended Objects: Magnification 19.14 Dispersion of Light

Worked Examples Problems

Chapter 20: Atomic physics 20.1 Atomic Models 20.2 The Spectrum of Hydrogen: the Rydberg Formula 20.3 The Bohr Postulates 20.4 The Bohr Theory of the Hydrogen Atom 20.5 The Quantum Mechanical (Schrödinger) Solution of the One-Electron Atom 20.6 The Radial Solution of the Lowest Energy State of Hydrogen 20.7 Interpretation of the One-Electron Atom Eigenfunctions 20.8 Intensities of Spectral Lines: Selection Rules 20.9 Quantisation of Angular Momentum 20.10 Magnetic Effects in One-Electron Atoms: the Zeeman Effect 20.11 The Stern-Gerlach Experiment: Electron Spin 20.12 The Spin–Orbit Interaction 20.13 Identical Particles in Quantum Mechanics: the Pauli Exclusion Principle 20.14 The Periodic Table: Multielectron Atoms 20.15 The Theory of Multielectron Atoms 20.16 Further Uses of the Solutions of the One-Electron Atom Worked Examples Problems

Chapter 21: Electrons in solids: quantum statistics 21.1 Bonding in Molecules and Solids 21.2 The Classical Free Electron Model of Solids 21.3 The Quantum Mechanical Free Electron Model: The Fermi energy 21.4 The Electron Energy Distribution at 0 K 21.5 Electron Energy Distributions at T>0 K 21.6 Specific Heat Capacity and Conductivity in the Quantum Free Electron

Model 21.7 The Band Theory of Solids 21.8 Semiconductors

21.9 Junctions in Conductors and Semiconductors: p-n Junctions 21.10 Transistors 21.11 The Hall Effect 21.12 Quantum Statistics: Systems of Bosons 21.13 Superconductivity Worked Examples Problems

Chapter 22: Nuclear physics, particle physics and astrophysics 22.1 Properties of Atomic Nuclei 22.2 Nuclear Binding Energies 22.3 Nuclear Models 22.4 Radioactivity 22.5 α-, β- and γ-decay 22.6 Detection of Radiation: Units of Radioactivity 22.7 Nuclear Reactions 22.8 Nuclear Fission and Nuclear Fusion 22.9 Fission Reactors 22.10 Thermonuclear Fusion 22.11 Subnuclear Particles 22.12 The Quark Model 22.13 The Physics of Stars 22.14 The Origin of the Universe Worked Examples Problems

Answers to Problems Chapter 2 Chapter 3 Chapter 4 Chapter 5 Chapter 6 Chapter 7

Chapter 8 Chapter 9 Chapter 10 Chapter 11 Chapter 12 Chapter 13 Chapter 14 Chapter 15 Chapter 16 Chapter 17 Chapter 18 Chapter 19 Chapter 20 Chapter 21 Chapter 22

Appendix A: Mathematical Rules and Formulas A.1 Perimeters, Areas and Volumes A.2 Plane Geometry A.3 Trigonometry A.4 Algebraic Identities A.5 The logarithmic and Exponential Functions A.6 Differentiation A.7 Integration A.8 Complex Numbers A.9 Series Expansions A.10 Analytical Geometry A.11 Vector Algebra A.12 Vector Calculus A.13 Orthogonal Coordinate Systems in three Dimensions

Appendix B: Some fundamental physical constants

Appendix C: Some Astrophysical and Geophysical Data C.1 The Sun C.2 The Earth C.3 The Moon C.4 The Planets C.5 The Milky Way Galaxy C.6 Cosmological Data

Bibliography

Index

Summary of Notations Used in Text

Appendix D: The periodic table

This edition first published 2011

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Library of Congress Cataloging–in–Publication Data

Mansfield, Michael, 1943–

Understanding physics / Michael Mansfield and Colm O'Sullivan. – 2nd ed.

p. cm.

Includes index.

Summary: Understanding Physics – Second edition is a comprehensive, yet compact, introductory

physics textbook aimed at physics undergraduates and also at engineers and other scientists taking ageneral 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 throughoutto enhance learning and understanding. Each topic is introduced from first principles so that the text issuitable for students without a prior background in physics. At the same time the book is designed toenable 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 thetext as the need arises and are presented in the context of the physical problems which they are usedto analyse. Particular aims of the book are to demonstrate to students that the easiest, most conciseand 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 norparticularly demanding. ‘Modern physics’ topics (relativity and quantum mechanics) are introducedat 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 areflective 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”–– Provided bypublisher.

Summary: “Understanding Physics –– Second edition is a comprehensive, yet compact, introductoryphysics textbook aimed at physics undergraduates and also at engineers and other scientists taking a

general physics course”–– Provided by publisher.

ISBN 978–0–470–74638–7 (hardback) –– ISBN 978–0–470–74637–0 (pbk.)

1. Physics. I. O'Sullivan, Colm. II. Title.

QC23.M287 2011

530––dc22

2010025111

A catalogue record for this book is available from the British Library.

ISBN 9780470746387 (Hbk) 9780470746370 (Pbk)

Preface to Second Edition

Goals and Objectives Understanding Physics is written primarily for students who are taking their first course in physics atuniversity level. While it is anticipated that many readers will have some previous knowledge ofphysics or of general science, each topic is introduced from first principles so that the text is suitablefor students without any prior background in physics. The book has been written to support moststandard first-year undergraduate university physics courses (and often beyond the first year) and canserve as an introductory text for both prospective physics majors and other students who will need toapply the principles and techniques of basic physics in subsequent courses. A principal aim of thisbook is to give the reader the foundation required to proceed smoothly to intermediate level coursesin physics and engineering and to courses in the chemical, computer, materials and earth sciences, allof which require a sound knowledge of basic physics Students with some previous knowledge of physics will find that they are already familiar withmany of the topics covered in the early sections. These readers should note, however, that thetreatment of these topics in Understanding Physics often differs from that given in school textbooksand is designed to lay the foundations for the treatment of new and more advanced topics. As authors,one of our aims is to integrate school physics more closely to that studied at university, encouragingstudents to appreciate the relevance of physics previously studied and to integrate it with the materialencountered at university. For these reasons we hope that students with previous knowledge ofphysics will take the opportunity to refresh and deepen their understanding of topics which they mayregard as familiar. Some knowledge of simple algebra, geometry and trigonometry is assumed but differential andintegral calculus, vector analysis and other more advanced mathematical methods are introducedwithin the text as the need arises and are presented in the context of the physical problems which theyare used to analyse. Historically, many mathematical techniques were developed specifically toaddress problems in physics and these can often be grasped more easily when applied to a relevantphysical situation than when presented as an otherwise abstract mathematical concept. Thesemathematical asides are indicated throughout the text by a grey background and it is hoped that bystudying these short sections, the reader will gain some insight into both the mathematical techniquesinvolved and the physics to which the techniques are applied. The mathematical asides, together with Appendix A (Mathematical Rules and Formulas), however,cannot substitute for a formal course in mathematical methods, rather they could be considered amathematical ‘survival kit’ for the study of introductory physics. It is hoped that most readers willeither have already taken or be studying an introductory mathematics course. In reality the totalamount of mathematics required is neither large nor particularly demanding.

Approach

It is no longer credible to describe the discoveries and developments made during the early years ofthe twentieth century as ‘modern physics’. This is not to deny the radical and revolutionary nature ofthese developments but rather is a recognition that they have long since become a part of mainstreamphysics. Quantum mechanics, relativity and our picture of matter at the subatomic level will surelyform part of the ‘classical’ tradition of twenty-first century physicists. On the other hand, thediscoveries of the seventeenth, eighteen and nineteenth centuries have lost none of their importance.The majority of everyday experiences of the material world can be understood in a fully satisfactorymanner in terms of classical physics. Indeed attempts to explain such phenomena in the language oftwentieth century physics, while possible in principle, tend to be unnecessarily complicated and oftenconfusing. In Understanding Physics, ‘modern’ (twentieth century) topics are introduced at an earlier stagethan is usually found in introductory textbooks and are integrated with the more ‘classical’ materialfrom which they have evolved. Although many of the concepts which are basic to twentieth centuryphysics are relatively easy to represent mathematically, they are not as intuitive as those of classicalphysics, particularly for students with an extensive previous acquaintance with ‘classical’ concepts.This book aims to encourage students to develop an intuition for relativistic and quantum concepts atas early a stage as is practicable. Understanding Physics has been kept to a compact format in order to emphasise, in a fully rigorousmanner, the essential unity of physics. At each stage new topics are carefully integrated with previousmaterial. Throughout the text references are given to other sources where more detailed discussionsof particular topics or applications may be found. In order to avoid breaking the flow and unity of thematerial within chapters, worked examples and problems are placed at the end of each chapter.Indications are given throughout the text as to when a particular worked example might be studied ora particular problem attempted. The number of problems has been limited so that a student mightreasonably expect to attempt all problems in a given chapter; other sources of suitable problems arewidely available, for example in other textbooks and on the internet. The internationally agreed system of units (SI) is now adopted almost universally in science andengineering and is used uncompromisingly in this text. In addition, we have adhered rigorously to therecommendations of the International Union of Pure and Applied Physics (IUPAP) on symbols andnomenclature (Cohen and Giacomo, 1987). The text takes a reflective approach towards the scientific method at all stages – that is, whilelearning the fundamentals of physics the student should also become familiar with the scientificmethod. In keeping with the title of the text, emphasis is placed on understanding of and insight intothe material presented. The book therefore seeks not merely to describe the discoveries and themodels of physics but also, in the process, to familiarise readers with the skills and techniques whichbeen have developed to analyse natural phenomena, skills and techniques which they can lookforward to applying themselves. This book does not seek to reveal and explain all the mysteries of thephysical universe but, instead, lays the foundations on which readers can build and (perhaps moreimportantly) encourages and equips readers to explore further.

Structure

Chapter 1 starts with a short overview of the way in which physics today describes the materialuniverse, from the very smallest building blocks of matter up to large scale bulk materials. It is aremarkable fact that the same basic principles seem to apply over the full range of distance scales –from subnuclear to intergalactic. The physical principles encountered in subsequent chapters areapplied to systems on all of these scales, as the need arises. The basic ideas of calculus areintroduced in Chapter 2 in the context of the description of motion in one dimension; readers with agood prior knowledge of this material may wish to skip this chapter, although such readers might findit profitable to use the chapter to refresh their memories. Chapters 3 to 7 introduce the main themes of classical dynamics. This is followed by anintroduction to relative motion (Chapter 8) which is an essential prerequisite to the study of thespecial theory of relativity (Chapter 9). Chapters 10 and 11, respectively, deal with the mechanicaland thermal behaviour of matter. A sound knowledge of wave motion (Chapter 12), a very importantpart of physics in its own right, is essential for a proper understanding of quantum mechanics(Chapter 13). The five subsequent chapters (14 to 18) cover the main aspects of classicalelectromagnetism and its application to wave and geometrical optics is covered in Chapter 19. The final three chapters (20, 21 and 22) – on atomic physics, on electrons in solids and on nuclearand particle physics and astrophysics – are a little more specialised and detailed than the others.Depending on the subjects which the reader plans to pursue subsequently, significant amounts of all orsome of these chapters might well be omitted. Some chapters have a few sections which contain slightly more demanding analyses or lessessential material than found in the rest of the book. These sections, (for example Section 5.11 onplanetary motion, elliptical orbits and Kepler's laws) indicated by a blue background, could beconsidered optional and may be omitted if appropriate.

Note on the Second Edition

Users of the first edition will notice a number of significant changes in the second edition. These havemostly arisen as a result of suggestions for improvement made by instructors, students and of our ownexperience with the book. New sections have been included on dissipative forces, forcedoscillations, nonlinear dynamics and on electromagnetic waves at interfaces between media. Acompletely new chapter (Chapter 19) on optics has been added, some of the material of which wascovered less fully in Chapter 12 of the first edition. The emphasis on integration of the various topicsinto a view of physics as a unified whole has been increased; for example, the concept of flux (andGauss' law) has been introduced at an earlier stage to enable it to be applied to gravitation.

Supplementary Resources

The Understanding Physics Website

A n Understanding Physics website can be accessed on the internet at the following URLhttp://www.wiley.com/go/mansfield. The website includes additional material, further problems and other teaching and learningresources provided on a section by section basis. In particular, it provides links to suitableinteractive exercises in the form of animations, simulations, tutorials, etc. and other multimediamaterials. All such resources have been selected for their suitability by the authors and have beenevaluated for quality by reputable international organisations such as the European Physical Society(EPS), MPTL (Multimedia in Physics Teaching and Learning) or MERLOT (Multimedia EducationalResource for Learning and Online Teaching). Students are encouraged to enhance their understanding and insight by using the website in parallelwith studying the text.

A Message for Students You should not expect to achieve an instant understanding of all topics studied. The learning processstarts through an understanding of concepts and then progresses. New material may not be fully absorbed at first reading but only after more careful study. From ourown personal experience, however, we can assure you that persistence will be rewarded and thatinitially challenging material will be revealed as being both simple and elegant. We have deliberately not provided end-of-chapter summaries. We feel that it is an important part ofthe learning exercise that students create such summaries for themselves. To assist this process,however, we have adopted a range of specific highlighting styles throughout the book (indicatingfundamental principles/laws, equations of state, definitions, important relationships, etc.). A key tothe more important examples of the notations used is located inside the front cover. Readers who are studying physics for the first time are starting on a great adventure; we hope thatthis book will help you to find the early stages of the journey both exciting and rewarding. We alsohope that it will prove to be a source of continuing support for your subsequent studies.

Acknowledgements Understanding Physics has benefited greatly from the many contributions, comments and criticismgenerously provided over many years by numerous individuals. The second edition, in particular, hasalso benefited greatly from many suggestions made by users of the first edition, both students andlecturers. Firstly, we wish to express our gratitude to our present and former colleagues in the Department ofPhysics at University College Cork. The many detailed discussions on physics and physics educationwhich we have enjoyed with them over decades have taught us much and have contributedsubstantially to the refinement of our understanding. We are sure that they will find in these pagesmany of their original ideas which we have exploited and developed, sometimes consciously,frequently unconsciously. In particular, we wish to acknowledge our debt to Frank Fahy, Joe Lennon,Rita O'Sullivan, Tony Deeney, John Delaney, Niall Ó Murchadha, Michel Vandyck, John McInerney,Stephen Fahy, Paul Callanan, Andy Ruth, Frank Peters, Thomas Busch, Paddy McCarthy and DavidNikogosyan, all of the Physics Department. The approach we have taken to the presentation ofelectromagnetism arose from original ideas developed by Frank Fahy in the early 1960s. Weacknowledge the support provided by the Department, under the leadership of John McInerney; inparticular we are extremely grateful to Stephen Fahy for generously providing the space andresources which enabled the second edition to be completed. Pat Twomey, John O'Riordan and RobinGillen provided essential technical support and Irene Horne, Susanna Kent, Karmen O'Shea andNiamh O'Sullivan provided keyboard assistance at critical stages in the project. We also acknowledge the advice and support received from other UCC colleagues, in particular,Garret Barden, Paul Brint, Peter Flynn, Donal Hurley, Paul Lambkin, Des McHale, Tom O'Donovan,Willie Reville, Brian Twomey and from David Rea of St. Colman's College, Fermoy. Without our students in University College Cork, it would not have been possible to have classtested the approaches, ideas and problems that are central to this book. They have acted as guinea-pigs for many years and we would like to thank them for their invaluable comments and criticisms andfor feedback that led to many improvements in the second edition. Our original external reviewers and a wide variety of users of the text have made majorcontributions to the development and refinement of Understanding Physics, particularly towardsimprovement in the second edition, for which the authors are particularly grateful. We appreciate theconsiderable time and effort that this required and we acknowledge their common commitment tophysics education. Particular thanks goes to the following for their helpful contributions: Claes Algström, Lars-ErikBerg, Eric Both, Paddy Bourke, Peter Bourke, Anne Breslin, Iris Choi, Malcolm Cooper, PeterDitlevsen, Nick van Eijndhoven, Tore Ericsson, Stephen Fahy, Sonja Feiner-Valkier, Matt Griffin,Lennart Häggström, Jan Petter Hansen, Jan Hedman, Donald Holcomb, Reyer Jochemsen, ChristorJohannesson, Leif Karlsson, Martijn Kemerink, John Mason, Leopold Mathelitsch, Vince McCarthy,Niklas Meinander, Alex Montwill, Jim O' Brien, Austin Phelps, Giancarlo Reali, Janez Strnad, TomSundius, Agneta Svensson, Edward Thomas, Jozefina Turlo, Ton van Leeuwen, Constantijn van dePas, David Van Baak, Anders Wallin, Tom Witt and many other instructors and student users aroundthe world.

Our friend and colleague, Joe Lennon, read every page of the manuscript and made many helpful,often vital, suggestions. His exceptional physical insight and his understanding of difficulties in thematerial from a student's point of view have been available to us throughout the development of boththe first and second editions and inform almost every page of the text. We have adopted almost all ofhis suggestions and we readily acknowledge that the book has been greatly enriched by his generoushelp. The authors wish to express our thanks for the support and encouragement received from ourpublishers. For the first edition we thank Clive Horwood, Stuart MacFarlane and Jim Wilkie atPraxis Publishing and Andrew Slade, Mary Seddon and Celia Carden at John Wiley and Sons. Thesecond edition has been brought to fruition thanks to the professionalism of a number of people atJohn Wiley and Sons, including Tanushree Mathur in Singapore and Jenny Cosham, Jon Peacock,Amie Marshall, Richard Davies, Emma Strickland, Alexandra Carrick and Steve Williams inChichester. We are particularly grateful to Aparajita Srivastava at Thomson Digital for hercooperation and flexibility throughout the typesetting/proofreading stage. Finally, and most importantly, we want to record our deep appreciation of the support we receivedfrom our wives, Madeleine and Denise, and our children Niamh, Eoin, Katie, Chris and Claire.

Colm O'Sullivan, Michael MansfieldCork, 1 June 2010

Chapter 1

Understanding the Physical Universe

Aims to show how matter can be described in terms of a series of models (mental pictures of the structures and workings ofsystems) of increasing scale, starting with only a few basic building blocks

to describe how, despite the great complexity of the material world, interactions between its building blocks can be reducedto no more than four distinct interactions

to describe how natural phenomena can be studied methodically through observation, measurement, analysis, hypothesisand testing (the scientific method)