FUNDAMENTALS OF PHYSICS
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21 Coulomb’s Law 641
21.1 COULOMB’S LAW 641
What Is Physics? 642
Electric Charge 642
Conductors and Insulators 644
Coulomb’s Law 645
21.2 CHARGE IS QUANTIZED 652
Charge Is Quantized 652
21.3 CHARGE IS CONSERVED 654
Charge Is Conserved 654
REVIEW & SUMMARY 656 QUESTIONS 657 PROBLEMS 659
22 Electric Fields 665
22.1 THE ELECTRIC FIELD 665
What Is Physics? 665
The Electric Field 666
Electric Field Lines 666
22.2 THE ELECTRIC FIELD DUE TO A CHARGED PARTICLE 668
The Electric Field Due to a Point Charge 668
22.3 THE ELECTRIC FIELD DUE TO A DIPOLE 670
The Electric Field Due to an Electric Dipole 671
22.4 THE ELECTRIC FIELD DUE TO A LINE OF CHARGE 673
The Electric Field Due to a Line of Charge 674
22.5 THE ELECTRIC FIELD DUE TO A CHARGED DISK 679
The Electric Field Due to a Charged Disk 679
22.6 A POINT CHARGE IN AN ELECTRIC FIELD 680
A Point Charge in an Electric Field 681
22.7 A DIPOLE IN AN ELECTRIC FIELD 683
A Dipole in an Electric Field 684
REVIEW & SUMMARY 687 QUESTIONS 687 PROBLEMS 689
23 Gauss’ Law 696
23.1 ELECTRIC FLUX 696
What Is Physics? 696
Electric Flux 697
23.2 GAUSS’ LAW 701
Gauss’ Law 702
Gauss’ Law and Coulomb’s Law 703
23.3 A CHARGED ISOLATED CONDUCTOR 705
A Charged Isolated Conductor 705
23.4 APPLYING GAUSS’ LAW: CYLINDRICAL SYMMETRY 708
Applying Gauss’ Law: Cylindrical Symmetry 708
23.5 APPLYING GAUSS’ LAW: PLANAR SYMMETRY 710
Applying Gauss’ Law: Planar Symmetry 711
23.6 APPLYING GAUSS’ LAW: SPHERICAL SYMMETRY 713
Applying Gauss’ Law: Spherical Symmetry 714
REVIEW & SUMMARY 715 QUESTIONS 715 PROBLEMS 717
24 Electric Potential 724
24.1 ELECTRIC POTENTIAL 724
What Is Physics? 724
Electric Potential and Electric Potential Energy 725
24.2 EQUIPOTENTIAL SURFACES AND THE ELECTRIC FIELD 729
Equipotential Surfaces 729
Calculating the Potential from the Field 730
24.3 POTENTIAL DUE TO A CHARGED PARTICLE 733
Potential Due to a Charged Particle 733
Potential Due to a Group of Charged Particles 735
24.4 POTENTIAL DUE TO AN ELECTRIC DIPOLE 736
Potential Due to an Electric Dipole 737
24.5 POTENTIAL DUE TO A CONTINUOUS CHARGE DISTRIBUTION 738
Potential Due to a Continuous Charge Distribution 738
24.6 CALCULATING THE FIELD FROM THE POTENTIAL 741
Calculating the Field from the Potential 741
24.7 ELECTRIC POTENTIAL ENERGY OF A SYSTEM OF CHARGED PARTICLES 743
Electric Potential Energy of a System of Charged Particles 743
24.8 POTENTIAL OF A CHARGED ISOLATED CONDUCTOR 746
Potential of a Charged Isolated Conductor 746
REVIEW & SUMMARY 749 QUESTIONS 750 PROBLEMS 751
25 Capacitance 759
25.1 CAPACITANCE 759
What Is Physics? 759
Capacitance 759
25.2 CALCULATING THE CAPACITANCE 761
Calculating the Capacitance 762
25.3 CAPACITORS IN PARALLEL AND IN SERIES 765
Capacitors in Parallel and in Series 766
25.4 ENERGY STORED IN AN ELECTRIC FIELD 770
Energy Stored in an Electric Field 771
25.5 CAPACITOR WITH A DIELECTRIC 774
Capacitor with a Dielectric 774
Dielectrics: An Atomic View 776
25.6 DIELECTRICS AND GAUSS’ LAW 778
Dielectrics and Gauss’ Law 778
REVIEW & SUMMARY 781 QUESTIONS 781 PROBLEMS 782
26 Current and Resistance 789
26.1 ELECTRIC CURRENT 789
What Is Physics? 789
Electric Current 790
26.2 CURRENT DENSITY 792
Current Density 793
26.3 RESISTANCE AND RESISTIVITY 796
Resistance and Resistivity 797
26.4 OHM’S LAW 801
Ohm’s Law 801
A Microscopic View of Ohm’s Law 803
26.5 POWER, SEMICONDUCTORS, SUPERCONDUCTORS 805
Power in Electric Circuits 805
Semiconductors 807
Superconductors 808
REVIEW & SUMMARY 808 QUESTIONS 809 PROBLEMS 810
27 Circuits 816
27.1 SINGLE-LOOP CIRCUITS 816
What Is Physics? 817
“Pumping” Charges 817
Work, Energy, and Emf 818
Calculating the Current in a Single-Loop Circuit 819
Other Single-Loop Circuits 821
Potential Difference Between Two Points 823
27.2 MULTILOOP CIRCUITS 826
Multiloop Circuits 826
27.3 THE AMMETER AND THE VOLTMETER 833
The Ammeter and the Voltmeter 833
27.4 RC CIRCUITS 833
RC Circuits 834
REVIEW & SUMMARY 838 QUESTIONS 839 PROBLEMS 840
28 Magnetic Fields 850
28.1 MAGNETIC FIELDS AND THE DEFINITION OF B → 850
What Is Physics? 850
What Produces a Magnetic Field? 851
The Definition of B → 851
28.2 CROSSED FIELDS: DISCOVERY OF THE ELECTRON 855
Crossed Fields: Discovery of the Electron 856
28.3 CROSSED FIELDS: THE HALL EFFECT 857
Crossed Fields: The Hall Effect 858
28.4 A CIRCULATING CHARGED PARTICLE 861
A Circulating Charged Particle 862
28.5 CYCLOTRONS AND SYNCHROTRONS 866
Cyclotrons and Synchrotrons 866
28.6 MAGNETIC FORCE ON A CURRENT-CARRYING WIRE 869
Magnetic Force on a Current-Carrying Wire 869
28.7 TORQUE ON A CURRENT LOOP 872
Torque on a Current Loop 872
28.8 THE MAGNETIC DIPOLE MOMENT 874
The Magnetic Dipole Moment 874
REVIEW & SUMMARY 876 QUESTIONS 877 PROBLEMS 879
29 Magnetic Fields Due to Currents 886
29.1 MAGNETIC FIELD DUE TO A CURRENT 886
What Is Physics? 886
Calculating the Magnetic Field Due to a Current 887
29.2 FORCE BETWEEN TWO PARALLEL CURRENTS 892
Force Between Two Parallel Currents 893
29.3 AMPERE’S LAW 894
Ampere’s Law 894
29.4 SOLENOIDS AND TOROIDS 899
Solenoids and Toroids 899
29.5 A CURRENT-CARRYING COIL AS A MAGNETIC DIPOLE 901
A Current-Carrying Coil as a Magnetic Dipole 902
REVIEW & SUMMARY 904 QUESTIONS 905 PROBLEMS 906
30 Induction and Inductance 915
30.1 FARADAY’S LAW AND LENZ’S LAW 915
What Is Physics? 915
Two Experiments 916
Faraday’s Law of Induction 916
Lenz’s Law 919
30.2 INDUCTION AND ENERGY TRANSFERS 923
Induction and Energy Transfers 923
30.3 INDUCED ELECTRIC FIELDS 927
Induced Electric Fields 928
30.4 INDUCTORS AND INDUCTANCE 932
Inductors and Inductance 932
30.5 SELF-INDUCTION 934
Self-Induction 934
30.6 RL CIRCUITS 935
RL Circuits 936
30.7 ENERGY STORED IN A MAGNETIC FIELD 940 Energy Stored in a Magnetic Field 940
30.8 ENERGY DENSITY OF A MAGNETIC FIELD 942 Energy Density of a Magnetic Field 942
30.9 MUTUAL INDUCTION 943
Mutual Induction 943
REVIEW & SUMMARY 945 QUESTIONS 946 PROBLEMS 947
31 Electromagnetic Oscillations and Alternating Current 956
31.1 LC OSCILLATIONS 956
What Is Physics? 957
LC Oscillations, Qualitatively 957
The Electrical–Mechanical Analogy 959
LC Oscillations, Quantitatively 960
31.2 DAMPED OSCILLATIONS IN AN RLC CIRCUIT 963
Damped Oscillations in an RLC Circuit 964
31.3 FORCED OSCILLATIONS OF THREE SIMPLE CIRCUITS 966
Alternating Current 966
Forced Oscillations 967
Three Simple Circuits 968
31.4 THE SERIES RLC CIRCUIT 974
The Series RLC Circuit 975
31.5 POWER IN ALTERNATING-CURRENT CIRCUITS 982
Power in Alternating-Current Circuits 982
31.6 TRANSFORMERS 985
Transformers 985
REVIEW & SUMMARY 989 QUESTIONS 990
PROBLEMS 991
32 Maxwell’s Equations; Magnetism of Matter 998
32.1 GAUSS’ LAW FOR MAGNETIC FIELDS 998
What Is Physics? 998
Gauss’ Law for Magnetic Fields 999
32.2 INDUCED MAGNETIC FIELDS 1000
Induced Magnetic Fields 1000
32.3 DISPLACEMENT CURRENT 1003
Displacement Current 1004
Maxwell’s Equations 1007
32.4 MAGNETS 1007 Magnets 1007
32.5 MAGNETISM AND ELECTRONS 1009 Magnetism and Electrons 1010 Magnetic Materials 1014
32.6 DIAMAGNETISM 1015
Diamagnetism 1015
32.7 PARAMAGNETISM 1016
Paramagnetism 1017
32.8 FERROMAGNETISM 1019
Ferromagnetism 1019
REVIEW & SUMMARY 1023 QUESTIONS 1024
PROBLEMS 1026
33 Electromagnetic Waves 1032
33.1 ELECTROMAGNETIC WAVES 1032
What Is Physics? 1032
Maxwell’s Rainbow 1033
The Traveling Electromagnetic Wave, Qualitatively 1034
The Traveling Electromagnetic Wave, Quantitatively 1037
33.2 ENERGY TRANSPORT AND THE POYNTING VECTOR 1040
Energy Transport and the Poynting Vector 1041
33.3 RADIATION PRESSURE 1043
Radiation Pressure 1043
33.4 POLARIZATION 1045
Polarization 1045
33.5 REFLECTION AND REFRACTION 1050
Reflection and Refraction 1051
33.6 TOTAL INTERNAL REFLECTION 1056
Total Internal Reflection 1056
33.7 POLARIZATION BY REFLECTION 1059
Polarization by Reflection 1059
REVIEW & SUMMARY 1061 QUESTIONS 1062 PROBLEMS 1063
34 Images 1072
34.1 IMAGES AND PLANE MIRRORS 1072
What Is Physics? 1072
Two Types of Image 1072
Plane Mirrors 1074
34.2 SPHERICAL MIRRORS 1076
Spherical Mirrors 1077
Images from Spherical Mirrors 1078
34.3 SPHERICAL REFRACTING SURFACES 1083
Spherical Refracting Surfaces 1084
34.4 THIN LENSES 1086
Thin Lenses 1087
34.5 OPTICAL INSTRUMENTS 1094
Optical Instruments 1094
34.6 THREE PROOFS 1098
REVIEW & SUMMARY 1100 QUESTIONS 1101
PROBLEMS 1102
35 Interference 1111
35.1 LIGHT AS A WAVE 1111
What Is Physics? 1111
Light as a Wave 1112
35.2 YOUNG’S INTERFERENCE EXPERIMENT 1117
Diffraction 1117
Young’s Interference Experiment 1118
35.3 INTERFERENCE AND DOUBLE-SLIT INTENSITY 1122
Coherence 1122
Intensity in Double-Slit Interference 1123
35.4 INTERFERENCE FROM THIN FILMS 1126
Interference from Thin Films 1127
35.5 MICHELSON’S INTERFEROMETER 1135
Michelson’s Interferometer 1135
REVIEW & SUMMARY 1138 QUESTIONS 1139
PROBLEMS 1140
36 Diffraction
1148
36.1 SINGLE-SLIT DIFFRACTION 1148
What Is Physics? 1148
Diffraction and the Wave Theory of Light 1149
Diffraction by a Single Slit: Locating the Minima 1150
36.2 INTENSITY IN SINGLE-SLIT DIFFRACTION 1153
Intensity in Single-Slit Diffraction, Qualitatively 1153
Intensity in Single-Slit Diffraction, Quantitatively 1155
36.3 DIFFRACTION BY A CIRCULAR APERTURE 1158
Diffraction by a Circular Aperture 1158
36.4 DIFFRACTION BY A DOUBLE SLIT 1162
Diffraction by a Double Slit 1162
36.5 DIFFRACTION GRATINGS 1166
Diffraction Gratings 1166
36.6 GRATINGS: DISPERSION AND RESOLVING POWER 1170
Gratings: Dispersion and Resolving Power 1170
36.7 X-RAY DIFFRACTION 1173
X-Ray Diffraction 1173
REVIEW & SUMMARY 1176 QUESTIONS 1177
PROBLEMS 1178
37 Relativity 1186
37.1 SIMULTANEITY AND TIME DILATION 1186
What Is Physics? 1186
The Postulates 1187
Measuring an Event 1188
The Relativity of Simultaneity 1190
The Relativity of Time 1191
37.2 THE RELATIVITY OF LENGTH 1196
The Relativity of Length 1196
37.3 THE LORENTZ TRANSFORMATION 1199
The Lorentz Transformation 1200
Some Consequences of the Lorentz Equations 1202
37.4 THE RELATIVITY OF VELOCITIES 1204
The Relativity of Velocities 1204
37.5 DOPPLER EFFECT FOR LIGHT 1205
Doppler Effect for Light 1206
37.6 MOMENTUM AND ENERGY 1209
A New Look at Momentum 1209
A New Look at Energy 1210
REVIEW & SUMMARY 1215 QUESTIONS 1216 PROBLEMS 1217
38 Photons and Matter Waves 1225
38.1 THE PHOTON, THE QUANTUM OF LIGHT 1225
What Is Physics? 1225
The Photon, the Quantum of Light 1226
38.2 THE PHOTOELECTRIC EFFECT 1227
The Photoelectric Effect 1228
38.3 PHOTONS, MOMENTUM, COMPTON SCATTERING, LIGHT INTERFERENCE 1230
Photons Have Momentum 1231
Light as a Probability Wave 1234
38.4 THE BIRTH OF QUANTUM PHYSICS 1236
The Birth of Quantum Physics 1237
38.5 ELECTRONS AND MATTER WAVES 1238
Electrons and Matter Waves 1239
38.6 SCHRÖDINGER’S EQUATION 1242
Schrödinger’s Equation 1242
38.7 HEISENBERG’S UNCERTAINTY PRINCIPLE 1244
Heisenberg’s Uncertainty Principle 1245
38.8 REFLECTION FROM A POTENTIAL STEP 1246
Reflection from a Potential Step 1246
38.9 TUNNELING THROUGH A POTENTIAL BARRIER 1248
Tunneling Through a Potential Barrier 1248
REVIEW & SUMMARY 1251 QUESTIONS 1252
PROBLEMS 1253
39 More About Matter Waves 1258
39.1 ENERGIES OF A TRAPPED ELECTRON 1258
What Is Physics? 1258
String Waves and Matter Waves 1259
Energies of a Trapped Electron 1260
39.2 WAVE FUNCTIONS OF A TRAPPED ELECTRON 1264
Wave Functions of a Trapped Electron 1264
39.3 AN ELECTRON IN A FINITE WELL 1268
An Electron in a Finite Well 1268
39.4 TWO- AND THREE-DIMENSIONAL ELECTRON TRAPS 1270
More Electron Traps 1271
Two- and Three-Dimensional Electron Traps 1272
39.5 THE HYDROGEN ATOM 1275
The Hydrogen Atom Is an Electron Trap 1276
The Bohr Model of Hydrogen, a Lucky Break 1276
Schrödinger’s Equation and the Hydrogen Atom 1278
REVIEW & SUMMARY 1286 QUESTIONS 1287 PROBLEMS 1288
40 All About Atoms 1293
40.1 PROPERTIES OF ATOMS 1293
What Is Physics? 1294
Some Properties of Atoms 1294
Angular Momentum, Magnetic Dipole Moments 1296
40.2 THE STERN–GERLACH EXPERIMENT 1300
The Stern–Gerlach Experiment 1300
40.3 MAGNETIC RESONANCE 1303
Magnetic Resonance 1303
40.4 EXCLUSION PRINCIPLE AND MULTIPLE ELECTRONS IN A TRAP 1304
The Pauli Exclusion Principle 1304
Multiple Electrons in Rectangular Traps 1305
40.5 BUILDING THE PERIODIC TABLE 1308
Building the Periodic Table 1308
40.6 X RAYS AND THE ORDERING OF THE ELEMENTS 1310
X Rays and the Ordering of the Elements 1311
40.7 LASERS 1314
Lasers and Laser Light 1315
How Lasers Work 1316
REVIEW & SUMMARY 1319 QUESTIONS 1320
PROBLEMS 1321
41 Conduction of Electricity in Solids 1327
41.1 THE ELECTRICAL PROPERTIES OF METALS 1327
What Is Physics? 1328
The Electrical Properties of Solids 1328
Energy Levels in a Crystalline Solid 1329
Insulators 1330 Metals 1330
41.2 SEMICONDUCTORS AND DOPING 1336
Semiconductors 1337
Doped Semiconductors 1338
41.3 THE p-n JUNCTION AND THE TRANSISTOR 1341
The p-n Junction 1341
The Junction Rectifier 1343
The Light-Emitting Diode (LED) 1344
The Transistor 1345
REVIEW & SUMMARY 1346 QUESTIONS 1347 PROBLEMS 1348
42 Nuclear Physics 1352
42.1 DISCOVERING THE NUCLEUS 1352
What Is Physics? 1352
Discovering the Nucleus 1352
42.2 SOME NUCLEAR PROPERTIES 1355
Some Nuclear Properties 1356
42.3 RADIOACTIVE DECAY 1362
Radioactive Decay 1362
42.4 ALPHA DECAY 1365
Alpha Decay 1365
42.5 BETA DECAY 1368
Beta Decay 1368
42.6 RADIOACTIVE DATING 1371
Radioactive Dating 1371
42.7 MEASURING RADIATION DOSAGE 1372
Measuring Radiation Dosage 1372
42.8 NUCLEAR MODELS 1373
Nuclear Models 1373
REVIEW & SUMMARY 1376 QUESTIONS 1377
PROBLEMS 1378
43 Energy from the Nucleus 1385
43.1 NUCLEAR FISSION 1385
What Is Physics? 1385
Nuclear Fission: The Basic Process 1386
A Model for Nuclear Fission 1388
43.2 THE NUCLEAR REACTOR 1392
The Nuclear Reactor 1392
43.3 A NATURAL NUCLEAR REACTOR 1396
A Natural Nuclear Reactor 1396
43.4 THERMONUCLEAR FUSION: THE BASIC PROCESS 1398
Thermonuclear Fusion: The Basic Process 1398
43.5 THERMONUCLEAR FUSION IN THE SUN AND OTHER STARS 1400
Thermonuclear Fusion in the Sun and Other Stars 1400
43.6 CONTROLLED THERMONUCLEAR FUSION 1402
Controlled Thermonuclear Fusion 1402
REVIEW & SUMMARY 1405 QUESTIONS 1405
PROBLEMS 1406
44 Quarks, Leptons, and the Big Bang 1410
44.1 GENERAL PROPERTIES OF ELEMENTARY PARTICLES 1410
What Is Physics? 1410
Particles, Particles, Particles 1411
An Interlude 1415
44.2 LEPTONS, HADRONS, AND STRANGENESS 1419
The Leptons 1419
The Hadrons 1421
Still Another Conservation Law 1422
The Eightfold Way 1423
44.3 QUARKS AND MESSENGER PARTICLES 1425
The Quark Model 1425
The Basic Forces and Messenger Particles 1428
44.4 COSMOLOGY 1431
A Pause for Reflection 1431
The Universe Is Expanding 1432
The Cosmic Background Radiation 1433
Dark Matter 1434
The Big Bang 1434
A Summing Up 1437
REVIEW & SUMMARY 1438 QUESTIONS 1438
PROBLEMS 1439
APPENDICES
A The International System of Units (SI) A-1
B Some Fundamental Constants of Physics A-3
C Some Astronomical Data A-4
D Conversion Factors A-5
E Mathematical Formulas A-9
F Properties of the Elements A-12
G Periodic Table of the Elements A-15
ANSWERS
To Checkpoints and Odd-Numbered Questions and Problems AN-1
INDEX I-1
As requested by instructors, here is a new edition of the textbook originated by David Halliday and Robert Resnick in 1963 and that I used as a first-year student at MIT. (Gosh, time has flown by.)
Constructing this new edition allowed me to discover many delightful new examples and revisit a few favorites from my earlier eight editions. Here below are some highlights of this 12th edition.
Figure 10.39 What tension was required by the Achilles tendons in Michael Jackson in his gravitydefying 45º lean during his video Smooth Criminals?
Figure 34.5.4 In functional near infrared spectroscopy (fNIRS), a person wears a close-fitting cap with LEDs emitting in the near infrared range. The light can penetrate into the outer layer of the brain and reveal when that portion is activated by a given activity, from playing baseball to flying an airplane.
10.7.2 What is the increase in the tension of the Achilles tendons when high heels are worn?
Figure 9.65 Falling is a chronic and serious condition among skateboarders, in-line skaters, elderly people, people with seizures, and many others. Often, they fall onto one outstretched hand, fracturing the wrist. What fall height can result in such fracture?
Figure 28.5.2 Fast-neutron therapy is a promising weapon against salivary gland malignancies. But how can electrically neutral particles be accelerated to high speeds?
Figure 29.63 Parkinson’s disease and other brain disorders have been treated with transcranial magnetic stimulation in which pulsed magnetic fields force neurons several centimeters deep to discharge.
Figure 2.37 How should autonomous car B be programmed so that it can safely pass car A without being in danger from oncoming car C?
Figure 4.39 In a Pittsburgh left, a driver in the opposite lane anticipates the onset of the green light and rapidly pulls in front of your car during the red light. In a crash reconstruction, how soon before the green did the other driver start the turn?
Figure 9.6.4 The most dangerous car crash is a head-on crash. In a head-on crash of cars of identical mass, by how much does the probability of a fatality of a driver decrease if the driver has a passenger in the car?
Figure
Evgeniy
In addition, there are problems dealing with
• remote detection of the fall of an elderly person,
• the illusion of a rising fastball,
• hitting a fastball in spite of momentary vision loss,
• ship squat in which a ship rides lower in the water in a channel,
• the common danger of a bicyclist disappearing from view at an intersection,
• measurement of thunderstorm potentials with muons, and more.
WHAT’S IN THE BOOK
• Checkpoints, one for every module
• Sample problems
• Review and summary at the end of each chapter
• Nearly 300 new end-of-chapter problems
In constructing this new edition, I focused on several areas of research that intrigue me and wrote new text discussions and many new homework problems. Here are a few research areas:
We take a look at the first image of a black hole (for which I have waited my entire life), and then we examine gravitational waves (something I discussed with Rainer Weiss at MIT when I worked in his lab several years before he came up with the idea of using an interferometer as a wave detector).
I wrote a new sample problem and several homework problems on autonomous cars where a computer system must calculate safe driving procedures, such as passing a slow car with an oncoming car in the passing lane.
I explored cancer radiation therapy, including the use of Augur‐Meitner electrons that were first understood by Lise Meitner.
I combed through many thousands of medical, engineering, and physics research articles to find clever ways of looking inside the human body without major invasive surgery. Some are listed in the index under “medical procedures and equipment.” Here are three examples:
(1) Robotic surgery using single‐port incisions and optical fibers now allows surgeons to access internal organs, with patient recovery times of only hours instead of days or weeks as with previous surgery techniques.
(2) Transcranial magnetic stimulation is being used to treat chronic depression, Parkinson’s disease, and other brain malfunctions by applying pulsed magnetic fields from coils near the scalp to force neurons several centimeters deep to discharge.
(3) Magnetoencephalography (MEG) is being used to monitor a person’s brain as the person performs a task such as reading. The task causes weak electrical pulses to be sent along conducting paths between brain cells, and each pulse produces a weak magnetic field that is detected by extremely sensitive SQUIDs.
THE WILEYPLUS ADVANTAGE
WileyPLUS is a research-based online environment for effective teaching and learning. The customization features, quality question banks, interactive eTextbook, and analytical tools allow you to quickly create a customized course that tracks student learning trends. Your students can stay engaged and on track with the use of intuitive tools like the syncing calendar and the student mobile app. Wiley is committed to providing accessible resources to instructors and students. As such, all Wiley educational products and services are born accessible, designed for users of all abilities.
Links Between Homework Problems and Learning Objectives In WileyPLUS, every question and problem at the end of the chapter is linked to a learning objective, to answer the (usually unspoken) questions, “Why am I working this problem? What am I supposed to learn from it?” By being explicit about a problem’s purpose, I believe that a student might better transfer the learning objective to other problems with a different wording but the same key idea. Such transference would help defeat the common trouble that a student learns to work a particular problem but cannot then apply its key idea to a problem in a different setting.
Animations of one of the key figures in each chapter. Here in the book, those figures are flagged with the swirling icon. In the online chapter in WileyPLUS, a mouse click begins the animation. I have chosen the figures that are rich in information so that a student can see the physics in action and played out over a minute or two instead of just being flat on a printed page. Not only does this give life to the physics, but the animation can be repeated as many times as a student wants.
Video Illustrations David Maiullo of Rutgers University has created video versions of approximately 30 of the photographs and figures from the chapters. Much of physics is the study of things that move, and video can often provide better representation than a static photo or figure.
Videos I have made well over 1500 instructional videos, with more coming. Students can watch me draw or type on the screen as they hear me talk about a solution, tutorial, sample problem, or review, very much as they would experience were they sitting next to me in my office while I worked out something on a notepad. An instructor’s lectures and tutoring will always be the most valuable learning tools, but my videos are available 24 hours a day, 7 days a week, and can be repeated indefinitely.
• Video tutorials on subjects in the chapters. I chose the subjects that challenge the students the most, the ones that my students scratch their heads about.
• Video reviews of high school math, such as basic algebraic manipulations, trig functions, and simultaneous equations.
• Video introductions to math, such as vector multiplication, that will be new to the students.
• Video presentations of sample problems. My intent is to work out the physics, starting with the key ideas instead of just grabbing a formula. However, I also want to demonstrate how to read a sample problem, that is, how to read technical material to learn problem-solving procedures that can be transferred to other types of problems.
• Video solutions to 20% of the end-of chapter problems. The availability and timing of these solutions are controlled by the instructor. For example, they might be available after a homework deadline or a quiz. Each solution is not simply a plug-and-chug recipe. Rather I build a solution from the key ideas to the first step of reasoning and to a final solution. The student learns not just how to solve a particular problem but how to tackle any problem, even those that require physics courage
• Video examples of how to read data from graphs (more than simply reading off a number with no comprehension of the physics).
• Many of the sample problems in the textbook are available online in both reading and video formats
Problem-Solving Help I have written a large number of resources for WileyPLUS designed to help build the students’ problem-solving skills.
• Hundreds of additional sample problems. These are available as stand-alone resources but (at the discretion of the instructor) they are also linked out of the homework problems. So, if a homework problem deals with, say, forces on a block on a ramp, a link to a related sample problem is provided. However, the sample problem is not just a replica of the homework problem and thus does not provide a solution that can be merely duplicated without comprehension.
• GO Tutorials for 15% of the end-of-chapter homework problems. In multiple steps, I lead a student through a homework problem, starting with the key ideas and giving hints when wrong answers are submitted. However, I purposely leave the last step (for the final answer) to the students so that they are responsible at the end. Some online tutorial systems trap a student when wrong answers are given, which can generate a lot of frustration. My GO Tutorials are not traps, because at any step along the way, a student can return to the main problem.
• Hints on every end-of-chapter homework problem are available (at the discretion of the instructor). I wrote these as true hints about the main ideas and the general procedure for a solution, not as recipes that provide an answer without any comprehension.
• Pre-lecture videos. At an instructor’s discretion, a pre-lecture video is available for every module. Also, assignable questions are available to accompany these videos. The videos were produced by Melanie Good of the University of Pittsburgh.
Evaluation Materials
• Pre-lecture reading questions are available in WileyPLUS for each chapter section. I wrote these so that they do not require analysis or any deep understanding; rather they simply test whether a student has read the section. When a student opens up a section, a randomly chosen reading question (from a bank of questions) appears at the end. The instructor can decide whether the question is part of the grading for that section or whether it is just for the benefit of the student.
• Checkpoints are available within each chapter module. I wrote these so that they require analysis and decisions about the physics in the section. Answers are provided in the back of the book.
• All end-of-chapter homework problems (and many more problems) are available in WileyPLUS. The instructor can construct a homework assignment and control how it is graded when the answers are submitted online. For example, the instructor controls the deadline for submission and how many attempts a student is allowed on an answer. The instructor also controls which, if any, learning aids are available with each homework problem. Such links can include hints, sample problems, in-chapter reading materials, video tutorials, video math reviews, and even video solutions (which can be made available to the students after, say, a homework deadline).
• Symbolic notation problems that require algebraic answers are available in every chapter.
• All end-of-chapter homework questions are available for assignment in WileyPLUS. These questions (in a multiple-choice format) are designed to evaluate the students’ conceptual understanding.
• Interactive Exercises and Simulations by Brad Trees of Ohio Wesleyan University. How do we help students understand challenging concepts in physics? How do we motivate students to engage with core content in a meaningful way? The simulations are intended to address these key questions. Each module in the Etext is linked to one or more simulations that convey concepts visually. A simulation depicts a physical situation in which time dependent phenomena are animated and information is presented in multiple representations including a visual representation of the physical system as well as a plot of related variables. Often, adjustable parameters allow the user to change a property of the system and to see the effects of that change on the subsequent behavior. For visual learners, the simulations provide an opportunity to “see” the physics in action. Each simulation is also linked to a set of interactive exercises, which guide the student through a deeper interaction with the physics underlying the simulation. The exercises consist of a series of practice questions with feedback and detailed solutions. Instructors may choose to assign the exercises for practice, to recommend the exercises to students as additional practice, and to show individual simulations during class time to demonstrate a concept and to motivate class discussion.
Icons for Additional Help When worked-out solutions are provided either in print or electronically for certain of the odd-numbered problems, the statements for those problems include an icon to alert both student and instructor. There are also icons indicating which problems have a GO Tutorial or a link to the The Flying Circus of Physics, which require calculus, and which involve a biomedical application. An icon guide is provided here and at the beginning of each set of problems.
FUNDAMENTALS OF PHYSICS—FORMAT OPTIONS
Fundamentals of Physics was designed to optimize students’ online learning experience. We highly recommend that students use the digital course within WileyPLUS as their primary course material. Here are students’ purchase options:
• 12th Edition WileyPLUS course
• Fundamentals of Physics Looseleaf Print Companion bundled with WileyPLUS Tutoring problem available (at instructor’s discretion) in WileyPLUS
• Fundamentals of Physics volume 1 bundled with WileyPLUS
• Fundamentals of Physics volume 2 bundled with WileyPLUS
• Fundamentals of Physics Vitalsource Etext
SUPPLEMENTARY MATERIALS AND ADDITIONAL RESOURCES
Supplements for the instructor can be obtained online through WileyPLUS or by contacting your Wiley representative. The following supplementary materials are available for this edition:
Instructor’s Solutions Manual by Sen-Ben Liao, Lawrence Livermore National Laboratory. This manual provides worked-out solutions for all problems found at the end of each chapter. It is available in both MSWord and PDF.
• Instructor’s Manual This resource contains lecture notes outlining the most important topics of each chapter; demonstration experiments; laboratory and computer projects; film and video sources; answers to all questions, exercises, problems, and checkpoints; and a correlation guide to the questions, exercises, and problems in the previous edition. It also contains a complete list of all problems for which solutions are available to students.
• Classroom Response Systems (“Clicker”) Questions by David Marx, Illinois State University. There are two sets of questions available: Reading Quiz questions and Interactive Lecture questions.The Reading Quiz questions are intended to be relatively straightforward for any student who reads the assigned material. The Interactive Lecture questions are intended for use in an interactive lecture setting.
• Wiley Physics Simulations by Andrew Duffy, Boston University and John Gastineau, Vernier Software. This is a collection of 50 interactive simulations (Java applets) that can be used for classroom demonstrations.
• Wiley Physics Demonstrations by David Maiullo, Rutgers University. This is a collection of digital videos of 80 standard physics demonstrations. They can be shown in class or accessed from WileyPLUS. There is an accompanying Instructor’s Guide that includes “clicker” questions.
• Test Bank by Suzanne Willis, Northern Illinois University. The Test Bank includes nearly 3,000 multiple-choice questions. These items are also available in the Computerized Test Bank, which provides full editing features to help you customize tests (available in both IBM and Macintosh versions).
• All text illustrations suitable for both classroom projection and printing.
• Lecture PowerPoint Slides These PowerPoint slides serve as a helpful starter pack for instructors, outlining key concepts and incorporating figures and equations from the text.
STUDENT SUPPLEMENTS
Student Solutions Manual (ISBN 9781119455127) by Sen-Ben Liao, Lawrence Livermore National Laboratory. This manual provides students with complete worked-out solutions to 15 percent of the problems found at the end of each chapter within the text. The Student Solutions Manual for the 12th edition is written using an innovative approach called TEAL, which stands for Think, Express, Analyze, and Learn. This learning strategy was originally developed at the Massachusetts Institute of Technology and has proven to be an effective learning tool for students. These problems with TEAL solutions are indicated with an SSM icon in the text.
Introductory Physics with Calculus as a Second Language (ISBN 9780471739104) Mastering Problem Solving by Thomas Barrett of Ohio State University. This brief paperback teaches the student how to approach problems more efficiently and effectively. The student will learn how to recognize common patterns in physics problems, break problems down into manageable steps, and apply appropriate techniques. The book takes the student step by step through the solutions to numerous examples.
A great many people have contributed to this book. Sen-Ben Liao of Lawrence Livermore National Laboratory, James Whitenton of Southern Polytechnic State University, and Jerry Shi of Pasadena City College performed the Herculean task of working out solutions for every one of the homework problems in the book. At John Wiley publishers, the book received support from John LaVacca and Jennifer Yee, the editors who oversaw the entire project from start to finish, as well as Senior Managing Editor Mary Donovan and Editorial Assistant Samantha Hart. We thank Patricia Gutierrez and the Lumina team, for pulling all the pieces together during the complex production process, and Course Developers Corrina Santos and Kimberly Eskin, for masterfully developing the WileyPLUS course and online resources, We also thank Jon Boylan for the art and cover design; Helen Walden for her copyediting; and Donna Mulder for her proofreading.
Finally, our external reviewers have been outstanding and we acknowledge here our debt to each member of that team.
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21.1 COULOMB’S LAW
Learning Objectives
After reading this module, you should be able to . . .
21.1.1 Distinguish between being electrically neutral, negatively charged, and positively charged and identify excess charge.
21.1.2 Distinguish between conductors, nonconductors (insulators), semiconductors, and superconductors.
21.1.3 Describe the electrical properties of the particles inside an atom.
21.1.4 Identify conduction electrons and explain their role in making a conducting object negatively or positively charged.
21.1.5 Identify what is meant by “electrically isolated” and by “grounding.”
21.1.6 Explain how a charged object can set up induced charge in a second object.
21.1.7 Identify that charges with the same electrical sign repel each other and those with opposite electrical signs attract each other.
21.1.8 For either of the particles in a pair of charged particles, draw a free-body diagram, showing the electrostatic force (Coulomb force) on it and anchoring the tail of the force vector on that particle.
21.1.9 For either of the particles in a pair of charged particles, apply Coulomb’s law to relate the magnitude of the electrostatic force, the charge magnitudes of the particles, and the separation between the particles.
Key Ideas
● The strength of a particle’s electrical interaction with objects around it depends on its electric charge (usually represented as q), which can be either positive or negative. Particles with the same sign of charge repel each other, and particles with opposite signs of charge attract each other.
● An object with equal amounts of the two kinds of charge is electrically neutral, whereas one with an imbalance is electrically charged and has an excess charge.
21.1.10 Identify that Coulomb’s law applies only to (point-like) particles and objects that can be treated as particles.
21.1.11 If more than one force acts on a particle, find the net force by adding all the forces as vectors, not scalars.
21.1.12 Identify that a shell of uniform charge attracts or repels a charged particle that is outside the shell as if all the shell’s charge were concentrated as a particle at the shell’s center.
21.1.13 Identify that if a charged particle is located inside a shell of uniform charge, there is no net electrostatic force on the particle from the shell.
21.1.14 Identify that if excess charge is put on a spherical conductor, it spreads out uniformly over the external surface area.
21.1.15 Identify that if two identical spherical conductors touch or are connected by conducting wire, any excess charge will be shared equally.
21.1.16 Identify that a nonconducting object can have any given distribution of charge, including charge at interior points.
21.1.17 Identify current as the rate at which charge moves through a point.
21.1.18 For current through a point, apply the relationship between the current, a time interval, and the amount of charge that moves through the point in that time interval.
● Conductors are materials in which a significant number of electrons are free to move. The charged particles in nonconductors (insulators) are not free to move.
● Electric current i is the rate dq/dt at which charge passes a point: i = dq dt .
● Coulomb’s law describes the electrostatic force (or electric force) between two charged particles. If the
particles have charges q1 and q2, are separated by distance r, and are at rest (or moving only slowly) relative to each other, then the magnitude of the force acting on each due to the other is given by
(Coulomb’s law),
where ε0 = 8.85 × 10 12 C2/N · m2 is the permittivity constant. The ratio 1/4πε0 is often replaced with the electrostatic constant (or Coulomb constant) k = 8.99 × 109 N · m2/C2.
● The electrostatic force vector acting on a charged particle due to a second charged particle is either directly toward the second particle (opposite signs
of charge) or directly away from it (same sign of charge).
● If multiple electrostatic forces act on a particle, the net force is the vector sum (not scalar sum) of the individual forces.
● Shell theorem 1: A charged particle outside a shell with charge uniformly distributed on its surface is attracted or repelled as if the shell’s charge were concentrated as a particle at its center.
● Shell theorem 2: A charged particle inside a shell with charge uniformly distributed on its surface has no net force acting on it due to the shell.
● Charge on a conducting spherical shell spreads uniformly over the (external) surface.
What Is Physics?
You are surrounded by devices that depend on the physics of electromagnetism, which is the combination of electric and magnetic phenomena. This physics is at the root of computers, television, radio, telecommunications, household lighting, and even the ability of food wrap to cling to a container. This physics is also the basis of the natural world. Not only does it hold together all the atoms and molecules in the world, it also produces lightning, auroras, and rainbows.
The physics of electromagnetism was first studied by the early Greek philosophers, who discovered that if a piece of amber is rubbed and then brought near bits of straw, the straw will jump to the amber. We now know that the attraction between amber and straw is due to an electric force. The Greek philosophers also discovered that if a certain type of stone (a naturally occurring magnet) is brought near bits of iron, the iron will jump to the stone. We now know that the attraction between magnet and iron is due to a magnetic force.
From these modest origins with the Greek philosophers, the sciences of electricity and magnetism developed separately for centuries—until 1820, in fact, when Hans Christian Oersted found a connection between them: An electric current in a wire can deflect a magnetic compass needle. Interestingly enough, Oersted made this discovery, a big surprise, while preparing a lecture demonstration for his physics students.
The new science of electromagnetism was developed further by workers in many countries. One of the best was Michael Faraday, a truly gifted experimenter with a talent for physical intuition and visualization. That talent is attested to by the fact that his collected laboratory notebooks do not contain a single equation. In the mid-nineteenth century, James Clerk Maxwell put Faraday’s ideas into mathematical form, introduced many new ideas of his own, and put electromagnetism on a sound theoretical basis.
Our discussion of electromagnetism is spread through the next 16 chapters. We begin with electrical phenomena, and our first step is to discuss the nature of electric charge and electric force.
Figure 21.1.1 (a) The two glass rods were each rubbed with a silk cloth and one was suspended by thread. When they are close to each other, they repel each other. (b) The plastic rod was rubbed with fur. When brought close to the glass rod, the rods attract each other.
Electric Charge
Here are two demonstrations that seem to be magic, but our job here is to make sense of them. After rubbing a glass rod with a silk cloth (on a day when the humidity is low), we hang the rod by means of a thread tied around its center (Fig. 21.1.la). Then we rub a second glass rod with the silk cloth and bring it near
the hanging rod. The hanging rod magically moves away. We can see that a force repels it from the second rod, but how? There is no contact with that rod, no breeze to push on it, and no sound wave to disturb it.
In the second demonstration we replace the second rod with a plastic rod that has been rubbed with fur. This time, the hanging rod moves toward the nearby rod (Fig. 21.1.1b). Like the repulsion, this attraction occurs without any contact or obvious communication between the rods.
In the next chapter we shall discuss how the hanging rod knows of the presence of the other rods, but in this chapter let’s focus on just the forces that are involved. In the first demonstration, the force on the hanging rod was repulsive, and in the second, attractive. After a great many investigations, scientists figured out that the forces in these types of demonstrations are due to the electric charge that we set up on the rods when they are in contact with silk or fur. Electric charge is an intrinsic property of the fundamental particles that make up objects such as the rods, silk, and fur. That is, charge is a property that comes automatically with those particles wherever they exist.
Two Types. There are two types of electric charge, named by the American scientist and statesman Benjamin Franklin as positive charge and negative charge. He could have called them anything (such as cherry and walnut), but using algebraic signs as names comes in handy when we add up charges to find the net charge. In most everyday objects, such as a mug, there are about equal numbers of negatively charged particles and positively charged particles, and so the net charge is zero, the charge is said to be balanced, and the object is said to be electrically neutral (or just neutral for short).
Excess Charge. Normally you are approximately neutral. However, if you live in regions where the humidity is low, you know that the charge on your body can become slightly unbalanced when you walk across certain carpets. Either you gain negative charge from the carpet (at the points of contact between your shoes with the carpet) and become negatively charged, or you lose negative charge and become positively charged. Either way, the extra charge is said to be an excess charge. You probably don’t notice it until you reach for a door handle or another person. Then, if your excess charge is enough, a spark leaps between you and the other object, eliminating your excess charge. Such sparking can be annoying and even somewhat painful. Such charging and discharging do not happen in humid conditions because the water in the air neutralizes your excess charge about as fast as you acquire it.
Two of the grand mysteries in physics are (1) why does the universe have particles with electric charge (what is it, really?) and (2) why does electric charge come in two types (and not, say, one type or three types). We are still working on the answers. Nevertheless, with lots of experiments similar to our two demonstrations scientists discovered that
Particles with the same sign of electrical charge repel each other, and particles with opposite signs attract each other.
In a moment we shall put this rule into quantitative form as Coulomb’s law of electrostatic force (or electric force) between charged particles. The term electrostatic is used to emphasize that, relative to each other, the charges are either stationary or moving only very slowly.
Demos. Now let’s get back to the demonstrations to understand the motions of the rod as being something other than just magic. When we rub the glass rod with a silk cloth, a small amount of negative charge moves from the rod to the silk (a transfer like that between you and a carpet), leaving the rod with a small amount of excess positive charge. (Which way the negative charge moves is not obvious and requires a lot of experimentation.) We rub the silk over the rod to increase the number of contact points and thus the amount, still tiny, of transferred charge. We hang the rod from the thread so as to electrically isolate it from
Figure 21.1.2 (a) Two charged rods of the same sign repel each other. (b) Two charged rods of opposite signs attract each other. Plus signs indicate a positive net charge, and minus signs indicate a negative net charge.
its surroundings (so that the surroundings cannot neutralize the rod by giving it enough negative charge to rebalance its charge). When we rub the second rod with the silk cloth, it too becomes positively charged. So when we bring it near the first rod, the two rods repel each other (Fig. 21.1.2a).
Next, when we rub the plastic rod with fur, it gains excess negative charge from the fur. (Again, the transfer direction is learned through many experiments.) When we bring the plastic rod (with negative charge) near the hanging glass rod (with positive charge), the rods are attracted to each other (Fig. 21.1.2b). All this is subtle. You cannot see the charge or its transfer, only the results.
Conductors and Insulators
We can classify materials generally according to the ability of charge to move through them. Conductors are materials through which charge can move rather freely; examples include metals (such as copper in common lamp wire), the human body, and tap water. Nonconductors—also called insulators—are materials through which charge cannot move freely; examples include rubber (such as the insulation on common lamp wire), plastic, glass, and chemically pure water. Semiconductors are materials that are intermediate between conductors and insulators; examples include silicon and germanium in computer chips. Superconductors are materials that are perfect conductors, allowing charge to move without any hindrance. In these chapters we discuss only conductors and insulators.
Conducting Path. Here is an example of how conduction can eliminate excess charge on an object. If you rub a copper rod with wool, charge is transferred from the wool to the rod. However, if you are holding the rod while also touching a faucet connected to metal piping, you cannot charge the rod in spite of the transfer. The reason is that you, the rod, and the faucet are all conductors connected, via the plumbing, to Earth’s surface, which is a huge conductor. Because the excess charges put on the rod by the wool repel one another, they move away from one another by moving first through the rod, then through you, and then through the faucet and plumbing to reach Earth’s surface, where they can spread out. The process leaves the rod electrically neutral.
In thus setting up a pathway of conductors between an object and Earth’s surface, we are said to ground the object, and in neutralizing the object (by eliminating an unbalanced positive or negative charge), we are said to discharge the object. If instead of holding the copper rod in your hand, you hold it by an insulating handle, you eliminate the conducting path to Earth, and the rod can then be charged by rubbing (the charge remains on the rod), as long as you do not touch it directly with your hand.
Charged Particles. The properties of conductors and insulators are due to the structure and electrical nature of atoms. Atoms consist of positively charged protons, negatively charged electrons, and electrically neutral neutrons. The protons and neutrons are packed tightly together in a central nucleus
Figure 21 1 3 A neutral copper rod is electrically isolated from its surroundings by being suspended on a nonconducting thread. Either end of the copper rod will be attracted by a charged rod. Here, conduction electrons in the copper rod are repelled to the far end of that rod by the negative charge on the plastic rod. Then that negative charge attracts the remaining positive charge on the near end of the copper rod, rotating the copper rod to bring that near end closer to the plastic rod.
The charge of a single electron and that of a single proton have the same magnitude but are opposite in sign. Hence, an electrically neutral atom contains equal numbers of electrons and protons. Electrons are held near the nucleus because they have the electrical sign opposite that of the protons in the nucleus and thus are attracted to the nucleus. Were this not true, there would be no atoms and thus no you.
When atoms of a conductor like copper come together to form the solid, some of their outermost (and so most loosely held) electrons become free to wander about within the solid, leaving behind positively charged atoms ( positive ions). We call the mobile electrons conduction electrons. There are few (if any) free electrons in a nonconductor.
Induced Charge. The experiment of Fig. 21.1.3 demonstrates the mobility of charge in a conductor. A negatively charged plastic rod will attract either end
of an isolated neutral copper rod. What happens is that many of the conduction electrons in the closer end of the copper rod are repelled by the negative charge on the plastic rod. Some of the conduction electrons move to the far end of the copper rod, leaving the near end depleted in electrons and thus with an unbalanced positive charge. This positive charge is attracted to the negative charge in the plastic rod. Although the copper rod is still neutral, it is said to have an induced charge, which means that some of its positive and negative charges have been separated due to the presence of a nearby charge.
Similarly, if a positively charged glass rod is brought near one end of a neutral copper rod, induced charge is again set up in the neutral copper rod but now the near end gains conduction electrons, becomes negatively charged, and is attracted to the glass rod, while the far end is positively charged.
Note that only conduction electrons, with their negative charges, can move; positive ions are fixed in place. Thus, an object becomes positively charged only through the removal of negative charges
Blue Flashes from a Wintergreen Candy
Indirect evidence for the attraction of charges with opposite signs can be seen with a wintergreen LifeSaver (the candy shaped in the form of a marine lifesaver). If you adapt your eyes to darkness for about 15 minutes and then have a friend chomp on a piece of the candy in the darkness, you will see a faint blue flash from your friend’s mouth with each chomp. Whenever a chomp breaks a sugar crystal into pieces, each piece will probably end up with a different number of electrons. Suppose a crystal breaks into pieces A and B, with A ending up with more electrons on its surface than B (Fig. 21.1.4). This means that B has positive ions (atoms that lost electrons to A) on its surface. Because the electrons on A are strongly attracted to the positive ions on B, some of those electrons jump across the gap between the pieces.
As A and B move away from each other, air (primarily nitrogen, N2) flows into the gap, and many of the jumping electrons collide with nitrogen molecules in the air, causing the molecules to emit ultraviolet light. You cannot see this type of light. However, the wintergreen molecules on the surfaces of the candy pieces absorb the ultraviolet light and then emit blue light, which you can see—it is the blue light coming from your friend’s mouth. FCP
Coulomb’s Law
Now we come to the equation for Coulomb’s law, but first a caution. This equation works for only charged particles (and a few other things that can be treated as particles). For extended objects, with charge located in many different places, we need more powerful techniques. So, here we consider just charged particles and not, say, two charged cats.
If two charged particles are brought near each other, they each exert an electrostatic force on the other. The direction of the force vectors depends on the signs of the charges. If the particles have the same sign of charge, they repel each other. That means that the force vector on each is directly away from the other particle (Figs. 21.1.5a and b). If we release the particles, they accelerate away from each other. If, instead, the particles have opposite signs of charge, they attract each other. That means that the force vector on each is directly toward the other particle (Fig. 21.1.5c). If we release the particles, they accelerate toward each other.
The equation for the electrostatic forces acting on the particles is called Coulomb’s law after Charles-Augustin de Coulomb, whose experiments in 1785 led him to it. Let’s write the equation in vector form and in terms of the particles shown in Fig. 21.1.6, where particle 1 has charge q1 and particle 2 has charge q2.
Figure 21.1.4 Two pieces of a wintergreen candy as they fall away from each other. Electrons jumping from the negative surface of piece A to the positive surface of piece B collide with nitrogen (N2) molecules in the air.
Always draw the force vector with the tail on the particle.
The forces push the particles apart.
Here too.
But here the forces pull the particles together.
Figure 21.1.5 Two charged particles repel each other if they have the same sign of charge, either (a) both positive or (b) both negative. (c) They attract each other if they have opposite signs of charge.
Figure 21.1.6 The electrostatic force on particle 1 can be described in terms of a unit vector r along an axis through the two particles, radially away from particle 2.
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Now then, notice this. About the end of August, 1846, a change came over me and I resolved to lead a better life, so I reformed; but it was just as well, anyway, because they had got to having guns and dogs both. Although I was reformed, the perturbations did not stop! Does that strike you? They did not stop, they went right on and on and on, for three weeks, clear up to the 23d of September; then Neptune was discovered and the whole mystery stood explained. It shows that I am so sensitively constructed that I perturbate when any other planet is disturbed. This has been going on all my life. It only happens in the watermelon season, but that has nothing to do with it, and has no significance: geologists and anthropologists and horticulturists all tell me it is only ancestral and hereditary, and that is what I think myself. Now then, I got to perturbating again, this summer-all summer through; all through watermelon time: and where, do you think? Up here on my farm in Connecticut. Is that significant? Unquestionably it is, for you couldn’t raise a watermelon on this farm with a derrick.
That perturbating was caused by the new planet. That Washington Observatory may throw as much doubt as it wants to, it cannot affect me, because I know there is a new planet. I know it because I don’t perturbate for nothing. There has got to be a dog or a planet, one or the other; and there isn’t any dog around here, so there’s got to be a planet. I hope it is going to be named after me; I should just love it if I can’t have a constellation.
MARJORIE FLEMING, THE WONDER CHILD
Marjorie has been in her tiny grave a hundred years; and still the tears fall for her, and will fall. What an intensely human little creature she was! How vividly she lived her small life; how impulsive she was; how sudden, how tempestuous, how tender, how loving, how sweet, how loyal, how rebellious, how repentant, how wise, how unwise, how bursting with fun, how frank, how free, how honest, how innocently bad, how natively good, how charged with quaint philosophies, how winning, how precious, how adorable--and how perennially and indestructibly interesting! And all this exhibited, proved, and recorded before she reached the end of her ninth year and “fell on sleep.”
Geographically considered, the lassie was a Scot; but in fact she had no frontiers, she was the world’s child, she was the human race in little. It is one of the prides of my life that the first time I ever heard her name it came from the lips of Dr. John Brown--his very own self--Dr. John Brown of Edinburgh--Dr. John Brown of Rab and His Friends--Dr. John Brown of the beautiful face and the sweet spirit, whose friends loved him with a love that was worship--Dr. John Brown, who was Marjorie’s biographer, and who had clasped an aged hand that had caressed Marjorie’s fifty years before, thus linking me with that precious child by an unbroken chain of handshakes, for I had shaken hands with Dr. John. This was in Edinburgh thirty-six years ago. He gave my wife his little biography of Marjorie, and I have it yet.
Is Marjorie known in America? No--at least to only a few. When Mr L. MacBean’s new and enlarged and charming
biography[17] of her was published five years ago it was sent over here in sheets, the market not being large enough to justify recomposing and reprinting it on our side of the water. I find that there are even cultivated Scotchmen among us who have not heard of Marjorie Fleming.
She was born in Kirkcaldy in 1803, and she died when she was eight years and eleven months old. By the time she was five years old she was become a devourer of various kinds of literature--both heavy and light--and was also become a quaint and free-spoken and charming little thinker and philosopher whose views were a delightful jumble of first-hand cloth of gold and second-hand rags.
When she was six she opened up that rich mine, her journals, and continued to work it by spells during the remainder of her brief life. She was a pet of Walter Scott, from the cradle, and when he could have her society for a few hours he was content, and required no other. Her little head was full of noble passages from Shakespeare and other favorites of hers, and the fact that she could deliver them with moving effect is proof that her elocution was a born gift with her, and not a mechanical reproduction of somebody else’s art, for a child’s parrot-work does not move. When she was a little creature of seven years, Sir Walter Scott “would read ballads to her in his own glorious way, the two getting wild with excitement over them; and he would take her on his knee and make her repeat Constance’s speeches in King John till he swayed to and fro, sobbing his fill.”
[Dr. John Brown.]
“Sobbing his fill”--that great man--over that little thing’s inspired interpretations. It is a striking picture; there is no mate to it. Sir Walter said of her:
“She’s the most extraordinary creature I ever met with, and her repeating of Shakespeare overpowers me as nothing else does.”
She spent the whole of her little life in a Presbyterian heaven; yet she was not affected by it; she could not have been happier if she had been in the other heaven.
She was made out of thunderstorms and sunshine, and not even her little perfunctory pieties and shop-made holiness could
squelch her spirits or put out her fires for long. Under pressure of a pestering sense of duty she heaves a shovelful of trade godliness into her journals every little while, but it does not offend, for none of it is her own; it is all borrowed, it is a convention, a custom of her environment, it is the most innocent of hypocrisies, and this tainted butter of hers soon gets to be as delicious to the reader as are the stunning and worldly sincerities she splatters around it every time her pen takes a fresh breath. The adorable child! she hasn’t a discoverable blemish in her make-up anywhere.
Marjorie’s first letter was written before she was six years old; it was to her cousin, Isa Keith, a young lady of whom she was passionately fond. It was done in a sprawling hand, ten words to the page--and in those foolscap days a page was a spacious thing:
“M D I --
“I now sit down on my botom to answer all the kind & beloved letters which you was so so good as to write to me. This is the first time I ever wrote a letter in my life.
“Miss Potune, a lady of my acquaintance, praises me dreadfully. I repeated something out of Deen Swift & she said I was fit for the stage, & you may think I was primmed up with majestick Pride, but upon my word I felt myself turn a little birsay-birsay is a word which is a word that William composed which is as you may suppose a little enraged. This horid fat Simpliton says that my Aunt is beautifull which is intirely impossible for that is not her nature.”
Frank? Yes, Marjorie was that. And during the brief moment that she enchanted this dull earth with her presence she was the bewitchingest speller and punctuator in all Christendom.
The average child of six “prints” its correspondence in rickety and reeling Roman capitals, or dictates to mamma, who puts the little chap’s message on paper. The sentences are labored, repetitious, and slow; there are but three or four of them; they deal in information solely, they contain no ideas, they venture no
judgments, no opinions; they inform papa that the cat has had kittens again; that Mary has a new doll that can wink; that Tommy has lost his top; and will papa come soon and bring the writer something nice? But with Marjorie it is different.
She needs no amanuensis, she puts her message on paper herself; and not in weak and tottering Roman capitals, but in a thundering hand that can be heard a mile and be read across the square without glasses. And she doesn’t have to study, and puzzle, and search her head for something to say; no, she had only to connect the pen with the paper and turn on the current; the words spring forth at once, and go chasing after each other like leaves dancing down a stream. For she has a faculty, has Marjorie! Indeed yes; when she sits down on her bottom to do a letter, there isn’t going to be any lack of materials, nor of fluency, and neither is her letter going to be wanting in pepper, or vinegar, or vitriol, or any of the other condiments employed by genius to save a literary work of art from flatness and vapidity. And as for judgments and opinions, they are as commodiously in her line as they are in the Lord Chief Justice’s. They have weight, too, and are convincing: for instance, for thirty-six years they have damaged that “horid Simpliton” in my eyes; and, more than that, they have even imposed upon me--and most unfairly and unwarrantably--an aversion to the horid fat Simpliton’s name; a perfectly innocent name, and yet, because of the prejudice against it with which this child has poisoned my mind for a generation I cannot see “Potune” on paper and keep my gorge from rising.
In her journals Marjorie changes her subject whenever she wants to--and that is pretty often. When the deep moralities pay her a passing visit she registers them. Meantime if a cherished love passage drifts across her memory she shoves it into the midst of the moralities--it is nothing to her that it may not feel at home there:
“We should not be happy at the death of our fellow creatures, for they love life like us love your neighbor & he will love you Bountifulness and Mercifulness are always rewarded. In my travels I met with a handsome lad named Charles Balfour Esge
[Esqr.] and from him I got offers of marage--ofers of marage did I say? nay plainly [he] loved me. Goodness does not belong to the wicked but badness dishonor befals wickedness but not virtue, no disgrace befals virtue perciverence overcomes almost al difficulties no I am rong in saying almost I should say always as it is so perciverence is a virtue my Csosin says pacience is a cristain virtue, which is true.”
She is not copying these profundities out of a book, she is getting them out of her memory; her spelling shows that the book is not before her The easy and effortless flow of her talk is a marvelous thing in a baby of her age. Her interests are as wide and varied as a grown person’s: she discusses all sorts of books, and fearlessly delivers judgment upon them; she examines whomsoever crosses the field of her vision, and again delivers a verdict; she dips into religion and history, and even into politics; she takes a shy at the news of the day, and comments upon it; and now and then she drops into poetry--into rhyme, at any rate.
Marjorie would not intentionally mislead anyone, but she has just been making a remark which moves me to hoist a dangersignal for the protection of the modern reader. It is this one: “In my travels.” Naturally we are apt to clothe a word with its present-day meaning--the meaning we are used to, the meaning we are familiar with; and so--well, you get the idea: some words that are giants to-day were very small dwarfs a century ago, and if we are not careful to take that vast enlargement into account when we run across them in the literatures of the past, they are apt to convey to us a distinctly wrong impression. To-day, when a person says “in my travels” he means that he has been around the globe nineteen or twenty times, and we so understand him; and so, when Marjorie says it, it startles us for a moment, for it gives us the impression that she has been around it fourteen or fifteen times; whereas, such is not at all the case. She has traveled prodigiously for her day, but not for ours. She had “traveled,” altogether, three miles by land and eight by water--per ferryboat. She is fairly and justly proud of it, for it is the exact equivalent, in grandeur and impressiveness, in the case of a
child of our day, to two trips across the Atlantic and a thousand miles by rail.
“In the love novels all the heroins are very desperate Isabella will not allow me to speak about lovers and heroins, and tiss too refined for my taste a loadstone is a curous thing indeed it is true Heroic love doth never win disgrace this is my maxum and I will follow it forever Miss Eguards [Edgeworth] tails are very good particularly some that are very much adopted for youth as Lazy Lawrence Tarelton False Key &c &c Persons of the parlement house are as I think caled Advocakes Mr Cay & Mr Crakey has that honour. This has been a very mild winter. Mr Banestors Budget is to-night I hope it will be a good one. A great many authors have expressed themselfs too sentimentaly.... The Mercandile Afares are in a perilous situation sickness & a delicante frame I have not & I do not know what it is, but Ah me perhaps I shall have it.[18] Grandure reigns in Edinburgh.... Tomson is a beautifull author and Pope but nothing is like Shakepear of which I have a little knolegde of. An unfortunate death James the 5 had for he died of greif Macbeth is a pretty composition but awful one Macbeth is so bad & wicked, but Lady Macbeth is so hardened in guilt she does not mind her sins & faults No.
“... A sailor called here to say farewell, it must be dreadful to leave his native country where he might get a wife or perhaps me, for I love him very much & with all my heart, but O I forgot Isabella forbid me to speak about love.... I wish everybody would follow her example & be as good as pious & virtious as she is & they would get husbands soon enough, love is a parithatick [pathetic] thing as well as troublesome & tiresome but O Isabella forbid me to speak about it.”
But the little rascal can’t keep from speaking about it, because it is her supreme interest in life; her heart is not capacious enough to hold all the product that is engendered by the everrecurring inflaming spectacle of man-creatures going by, and the surplus is obliged to spill over; Isa’s prohibitions are no sufficient dam for such a discharge.
“Love I think is the fasion for everybody is marring [marrying].... Yesterday a marrade man named Mr John Balfour Esg [Esq.] offered to kiss me, & offered to marry me though the man was espused [espoused], & his wife was present & said he must ask her permission but he did not, I think he was ashamed or confounded before 3 gentleman Mr Jobson and two Mr Kings.”
I must make room here for another of Marjorie’s second-hand high-morality outbreaks. They give me a sinful delight which I ought to grieve at, I suppose, but I can’t seem to manage it:
“James Macary is to be transported for murder in the flower of his youth O passion is a terible thing for it leads people from sin to sin at last it gets so far as to come to greater crimes than we thought we could comit and it must be dreadful to leave his native country and his friends and to be so disgraced and affronted.”
That is Marjorie talking shop, dear little diplomat--to please and comfort mamma and Isa, no doubt.
This wee little child has a marvelous range of interests. She reads philosophies, novels, baby books, histories, the mighty poets--reads them with burning interest, and frankly and freely criticizes them all; she revels in storms, sunsets, cloud effects, scenery of mountain, plain, ocean, and forest, and all the other wonders of nature, and sets down her joy in them all; she loves people, she detests people, according to mood and circumstances, and delivers her opinion of them, sometimes seasoned with attar of roses, sometimes with vitriol; in games, and all kinds of childish play she is an enthusiast; she adores animals, adores them all; none is too forlorn to fail of favor in her friendly eyes, no creature so humble that she cannot find something in it on which to lavish her caressing worship.
“I am going to-morrow to a delightfull place, Braehead by name, belonging to Mrs. Crraford [Crauford], where there is ducks cocks hens bobblyjocks 2 dogs 2 cats and swine which is delightful. I think it is shocking to think that the dog and cat should bear them and they are drowned after all.”
She is a dear child, a bewitching little scamp; and never dearer, I think, than when the devil has had her in possession and she is breaking her stormy little heart over the remembrance of it:
“I confess I have been very more like a little young divil than a creature for when Isabella went up stairs to teach me religion and my multiplication and to be good and all my other lessons I stamped with my foot and threw my new hat which she had made on the ground and was sulky and was dreadfully passionate, but she never whiped me but said Marjory go into another room and think what a great crime you are committing letting your temper git the better of you. But I went so sulkily that the devil got the better of me but she never never never whips me so that I think I would be the better of it & the next time that I behave ill I think she should do it for she never does it.... Isabella has given me praise for checking my temper for I was sulky even when she was kneeling an whole hour teaching me to write.”
The wise Isabella, the sweet and patient Isabella! It is just a hundred years now (May, 1909) since the grateful child made that golden picture of you and laid your good heart bare for distant generations to see and bless; a hundred years--but if the picture endures a thousand it will still bring you the blessing, and with it the reverent homage that is your due. You had the seeing eye and the wise head. A fool would have punished Marjorie and wrecked her, but you held your hand, as knowing that when her volcanic fires went down she would repent, and grieve, and punish herself, and be saved.
Sometimes when Marjorie was miraculously good, she got a penny for it, and once when she got an entire sixpence, she recognized that it was wealth. This wealth brought joy to her heart. Why? Because she could spend it on somebody else! We who know Marjorie would know that without being told it. I am sorry--often sorry, often grieved--that I was not there and looking over her shoulder when she was writing down her valued penny rewards: I would have said, “Save that scrap of manuscript, dear; make a will, and leave it to your posterity, to save them from want when penury shall threaten them; a day will come when it
will be worth a thousand guineas, and a later day will come when it will be worth five thousand; here you are, rejoicing in copper farthings, and don’t know that your magic pen is showering gold coin all over the paper.” But I was not there to say it; those who were there did not think to say it; and so there is not a line of that quaint precious cacography in existence to-day.
I have adored Marjorie for six-and-thirty years; I have adored her in detail, I have adored the whole of her; but above all other details--just a little above all other details--I have adored her because she detested that odious and confusing and unvanquishable and unlearnable and shameless invention, the multiplication table:
“I am now going to tell you the horible and wretched plaege [plague] that my multiplication gives me you can’t conceive it the most Devilish thing is 8 times 8 & 7 times 7 it is what nature itself cant endure.”
I stand reverently uncovered in the presence of that holy verdict.
Here is that person again whom I so dislike--and for no reason at all except that my Marjorie doesn’t like her:
“Miss Potune is very fat she pretends to be very learned she says she saw a stone that dropt from the skies, but she is a good christian.”
Of course, stones have fallen from the skies, but I don’t believe this “horid fat Simpliton” had ever seen one that had done it; but even if she had, it was none of her business, and she could have been better employed than in going around exaggerating it and carrying on about it and trying to make trouble with a little child that had never done her any harm.
“... The Birds do chirp the Lambs do leap and Nature is clothed with the garments of green yellow, and white, purple, and red.
“... There is a book that is called the Newgate Calender that contains all the Murders: all the Murders did I say, nay all Thefts & Forgeries that ever were committed & fills me with horror & consternation.”
Marjorie is a diligent little student, and her education is always storming along and making great time and lots of noise:
“Isabella this morning taught me some French words one of which is bon suar the interpretation is good morning.”
It slanders Isabella, but the slander is not intentional. The main thing to notice is that big word, “interpretation.” Not many children of Marjorie’s age can handle a five syllable team in that easy and confident way. It is observable that she frequently employs words of an imposingly formidable size, and is manifestly quite familiar with them and not at all afraid of them.
“Isa is teaching me to make Simecolings nots of interrigations periods & commas &c. As this is Sunday I will meditate uppon senciable & Religious subjects first I should be very thankful I am not a beggar as many are.”
That was the “first.” She didn’t get to her second subject, but got side-tracked by a saner interest, and used her time to better purpose.
“It is melancholy to think, that I have so many talents, & many there are that have not had the attention paid to them that I have, & yet they contrive to be better then me.
“... Isabella is far too indulgent to me & even the Miss Crafords say that they wonder at her patience with me & it is indeed true for my temper is a bad one.”
The daring child wrote a (synopsized) history of Mary Queen of Scots and of five of the royal Jameses in rhyme--but never mind, we have no room to discuss it here. Nothing was entirely beyond her literary jurisdiction; if it had occurred to her that the laws of Rome needed codifying she would have taken a chance at it.
Here is a sad note:
“My religion is greatly falling off because I dont pray with so much attention when I am saying my prayers and my character is lost a-mong the Breahead people I hope I will be religious again but as for regaining my character I despare of it.”
When religion and character go, they leave a large vacuum. But there are ways to fill it:
“I’ve forgot to say, but I’ve four lovers, the other one is Harry Watson, a very delightful boy.... James Keith hardly ever Spoke to me, he said Girl! make less noise.... Craky hall ... I walked to
that delightfull place with a delightful young man beloved by all his friends and espacialy by me his loveress but I must not talk any longer about him for Isa said it is not proper for to speak of gentalman but I will never forget him....
“The Scythians tribe live very coarsely for a Gluton Introduced to Arsaces the Captain of the Army, 1 man who Dressed hair & another man who was a good cook but Arsaces said that he would keep 1 for brushing his horses tail and the other to fead his pigs....
“On Saturday I expected no less than three well-made bucks, the names of whom is here advertised. Mr. Geo. Crakey [Cragie], and Wm. Keith and Jn Keith--the first is the funniest of every one of them. Mr. Crakey and I walked to Craky-hall [Craigiehall] hand and hand in Innocence and matitation sweet thinking on the kind love which flows in our tender hearted mind which is overflowing with majestic pleasure no one was ever so polite to me in the hole state of my existence. Mr. Craky you must know is a great Buck and pretty good-looking.”
For a purpose, I wish the reader to take careful note of these statistics:
“I am going to tell you of a melancholy story. A young turkie of 2 or 3 months old, would you believe it, the father broke its leg, & he killed another! I think he ought to be transported or hanged.”
Marjorie wrote some verses about this tragedy--I think. I cannot be quite certain it is this one, for in the verses there are three deaths, whereas these statistics do not furnish so many. Also in the statistics the father of the deceased is indifferent about the loss he has sustained, whereas in the verses he is not. Also in the third verse, the mother, too, exhibits feeling, whereas in the two closing verses of the poem she--at least it seems to be she--is indifferent. At least it looks like indifference to me, and I believe it is indifference:
“Three turkeys fair their last have breathed, And now this world forever leaved; Their father, and their mother too, They sighed and weep as well as you; Indeed, the rats their bones have cranched. Into eternity theire launched. A direful death indeed they had, As wad put any parent mad; But she was more than usual calm, She did not give a single dam.”
The naughty little scamp! I mean, for not leaving out the l in the word “Calm,” so as to perfect the rhyme. It seems a pity to damage with a lame rhyme a couplet that is otherwise without a blemish.
Marjorie wrote four journals. She began the first one in January, 1809, when she was just six years old, and finished it five months later, in June.
She began the second in the following month, and finished it six months afterward (January, 1810), when she was just seven. She began the third one in April, 1810, and finished it in the autumn.
She wrote the fourth in the winter of 1810-11, and the last entry in it bears date July 19, 1811, and she died exactly five months later, December 19th, aged eight years and eleven months. It contains her rhymed Scottish histories.
Let me quote from Dr. John Brown:
“The day before her death, Sunday, she sat up in bed, worn and thin, her eye gleaming as with the light of a coming world, and with a tremulous, old voice repeated a long poem by Burns-heavy with the shadow of death, and lit with the fantasy of the judgment seat--the publican’s prayer in paraphrase, beginning:
“‘Why am I loth to leave this earthly scene? Have I so found it full of pleasing charms? Some drops of joy, with draughts of ill between, Some gleams of sunshine ’mid renewing storms.’
“It is more affecting than we care to say to read her mother’s and Isabella Keith’s letters written immediately after her death. Old and withered, tattered and pale, they are now; but when you read them, how quick, how throbbing with life and love! how rich in that language of affection which only women, and Shakespeare, and Luther can use--that power of detaining the soul over the beloved object and its loss.”
Fifty years after Marjorie’s death her sister, writing to Dr. Brown, said:
“My mother was struck by the patient quietness manifested by Marjorie during this illness, unlike her ardent, impulsive nature; but love and poetic feeling were unquenched. When Dr. Johnstone rewarded her submissiveness with a sixpence, the request speedily followed that she might get out ere New Year’s Day came. When asked why she was so desirous of getting out, she immediately rejoined: ‘Oh, I am so anxious to buy something with my sixpence for my dear Isa Keith.’ Again, when lying very still, her mother asked her if there was anything she wished: ‘Oh yes, if you would just leave the room door open a wee bit, and play the Land o’ the Leal, and I will lie and think and enjoy myself’ (this is just as stated to me by her mother and mine). Well, the happy day came, alike to parents and child, when Marjorie was allowed to come forth from the nursery to the parlor. It was Sabbath evening, and after tea. My father, who idolized this child, and never afterward in my hearing mentioned her name, took her in his arms; and while walking her up and down the room she said: ‘Father, I will repeat something to you; what would you like?’ He said, ‘Just choose for yourself, Maidie.’ She hesitated for a moment between the paraphrase, ‘Few are thy days and full of woe,’ and the lines of Burns already quoted, but decided on the latter; a remarkable choice for a child. The repeating of these lines seemed to stir up the depths of feeling in her soul. She asked to be allowed to write a poem. There was a doubt whether it would be right to allow her, in case of hurting her eyes. She pleaded earnestly, ‘Just this once’; the point was yielded, her slate was given her, and with great rapidity she
wrote an address of fourteen lines ‘To my loved cousin on the author’s recovery.’”
The cousin was Isa Keith.
“She went to bed apparently well, awoke in the middle of the night with the old cry of woe to a mother’s heart, ‘My head, my head!’ Three days of the dire malady, ‘water in the head,’ followed, and the end came.”
17. Marjorie Fleming. By L. MacBean. G. P. Putnam’s Sons, publishers, London and New York.
Permission to use the extracts quoted from Marjorie’s Journal in this article has been granted me by the publishers.
18. It is a whole century since the dimly conscious little prophet said it, but the pathos of it is still there.
