PPO Ms R WML O) Physic HALLIDAY - RESNICK - KRANESUPPLEMENTS Instructor’s Supplements Instructor's Solutions Manual by PAUL STANLEY, California Lutheran University. This man- tual provides worked-out solutions forall of the end-of-chapter problems. Instructor's Manual by J. RICHARD CHRISTMAN, U.S. Coast Guard Academy. This manval includes suggested syllabi, lecture notes, list of the problems that appear in the Student Soli tions Manual, a complete list of answers to the problems, a comparison of the problems with the Fourth Edition, and a list of computer projects. Test Bank by J. RICHARD CHRISTMAN, US. Coast Guard Academy. This manual includes ‘more than 2200 multiple-choice questions. These items are also available in the Computerized ‘Test Bank (see below). Instructor's Resource CD. This CD contains: + Allof the lnstructor’s Solutions Manual in both LaTex and pat files *+ Computerized Test Bank, in both IBM and Macintosh versions, with full editing features to help the instructor customize tests. * All text illstrations, suitable for both classroom projection and printing. Wiley Physics Simulations. This CD contains 50 interactive simulations covering all major topic areas in the introductory physics course. They are programmed in Java and can be used ax lecture demonstrations or as on-line student assignments. Wiley eGrade. eGrade is a powerful on-line homework management system that allows instruc- tors to assign and grade homework using the web. Student’s Supplements Study Guide by J. RICHARD CHRISTMAN, U.S. Coast Guard Academy. This student study guide provides an array of study aids and problem-solving help. ‘Student Solutions Manual by PAUL STANLEY, California Lutheran University. This manual provides students with complete worked-out solutions to 25 percent of the problems found at the ‘end of each chapter of the textPHYSICSDavid Halliday Professor of Physics University of Pittsburgh Robert Resnick Professor of Physics Rensselaer Polytechnic Institute Kenneth S. Krane Professor of Physics Oregon State University With the assistance of Paul Stanley California Lutheran University JOHN WILEY & SONS, INC. NewYork | Chichester Welnhelm Brisbane; Singapore. {TorontoACQUISITIONS EDITOR Star. oho SENIOR PRODUCTIONEDITOR _Flizabeth Swain SENIOR MARKETING MANAGER fob Smith ILLUSTRATION EDITOR ‘nna Melhor PHOTO EDITORS Sore Wight and Hilary Nowmen ‘TEXT DESIGNER Lee Geldscin (COVER DESIGNER David Levy ‘Cover photo couresy IBM Research, Almaen Research Comer Linear create by magicering Ar. “This book was set ia 10/12 Times Ronan by Progessve Infermation Technologies sd was pind anc bound by Courier Wesord. The cover ws printed by Lehigh “This book is printed on acid-free paper ‘Copyriaht © 1960, 1962, 1966, 1978, 19,2002 ohn Wiley & Sons, Ine All ihts sere ‘No partof his publication maybe reproduced, tured ina revival system or tnnsmited in any form or by any means, elscori, mechanical, photocopying reconing, scanning or oherwis, except as permitted under Sections 107 of 108 of te 1976 United. Sates Copyright Ad, witdout ether te prior writen permission ofthe Publisher, of authorization throurh payment of the approntiat er-copy fest the CopyishtClearince (Center, 222 Roseweed Drive, Danvers, MA(1023, (078) 780-8400, fax (78) 750-4470 Rouen to the Plisher for permission shouldbe aes the Pen ssone Depaimert Iehn Wiley & Sons, Ine, 605 Third Avenue. New York, NY 10158-2012, (212) 880-8011, fx (212) 850.6008, E-Mta PERMREQUWILEY.COM ‘Teorder books or fr cusiomer servis, cl 100) CALL WILEY (25 5945). Library of Congress Cataloging in Publizction Data: Halliday, Davi, 1916— ‘Physcs.—~ She. / David Hida, Robe Resnick, Kenseth S. Kane pom -Kesmck’s me appears ston ¥ | ofthe Sth ed; Hlliday’s name appears rst nv. 2c the Sh Inclusesbsliogrphical references and indexes, ISBN 0-471-32057-9 (1 cide paper) ~~ ISBN 978-0-471-40194-0(4 2 acidrce ape) 1 Physics. L Remick, Roben, 1923— HL Krane, Kenneth SI Tile. Qa 35 2002 530 de2t 2001017605: Pintedin the United Stats of America 198765cc PREFACE TO VOLUME 2 7 [ne 1960 as Physics for Students of Science and Engineering by David Halliday and Robert Resnick. For four decades this ‘book has provided the standard for the calcults-based intro: ductory survey course and has been known for the clarity and completeness of its presentation. In the present edition ‘we have striven to inerease accessibility without sacrificing the level or the rigor of its content. The text has been sub- stantially rewriuen 1 make the macrial flow more smoothly and to ease the student's entry into new subjects. ‘We have attempted to provide more practical examples and to proceed from the particular to the general when new top- ics are introduced. This edition features many changes in the pedagogy as ‘well as in the ondering of material in the chapters. Those ‘who are familiar with the fourth edition ofthis text will find the same topics but in a slightly revised order. In making these revisions, we have sought the advice of users of past ditions and have taken into consideration the results of physics education research. Among the changes we have ‘made in this edition are the following: 1, Owing to a rearrangement that resulted in the elimi- nation of two chapters from Volume 1, the chapters in Vol- ume 2 have been renumbered beginning with 25 (which comesponds to Chapter 27 of the fourth editioa). 2, Students often have difficulties with integrating over continuous charge distributions in the calculation of electric fields, a procedure that is both conceptually abstract and ‘computationally challenging. In order to deal eailier with the conceptual difficulties, we introduce the procedure in connection with electric forces rather than elects fields; for example, in Chapter 25 we discuss the calculation of the force excried by @ line of charge on a poiat charge. Students generally have a greater physical intuition for forces than fields, and in this way we can establish the mathematical procedure in a more physical contest. Later we will repeat the calculations for fields and potentials. For similar rea~ sons, we introduce the shell theorems in Chapter 25 in the context of forces, which parallels their introduction in Chapter 14 of Volume 1 in the discussion of the gravita- tional force. vit 3. The discussion of Rutherford scattering has been ‘moved from the chapter on Gauss’ lew in the previous edi- tion to the discussion of electric fields in Chapter 26. 4. In Chapter 27 Gauss’ Law), we have expanded the discussion of the relationship beiweea electric flux and field lines, and we now discuss the conveatioral applications of Gauss" law to continucus charge distributions before its ap- plications to conductor. 5S. Chapter 29 (The Electrical Properties of Materials) is ‘anew chapter tha! incorporates material on conductors and dielectrics that appeared in the previous edition in the two chapters on capacitors and curreat. We betieve that this ma- terial stands on its own, and by introducing it in this way wwe can more easily contrast the behavior of conductors and insulators in elecuic fields. 6. Physics education research consistently shows that stu- denis have significant difficulties in understanding the bekav- ior of simple DC circuits. We have therefore expanded our presentation ofthis topic while simultaneously decreasing the coverage of multiloop circuits and messuring instruments 7. We now begin our introduction to the sources of the ‘magnetic field (Chapter 33) with a presertation of the field due to a single moving charge, and then move to the field due to a curtent element. This enables a better correspon- dence with the way magnetic fields are introduced in the previous chapter (treating the force on a single moving charge first end then the force on a curtent element). We also now provide a direct calculation of the axial field of a solenoid using the Biot~Savari law before repeating the calculation using Ampire’s law. 8. The introduction of the magnetic dipole moment has been delayed until Chapter 35 (Magnetic Properties of Ma- terials). This has been done in pert to avoid overloading stu- denis with new material in the first chapter on magnetic, fields as well as to provide a more coherent approach by in- troducing the magnetic dipole in the context in which it will be most directly applied. We have shortened somewhat the discussion of atomic and nuclear magnetism here. prefer- ring to delay a more detailed discussion until a later chapter following the introduction of some of the rudiments of atomic structure along with electron spin.9. We have reconfigured Chapters 40, 41, 42, and 43 of the previous edition into Chapters 38 and 39 of the present edition. Chapter 38 now treats Maxwell's equations and their applications to electromagnetic waves, material that ‘was included in Chapters 40 and 41 of the fourth edition, Chapter 39 introduces properties of light waves, including reflection and retraction, and thus incorporates material that previously appeared in Chapters 41, 42, and 43. Image for- ‘mation by plane mirrors now appears in the following chap- ter (40), where it fits more naturally with the discussion of image formation by mirrors and lenses. 10. In the fourth edition, topics from modern physics ‘were “sprinkled” throughout the text, generally in sections labeled as “optional.” In this edition we continue to use ex- ‘amples from modern physics where appropriate throughout the text, but the separate sections on moder physics have been consolidated into Chapters 45-52, which treat topics from quantum physics and its applications to atoms, solids, and nuclei. We strongly believe that relativity and quantum, physics are essential parts of an introductory survey course ‘at this level, but that justice 1o these subjects is better ac- complished by a coherent, unified presentation rather than a collection of isolated expositions. As was the case in the fourth edition, we continue to place the chapter on special relativity among the classical mechanics chapters in Vol- ‘ume 1, which reflects our strong belief that special relativ- ity belongs squarely among the kinematics and mechanics cchapters dealing with classical physics. Chapters 45-48, ‘which treat quantum physics and its applications to atoms, have been substantially rewriten from the fourth edition. ‘Chapter 45 introduces the usual early experiments suggest- ing the particle-like properties of electromagnetic radiation. (thermal radiation, the photoelectric effect, Compton scat- tering). However, unambiguous evidence for the particle- ‘wave duality of light comes only from modern delayed cchoice experiments, which we now also treat in Chapter 45, ‘The rudiments of the Schridinger theory are now treated in Chapter 46, with detailed applications to potential wells ‘and to the hydrogen atom in Chapter 47. Chapter 48, which lueals atomic suucture, is similar to Chapter 32 of the fourth edition with the addition of new material on atomic ‘magnetism, ‘The endof-chapter material in this edition differs sig- nificantly from that of the previous edition. The previous problem sets (which were all keyed to chapter sections) hhave been carefully edited and placed into two groups: ex- cercises and problems. Exercises, which are keyed to text sections, generally represent direct applications of the ma- terial in the associated section. Their purpose is usually to help students become familiar with the concepts, important formulss, units and dimensions, and so forth. Problems, which are not keyed to text sections, often require use of concepts from different sections or even from previous chapters. Some problems call for the student to estimate or independently to locate the data needed to solve the prob- om In editing and grouping the exercises and problems, ‘we have also eliminated some problems from the previous dition. A problem supplement will incorporate mest of the ‘missing problems as well as a selection of new exercises and problems. As before, answers to odd-numbered exer- cises and problems are given in the text and those to the even-numbered exercises and problems can be found in the Instructor's Manual that is available to instructors. Multiple-choice questions and computer problems have also been added to the end-of-chapter material. The multi- ple-choice questions are generally conceptual in nature and ‘often call for unusual insights into the material. Answers to the multiple-choice questicns can be found in the instruc- tor's manual. The computer problems may require familiar- ity with spread-sheet techniques or with symbolic manipu- lation routines such as Maple or Mathematica. ‘The development of the ead-of-chapter material has been undertaken with the substantial assistance of Paul Stanley of California Lutheran University. We have been Fortunate to have had the benefits of his insights and cre- tivity in this project. We have striven to develop a textbook that offers as complete and rigorous a survey of introductory physics as is possible at this level. It is, however, important to assert that few (if any) instructors will want to follow the entire text from start to finish, especially in a one-year course. ‘There are many alternate pathways through this text. The instructor who wishes to teat fewer topics in greater depth (often called the “less is more” approach) will be able to se- lect from among these pathways. Some sections or subsec- tions are explicitly labeled as “optional” indicating that they can be skipped without loss of continuity. Depending ‘on the course design, other sections or even entire chapters can be skipped or treated lightly. The Instrucior’s Manual available as a companion volume, offers suggestions for ab- Dreviating the coverage. Even so, the complete presentation remains in the text where the curious student can seek out the omitted topics and be rewarded with a broader view of the subject. We hope that the text can thus be regarded as a sort of “road map” through physics; many roads, scenic or direct, can be taken, and all roads need not be utilized on the first journey. The eager traveler may be encouraged to return to the map to explore areas missed on previous jour- neys. The text is available in two volumes. Volume | covers kinematics, mechanics, and thermodynamics, the present ‘volume covers clectromagnetism, optics, and quantum physics and its applications. Supplements available include: Instructor's Solutions Manual Instructor's Manual ‘Student Solutions Manual Student Study Guide Physics Simulations ‘Grade Homework Management System Instructor's Resource CD ‘Test BankPREFACE To VOLUME 2 1* In preparing this edition, we have benefited from the advice of a dedicated team of reviewers who have, individually or collectively, carefully offered comments and criticisms on nearly every page ofthe text: Richard Bukrey, Loyola University Duane Carmony, Purdue University J. Richard Christman, U. S. Coest Guard Academy Paul Dixon, Californie State Universty-San Bernadino Join Federici, New Jersey Institute of Technology David Gavenda, University of Texas-Austin Stuart Gazes, University of Chicago James Gerhart, Univesity of Washington John Gruber, San Jose Stats University Martin Hackworth, Idaho State University Jonathan Hall, Pennsylvania State University, Behrend Osari Karmon, Diablo Valley College Jim Napolitano, Rensselaer Polytechnic Institute Donald Naugle, Texas A&M University Douglas Osteroff, Stanford University Harvey Picker, Tainity College Anthony Pitucco, Pima Community College Robert Scherrer, Ohio State University John Toutonghi, Seattle University We are deeply indebted to these individuals for their efforts, aand for the insights they have provided to the authors. We would also like to acknowledge the advice of the Physics, Education Group at the University of Washington, espe- cially Paula Heron and Lillian McDermott. The staff at John Wiley & Sons has provided constant support for this project, for which we are exceptionally grateful. We would especially like to thank Stuart Johnson for his management of this project and his dedication to its, completion, Essential conuibutions to the quality of this, text have beea made by production editor Elizabeth Swain, ‘phoio editor Hilary Newman, illustration editor Anna Mel- horn, and designer Karin Kinckloe. Without the skill and efforts of these individuals this project would not have been possible. Despite the best efforts of authors, reviewers, and edi- tors, it in inevitable that errors may appear in the text, and ‘we welcome communication from users with corrections or comments on the content or pedagogy. We read all of these communications and respoad to as many as possible, but ‘we regret not being able to respond to all of them, Never theless, we encourage readers’ comments, which can be sent to www.wiley.com/collegelhalliday.CONTENTS 25: ELECTRIC CHARGE AND COULOMB'S LAW 567 25-1 Electromagnetism: A Preview 567 252 Eketric Charge 568 253 Conductors and Insulators 571 254 Coulomb’sLaw 573 25.5 Continuous Charge Distributions $76 25-6 Conservation of Charge 580 Questions and Problems 581 enna 26 THE ELECTRIC FIELD 587 26-1 What Isa Field? 587 262 The Electric Field $88 263 The Electric Field of Point Charges 500 264 Electric Field of Continuous Charge Distritutions 592 265 Electric Field Lines 595 2646 APoirt Charge in an Electric Field 597 26-7 ADipole in an Electic Field 600 268 The Nuclear Medel of the Atom (Optional) 602 Questions and Problems 603 27 GAUSS’ LAW 611 27-1 What is Gauss’ Law All About? 611 272 The Flux of a Vector Field 612 273 The Flux of the Electic Field 613 274 Gauss'Law 616 275 Applications of Gauss’ Lew 617 276 Gauss’ Law and Conductors 621 27-7 Experimental Tests of Gauss’ Law and Coulomb's Law 624 Questions and Problems 626 28 ELECTRIC POTENTIAL ENERGY AND POTENTIAL 635 28-1 Potential Energy 635 28-2 Electric Potential Energy 636 28-3 Electric Potential 639 28-4 Calculating the Potential from the Field 640 28-5 Potential Due to Point Charges 641 28-6 Electric Potential of Continuous Charge Distributions 044 28-7 Calculating the Field from the Potential 645, 28-8 Equipotential Surfaces 648 28-9 The Potential ofa Charged Conductor 649 28-10 The Electrostatic Accelerator (Optional) 651 Questions and Problems 652 29 ‘THE ELECTRICAL PROPERTIES OF MATERIALS 661 29-1 Types of Materials 661 29-2. A Conductor in an Electric Field Static Conditions 662 29-3 A Conductor in an Electric Field: Dynamic Conditions 663 29-4 Ohmic Materials 665 29-5 Ohm's Law: Microscopic View 668 29.6 Anlnsulatorin an Electric Field 670 Questions and Problems 672 _cunrren 30 CAPACITANCE 679 30-1 Capacitors 679 30-2 Capacitance 679 30-3 Calculating the Capacitance 681 30-4 Capacitors in Series and Parallel 683 30-5 Energy Storage in an Electric Field 685 30-6 Capacitor with Dieleciic 687 Questions and Problems 690DC CIRCUITS 701 31-1 Electric Curent 701 31-2 Electromotive Force 703 B13 Analysis of Circuits 704 31-4 Electric Fields in Circuits 709 31-3 Resistors in Series and Parallel 710 31-6 Energy Transfers in an Electric Circuit 713, 31-7 RC Circuits 713 Questions and Problems 716 32 THE MAGNETIC FIELD 725 32:1 Magnetic Interactions and Magnetic Poles 725 32.2 The Magnstic Force on a Moving Charge 727 32.3 Circulating Charges 731 32-4 The Hall Effect 734 32.5 The Magnetic Force on a Current- Carrying Wire 736 32.6 The Torque on Current Loop 738 Questions and Problems 740 cuarrer JF THE MAGNETIC FIELD OFA CURRENT 749 33-1 The Magnetic Field due toa Moving Charge 749 33.2 The Magnetic Field of a Current 752 33.3 Two Parallel Currents 756 33-4 The Magnatic Field of a Solenoid 758 33.5 Ampire’s Law 760 33-6 Electromagnetism and Frames of Reference (Optional) 764 Questions and Problems 765 34 FARADAY’S LAW OF INDUCTION 775 34-1 Faradsy's Experiments 775 34.2 Faraday’s Law of Induction 776 343 Lenz’ Law 777 344 Motional emf 780 34-5 Generators and Motors 782 34-6 Induced Electric Fields 783 347 Induction and Relative Motion (Optional) 786 Questions and Problems 789 cuarrer 3D MAGNETIC PROPERTIES OF MATERIALS 801 35-1 The Magnetic Dipole 801 35.2 The Force on a Dipole ina Nonuniform Field 804 35-3 Atomicand Nuclear Magnetism 805 35-4 Magnetization 807 35-5 Magnetic Materials 808 35-6 The Magnetism of the Planets (Optional) 811 35-7 Gauss’ Law for Magnetism 814 Questions and Problems 816 cuarrer 36 INDUCTANCE 823 36-1 Inductance $23 36-2 Calculating the Inductance 824 36-3 LRCircuits 826 36-4. Energy Storage in a Magnetic Field 827 36-5 Electromagnetic Oscillations: Qualitative 830 36-6 Electromagnetic Oscillations: Quantitative 332 36-7 Damped and Forced Oscillations $33, ‘Questions and Problems 836 cuarrer 37 ALTERNATING CURRENT CIRCUITS 845 37-1 Alternating Currents 845 37-2 Three Separate Elements 846 37-3 The Single Loop RLC Circuit 848 37-4 Power in AC Circuits 851 37-5 The Transformer (Optional) 852 ‘Questions and Problems 854 38 MAXWELL’S EQUATIONS AND ELECTROMAGNETIC WAVES 861 38-1 The Basic Equations of Electromagnetism 861 38-2 Induced Magnetic Fields and the Displacement Current 862 38-3 Maxwell’s Equations 864 38-4 Generating an Electromagactic Wave | 866 38-5 Traveling Waves and Maxwell's Equations 868, 38-6 Energy Transport and the Poynting Vector $70 38-7 Radiation Pressure $72 Questions and Problems 874 cnaprer 39 LIGHT WAVES 883 39-1 ‘The Electromagnetic Spectrum 883, 39-2 Visible Light $86 39-3 The Speed of Light 887 39-4 Reflection and Refraction of Light Waves 890 39-5 Total Internal Reflection 897 39-6 The Doppler Effect for Light 899 ‘Questions and Problems 902paeen40) MIRRORS AND LENSES 913 40-1 Image Formation by Mirrors and Lenses 913 40.2 Plane Mirrors 914 40.3 Spherical Mirrors 917 404 Spherical Refracting Surfaces 921 40-5 Thin Lenses 923 406 Optical Instruments 928 (Questions and Problems 930 41 INTERFERENCE 941 41-1 Two-Source Interference 941 41-2 Double-Slit Interference 942 41-3 Coherence 944 41-4 Intensity in Double-Slit Interference 946 41-5 Interference from Thin Fllms 948 41-6 Michelson’s Interferometer 953, Questions and Problems 955 ccunnren 42 DIFFRACTION 963 42-1 Difiraction and the Wave Theory of Light 963 422 Single Slit Diffraction 965 423 Intensity in Single-Slit Diffraction 967 42-4 Diffraction at a Circular Aperture 970 425 Double-Slit Intecference and Diffraction Combined 971 Questions and Problems 975 gins GRATINGS AND SPECTRA 981 43-1 Multiple Slits 981 432 Diffraction Gratings 985 43.3 Dispersion and Resolving Power 986 434 X-ray Diffraction 988 43.5 Holography (Optional) 992 Questions and Problems 994 curren 44 POLARIZATION 999 44-1 Polarization of Electromagnetic Waves 999 44.2 Polarizing Sheets 1001 44.3 Polarization by Reflection 1003 444 Double Refraction 1004 445 Circular Polarization 1006 44-6 Polarization by Scattering 1008 Questions and Problems 1010 Eas) THE NATUREOFLIGHT 1015 45-1 Introducing the Photon 1015 45-2 Thermal Radiation 1016 45-3 The Photoelectric Effect 1019 45-4 The Compton Effect 1021 45-5 The Photon Revealed 1023 45-6 Photons and Waves 1024 45-7 Slowing Down Atoms by Photon Bombarément 1026 Questions and Problems 1028 46 THE NATUREOFMATTER 1035 46-1 Matter Waves 1035 46-2. Testing DeBroglie's Hypothesis 1036 46-3 Waves and Particles 1041 46-4 Heisenberg's Uncertainty Principle 1042 46-5 The Wave Function 1044 46-6 Schridinger's Equation 1045 46-7 Barrier Tunneling 1046 Questions and Problems 1049 vamrand 7, ELECTRONS IN POTENTIAL WELLS 1055 47-1 Electrons, Frve and Bound 1055 47-2 An Electron Trapped in a Potential Well 1055 47-3 An Electron Trapped in a Finite Well 1060 47-4 AnElectron Trapped in an Atom 1062 47-5 The Ground State of the Hydrogen Atom 1055 47-6 Angular Momentum of Electrozs in Atoms 1066 47-7 An Excited State of the Hydrogen Aiom 1069 47-8 Counting the States of Hyérogen 1070 Questions and Problems 1072 cuvren ATOMIC STRUCTURE 1079 48-1 The X-ray Spectrum of Atoms 1079 448-2 X Rays and the Numbering of the Elements 1081 48-3 Building Atoms 1082 48-4 ‘The Periodic Table 1083, 48-5 Atomic Magnetism 1086 48-6 The Stem-Gerlach Experiment 1087 48-7 Nuclear Magnetic Resonance 1089 48-8 Magnetism and Atomic Radiations (Optional) 1090 48-9 Lasers and LaserLight 1092 Questions and Problems 1096xWw pane AG) ELECTRICAL CONDUCTION IN SOLIDS 1103 49-1 Quantum Theory of Solids 1103 49.2 Conduetion Flectronsin a Metal 1104 49-3. Filling the Allowed Sates 1105 49-4. Electrical Conduction in Metals 1108 49-5 Bands and Gaps 1109 49-6 Conductors, Insulators, and Semiconductors 1111 49-7 DopedSemiconductors 1112 49-8 The pnJunction 1114 49.9 Optical Electronics 1117 49-10 The Transistor 1119 49-11 Superconductors 1120 Questions and Problems 1122 enean'50 NUCLEAR PHYSICS 1129 50-1 Discovering the Nucleus 1129 50-2 Some Nuclear Properties 1131 50-3 Radioactive Decay 1135 30-4 Alpha Decay 1136 50-5 Beta Decay 1138 50-6 Measuring Ionizing Radiation 1139 50-7 Natural Radioactivity 1140 50-8 NuclearReaetions 1141 50-9 Nuclear Models (Optional) 1143, Questions and Problems 1145 ENERGY FROM THENUCLEUS 1153 51-1 The Atom and the Nucleus 1153 51-2 Nuclear Fission: The Basic Process 1154 51-3 Theory of Nuclear Fission 1155 51-4 Nuclear Reactors: The Basic Principles 1157 51-5 A Natural Restor 1159 51-6 Thermonuclear Fusion: The Basic Process 1161 51-7 Thermonuclear Fusion in Stars 1162 51-8 Controlled Thermonuclear Fusion 1164 Questions and Problems 1167 cuarter 32 PARTICLE PHYSICS AND COSMOLOGY 1173 52-1 Particle Interactions 1173 52-2 Families of Particles 1176 52-3 Conservation Laws 1179 52-4 The Quark Model 1181 52-5 The Big Bang Cosmology 1186 52-6 Nucleosysthesis 1190 52-7 The Age of the Universe 1192 Questions and Problems 1194 APPENDICES . The International System of Units (1) A-1 Fundamental Physcial Constants A-3 ‘Astronomical Data A-4 Properties of the Elements A-6 Periodic Table of the Elements A:9 Elementary Particles A-10 Conversion Factors A-12 Vectors A-I7 ‘Mathematical Formulas A-20 ‘Nobel Prizes in Physics A-22 He nommoom > ANSWERS TO ODD-NUMBERED PROBLEMS A-26 PHOTO CREDITS P-1 INDEX L-1ELECTRIC CHARGE AND COULOMB’S LAW @ begin here a detailed study of electromagnet- ism, which will extend throughout most of the remainder of this text. Electromagnetic forces are responsible ‘for the structure of atoms and for the binding of atoms in molecules and solids. Many properties of materi als that we have studied so far are electromagnetic in their nature, such as the elasticity of solids and the surjace tension of liquids. The spring force, friction, and the normal force all originate with the electromag netic force between atoms. Among the examples of electromagnetism that we shall study are the force between electric charges, such as occurs between an electron and the nucleus in an atom; the motion of a charged body subject to an external electric jorce, suci as an electron in an oscilloscope beam; the flow of electric charges through circuits and the behavior of circuit elements; the force between permanent mognets and the properties of ‘magnetic materials; and electromagnetic radiation, which whimaiely leads to the study of optics, the nature ‘and propagation of light. In this chapter we begin with a discussion of electric charge, some properties of charged bodies, and the fundamental electric force between two charged bodies. 25-1 ELECTROMAGNETISM: A PREVIEW ‘What do the following have in common? 1. You turn on the light switch in your room, The con- sumpticn of fuel at a power plant produces electromagnetic, energy by causing a loop of electrically conducting wire to rotate in the vicinity of a magnet. Ultimately some of this energy is transferred to the elecrrons in the filament of your lightbulb, waich can transform the electrical energy into visible light. 2. You enter a command on your computer keyboard. A stream of electrons is formed to transmit your instructions There sre many thousands of possible pathways for the electrons through the computer circuitry, but most are blocked by electronic gates. Electrons can move only through the gates that have been opened by your command 567 so that the stream of electrons ceackes its destination and your command is executed, 3. You push the channel select button on the remote control of your TY set. Electromagnetic waves travel from the remote control unit to a receptor on the set, which then tunes the set to accept ancther electromagnetic wave that originates from a satellite orbiting high above the Earth ‘The waves from the satellite provide instructions for your set to use electric and magnetic forces to focus and direct a ‘beam of electrons that strikes the surface of the picture tube and produces a visible image. ‘The common factor in these diverse phenomena is that they all depend on forces that we describe as electric or ‘magnetle 10 control and disect the flow of energy or parti- cles. These forces form the basis of our study of eleciro- ‘magnetism. We will find in our study that all electromag- netic effects can be explained by a sot of four besicequations, called Maxwell's equations. These equations represent individual laws of electromagnetism, just a: we have previously discussed equations that represent New- tons’ laws of mechanics or the laws of thermodynamics. ‘Our study will first consider electric phenomena and then magnetic phenomena, Later we will show thet the two cannot be separated; certain electric phenomena product ‘magnetic efiects, and certain magnetic phenomena product electric effects. This leads us to unify electric and magnetic phenomena under the common name of electromagnetism. ‘The development of the laws of electromagnetism and their unification was a great triumph of 19th-century physics. ‘Their application has led directly toa great range of devi of practical use, such as motors, radios and televisions, radar, microwave ovens, and cellular phones. ‘The development of electromagnetic theory continued in the 20th century with three very significant advance- ‘ments. In 1905, Albert Einstein showed that, to a moving observer, electric effects could appear as magnetic effects, ‘and thus observers in relative motion could disagree in as- signing their measurements to electric or magnetic causes. This conclusion formed the basis of the special theory of relativity, which ultimately was to revolutionize our con- cepts of space and time. The second development was the introduction of a quantum theory of electromagnetism, called quantum electrodynamics, which reached its fruition around 1949 and enabled properties of the atom to be cal- culated with incredible precision, currently about 11 signifi- ‘cant figures. The third development of the 20th century was the unification of electromagnetism with another force, called the “weak” force, which is responsible for certain ra- 008C Elctric and magnetic minerals (ancient Greoks) 4600 AD Etre and magnetic atractons (Gibert) 1700 _ Force betwaen dlectre charges (Coulomb) eS +49co——}— invention of attery (alta) 1020 Currents deflact magnetic compass (Cerstod) Magnatic fields caused by currerts (Ampére) \Qtcentical ‘conduction (Ohm) \ Electric motor (Henry) ‘Currents induced by magnetic fields (Faraday) \ Equations of electromagnetism (Maxwell) ter 7S eects he) test //|\\ oscar ot easton onsen 007/ | \ toes Specal teary otreatty inten) 1040 ~ ~Quanum secttedynanics 1967 ~ ” soctovnal theory (Glashow, Weinberg, Salam) co FIGURE 25-1. Timeline of major developments in electro- ‘magnetism diosctive decay processes and other interactions between particles Jusi as electric and magnetic effects were unified into the electromagnetic interaction, so electromagnetic and weak effects were shown in the 1960s to be unified under the eleciroweak interaction. For our study of electric and ‘magnetic forees, however, the electroweak interaction does not yield anything new, and it is more convenient to con- sider the seperate electromagnetic interaction. Figure 25-1 is. time line of some of the major events in the development of our understanding of electromagnetism. 25-2 ELECTRIC CHARGE ‘After you pass a plastic comb through your hair a few times, you will find thet the comb can exet a force on indi- ‘vidual strands of your hair. You may also observe that, nce the strands of hair are attracted to the comb and come into contact with it, they may no longer be attracted to it It seems reasonable to conclude that the attraction be- teen the comb and the hair isa result of some physical en- tity being transferred from one to the other when they rub together, with the same physical entity being transferred back again to neutralize the attraction when they come into contact. This physical entity is called electric charge, and today we understand this tansfer on the basis of electrons that can be removed from the atoms of one object and at- tacked to the atoms of the cher object. The transfor of electric charge by means of friction is @ commonly observed phenomenon. It was known to the an- cient Greeks, who observed that pieces of amber rubbed swith fur could attract bits of straw. When you walk across a carpet and are shocked by touching @ metal éoor knob, or ‘when a lighting flash stretches between a loud and the ground, you are observing the effects of this transfer of charge. ‘Whea we “cherge” an object (thet is, when we transfer charge to i), we find that it can exert fore: on another charged objest. Early observations that this force can be ei- ther attractive or repulsive led to the conclusion that there are two kinds of electrical charge, which are called positive and negative. Although effects resulting from the transfer of charge can be powerful, itis remarkable that they originate from the transfer of only a tiny fraction of the electric cherge that is contained in objects. Ordinary matter is made of electrically neutral atoms or molecules that contain equal amounts of positive charge (he mucleus) and negaive charge (the electrons). When two objects rub together, rel- atively few electons from the atoms of one object are The postive and negntive labels or electric charge wore chosen arbiter Aly by Benjamin Franklin (1706-1790) who, among hs ober aecomplish- tutta may have enabled fis diplomatic triumphs in Fanee during the ‘American War of Independence,Thread > cc) FIGURE 25-2. (a) Tvo sinilarly charged rods repel each ther (b) Two oppesitely charged rods atract each other. transferred to the other; most of the electrons remain undisturbed. It is this slight upset of the balance between the enormous but equal amounts of positive and negative charge in an object that is responsible for most commonly observed electrical effects. ‘When we rub a plastic rod with fur, electwons are uans- fered to the rod; because it has an excess of electrons (which carry a negative charge), the rod becomes negatively charged. The fur now has « deficiency of electrons and so it is positively charged. We can see the attraction of the rod for individual strands of the fur, which results from the charge on each. In a similar way, we can rub a glass rod with silk and observe that both become charged and can at- tract one another. In each case, we have transferred a rela tively small number of electrons and upset the electrical neutrality ofthese objects. Let us charge a glass rod by rubbing one end of it with silk and then suspend it from a thread, asin Fig. 25-2. If we place a similarly charged glass rod nearby, we find that the two rods repel one another, as in Fig 25-2a, However, # we place a charged plastic rod (charged by rubbing with fur) nearby, he two rods attract one another, as in Fig. 25-20, We account for the existence of these two kinds of fores in tems of two kinds of charge. When plastic is, rubbed with fur, electrons are transferred to the plastic and it becomes negatively charged. When glass is rubbed with silk, electrons are transferred to the silk, leaving the glass with a deficiency of electrons and therefore 4 net positive charge. The forces observed in Fig. 25-2 can be summa- rized by the following rule: Charges of the same sign repel one another, and charges of the opposite sign attract one another. In Section 25-4, we put this rule into quantitative form, as, Coulomb's law of force. We consider only charges that are either at rest with respect to each other or moving very FIGURE 25-3. A cartier bead from a Xerox photvcopier, cov- ‘ered with toner particles that stick to it by clectostae atractin, ‘The diameter of the bead is about 0.3 mm. slowly, restriction that defines the subject of eleciro- staties. Electrical forces between charged bodies have many in- dustrial applicatioas, including clecuostaiie paint spraying and powder coating, fly-ash precipitation, nonimpact ink-jet printing, and photocopying. Figure 25-3 for example, shows a tiny carrier bead in a photocopying machine, cov- cred with particles of black powder called toner, that stick to the carrier bead by electrostatic forces. These negatively charged toner particles are eventually attracted from their carrier beads to & positively charged latent image of the document 1o be copied, which is formed on a rotating drum. A charged sheet of paper then attracts the toner particles, from the drum to itself, after which they are heat-used in place to make the final copy. The act electric charge of an object is usually repre- sented by the symbol q. The charge is a scalar quantity. It cean he positive or negative, depending on whether the ob- ject has a net positive or negative charge. Electric charge is ‘measured in units of coulombs (C). The coulomb is a very large unit of charge: it takes about 6 X 10" electrons to make one coulomb of charge. ‘The coulomb cannot be derived from previously defined units. Because electric charge is a new quantity, we are free to define its basic unit in any convenient way. One possible way would be in terms of the force exerted between 1wo standard charges at a given separation, such as the quantity Of charge thet exerts a force of one newton on a similar charge a distance of ene meter away. However, the force ‘between static charges is difficult to measure, and so in practice itis more useful to define the coulomb in terms of the magnetic force between current-carrying wires (which is discussed in Chapter 33). This force can be measured more precisely than the electric force between static370 CHAPTER 25 / ELECTRIC CHARGE AND COULOMB'S LAW charges. It is therefore more convenient to define an SI base Unit in tems of curret (rate of flow of cleric charge per Unit time). The coulomb as a unit for electric charge is then a derived unit, obained from the fundamental units of cur- rent ané time (see Appendix A) Electric Charge Is Quantized ‘When we transfer electric charge from one object to an- other, the transfer camot be done in arbitrarily small units. ‘That is, the flow of charge as a current is not a continuous flow, bat is made up of discrete elements.* Experiments show that the electric charge always exists only in quanti ties that are integer multiples of a certain elementary quan- tity of charge e. That is, gunmen 22,83, 51) “where ( four significant Sgures) 1.62 x 10°. ‘The elementary charge e is one of the fundamental com- stants of nature whose experimental value has been deter- ‘mined to an uncertainty of about 4 pars in 10'. The eleciron and the proton are examples of commonly occurring particles that each carry one fundamental unit of charge. The clectron has a charge of — e and the proton has a charge of +. Some particles, such as the neutzon, carry rno net electric charge. Other elementary particles are known that carry charges that are small multiples of o, ust ally + 1, +2, or * 3, Eack particle has a corresponding an- tiparticle, which has the same mass but the opposite elec: ‘ric charge: the anticlectron, which is known as the positron, has a charge of ~e. Antiparticles do not com- ‘monly exist in nature, but can be exeated in decays and re- actions of nuclei and elementary particles. Equation 25-1 tells us that itis possible to have a net charge on an object of + 10e or —6e but newer 3576. When the values of a property are restricted to discrete ‘multiples of a basic quantity, we say that the propery is quantized ‘Because the elementary charge is small, under ordinary circumstances we are not aware of the discrete nature of the flow of charge. For example, in a wire of an electronic cir- cuit in which small eurrens of one milliampere are typical, 6 X 10 electrons pass through ary cross section of the ‘wire every second! ‘Ordinary atoms are electrically neutral, which means thet they contain equal quantities of postive and negative charge. The nucleus of the atom contains Z protons (where Z is called the atomic number of the ator) and thus @ charge of +Ze. In @ neutral atom, Z negatively charged ‘te Franklin's day, elecrc charge was thought to be a substance and to vidi aims and mslcules mater is discrete, Simin, the “electric electrons circulate about the nucleus, I soften possible to remove one or more electrons from an atoc, cresting an fon that has an excess postive charge of +e, +2e, ... . For example, if we could remove all of the electrons from an atom of uranium (Z = 92), we would ereate a particle with a charge of +92e, Under certin circumstances, we ean even attach an exra electron to a neutral atom, creating & negatively charged ion ‘Although we believe electrons to be fundamental parti- cles with no substructure, protons are not fundamental par ticles. They are made up of more elementary entities called quarks, The quarks are assigned fractional eletric charges of —le and +2. The proton is campoted of three quarks, two with chirges of +e and one with charge of —‘e, ‘which ada up to a net charge of ~ , Experimental evden for the existence of quarks inside the proton is very strong (for example, high-energy electrons can be made to scatter from the fractionally charged quarks inside the proton, but, no matter how violently the protons re made to calide, no free quark his been released. AS a resul, no free particle with a factional charge has ever been abeerved. Th fact can be understood if the attractive fare that ene quark ex- ents on another increases with their seperation. This is in contrast to the electromagnetic and gravitational forces, both of which decrease as the distance between a pair of in terasting bodies increases, SAMPLE PROBLEM 25-1. A penny, being electrically neutral, contains equal amourts of positive and negative charge. ‘What is the magnitude of these equal charges? Solution The charge q is given by NZe, in which N is dhe number of atom in a penny and Ze isthe mageitude ofthe positive and the negative charges cartzd by cach tom. The number V of atoms in a penny, assumed for simplicity to bbe made of coppe, is N,mlM, in which N, isthe Avogaro con- stan. The mass m of the coins 3.11 g, and the mess Mf of I mol of copper (called its molar mass) is 63.5 g. Wetind Ngm _ (602 X 10% atoms/mo1\3.11 8) ae GS plo! = 295 x 10 atoms. Every neural atom has a negative charge of megnitede Ze as- sociated vith is eletrons and a positive charge ofthe same mag- nitude associated with its nacleus. Here ¢ is the elementary chaig, 160 X 10-" C, and Z is the atomic numberof the ele- ‘ment in cuostion. For copper, Z is 29. The magnitude of the otal negative or positive charge ins peny is then 4 = NZe = (2.85 X 10)299(1.60 X 10" C) = 137K 10. “This isan enormous charge. By camparson, the charge that you sight get by rbbing aplastic rod is pesbaps 10-°C, smaller by a factor of about 10% For another comparison, it would tke 1-2 days ors chare of 1.37 X 10° Ct low through the filament of a ‘ypizal lightbulb. There isa lotof eletie charge in edinary mate.