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Some Physical Constants

Speed of light c 3.00 × 108 m/sGravitational constant G 6.67 × 10-11 N·m2/kg2

Coulomb’s constant 1/4πε0 8.99 × 109 N·m2/C2

Permittivity constant ε0 8.85 × 10-12 C2/(N·m2)Permeability constant µ0 4π × 10-7 N/A2

Planck’s constant h 6.63 × 10-34 J·sBoltzmann’s constant kB 1.38 × 10-23 J/K Elementary charge e 1.602 × 10-19 CElectron mass me 9.11 × 10-31 kgProton mass mp 1.673 × 10-27 kgNeutron mass mn 1.675 × 10-27 kgAvogadro’s number NA 6.02 × 1023

Commonly Used Physical Data

Gravitational field strength g = W g 9.80 N/kg = 9.80 m/s2

(near the earth’s surface)Mass of the earth Me 5.98 × 1024 kgRadius of the earth Re 6380 km (equatorial)Mass of the sun M⊙ 1.99 × 1030 kgRadius of the sun R⊙ 696,000 kmMass of the moon 7.36 × 1022 kgRadius of the moon 1740 kmDistance to the moon 3.84 × 108 mDistance to the sun 1.50 × 1011 mDensity of water† 1000 kg/m3 = 1 g/cm3

Density of air† 1.2 kg/m3

Absolute zero 0 K = -273.15°C = -459.67°FFreezing point of water‡ 273.15 K = 0°C = 32°FBoiling point of water‡ 373.15 K = 100°C = 212°FNormal atmospheric pressure 101.3 kPa†At normal atmospheric pressure and 20°C.‡At normal atmospheric pressure.

Useful Conversion Factors

1 meter = 1 m = 100 cm = 39.4 in = 3.28 ft1 mile = 1 mi = 1609 m = 1.609 km = 5280 ft1 inch = 1 in = 2.54 cm1 light-year = 1 ly = 9.46 Pm = 0.946 × 1016 m1 minute = 1 min = 60 s1 hour = 1 h = 60 min = 3600 s1 day = 1 d = 24 h = 86.4 ks = 86,400 s1 year = 1 y = 365.25 d = 31.6 Ms = 3.16 × 107 s1 newton = 1 N = 1 kg·m/s2 = 0.225 lb1 joule = 1 J = 1 N·m = 1 kg·m2/s2 = 0.239 cal1 watt = 1 W = 1 J/s1 pascal = 1 Pa = 1 N/m2 = 1.45 × 10–4 psi1 kelvin (temperature difference) = 1 K = 1°C = 1.8°F1 radian = 1 rad = 57.3° = 0.1592 rev1 revolution = 1 rev = 2π rad = 360°1 cycle = 2π rad1 hertz = 1 Hz = 1 cycle/s

Standard Metric Prefixes (for powers of 10)

Power Prefix Symbol1018 exa E1015 peta P1012 tera T109 giga G106 mega M103 kilo k10-2 centi c10-3 milli m10-6 micro µ10-9 nano n10-12 pico p10-15 femto f10-18 atto a

1 m/s = 2.24 mi/h = 3.28 ft/s1 mi/h = 1.61 km/h = 0.447 m/s = 1.47 ft/s1 liter = 1 l = (10 cm)3 = 10-3 m3 = 0.0353 ft3

1 ft3 = 1728 in3 = 0.0283 m3

1 gallon = 1 gal = 0.00379 m3 = 3.79 l ≈ 3.8 kg H2OWeight of 1-kg object near the earth = 9.8 N = 2.2 lb

1 pound = 1 lb = 4.45 N1 calorie = energy needed to raise the temperature of 1 g

of H2O by 1 K = 4.186 J1 horsepower = 1 hp = 746 W1 pound per square inch = 6895 Pa1 food calorie = 1 Cal = 1 kcal = 1000 cal = 4186 J1 electron volt = 1 eV = 1.602 × 10-19 J

T = ( 1K ____ 1°C

) (T[C] + 273.15°C)

T = ( 5K ___ 9°F

) (T[F] + 459.67°F)

T[C] = ( 5°C ____ 9°F

) (T[F] - 32°F)

T[F] = 32°F + ( 9°F ____ 5°C

) T[C]

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Electromagnetic Units and Conversion Factors

1 coulomb = 1 C = unit of charge = total charge of 6.242 × 1018 protons1 N/C = unit of electric field strength = 1 V/m1 volt = 1 V = unit of energy per unit charge = 1 V = 1 J/C = 1 N·m/C = 1 kg·m2/(C·s2)1 ampere = 1 A = unit of current = 1 C/s1 ohm = 1 Ω = unit of resistance = 1 V/A = 1 J·s/C2 = 1 kg·m2/(C2s)1 farad = 1 F = unit of capacitance = 1 C/V = 1 s/Ω = 1 C2/J = C2s2/(kg·m2)1 watt = 1 W = unit of power (rate of energy conversion) = 1 J/s = 1 V·A = 1 V2/Ω1 tesla = 1 T = unit of magnetic field strength = 1 N·s/(C·m) = 1 kg/(C·s)1 gauss = 1 G = unit of magnetic field strength = 10–4 T1 henry = 1 H = unit of inductance = V·s/A = 1 Ω·s = kg·m2/C2

units of conductivity = (Ω·m)–1

units of current density = A/m2

W @ B = c W B = represents the magnetic field expressed N/C (same units as electric field)(µ 0 ε 0)-1 = c 2 ⇒ 1/(4π ε 0) = µ 0 c 2/4π(cε 0)–1 = 377 Ω

Some Useful Indefinite Integrals

∫ x n dx = 1 _____ n + 1

x n + 1 (n ≠ -1) ∫ dx __________ (x 2 + a 2 )1/2

= ln [x + (x 2 + a 2)1/2] ∫ x dx __________ (x 2 + a 2 )1/2

= (x 2 + a 2)1/2

∫ dx ___ x = lnx ∫ dx _______ x 2 + a 2

= 1 __ a tan-1 ( x __

a ) ∫ x dx __________

(x 2 + a 2 )3/2 = -1 __________

(x 2 + a 2 )1/2

∫ e ax dx = 1 __ a e ax ∫ dx __________

(x 2 + a 2 )3/2 = 1 __

a 2 x __________ (x 2 + a 2 )1/2

∫ x 2 dx __________ (x 2 + a 2 )3/2

= -x __________ (x 2 + a 2 )1/2

+ ln [x + (x 2 + a 2)1/2]

Standard Electric and Magnetic Field Patterns

Field pattern( W F = W E or W B )

Created by Divergence CurlGaussian Surface (GS)Amperian Loop (AL)

General (anything) W ∇ · W F = ∂Fx ____ ∂x

+ ∂Fy ____ ∂y

+ ∂Fz ___ ∂z

W ∇ × W F =

[ ∂Fz ___ ∂y

- ∂Fy ____ ∂z

∂Fx ____ ∂z

- ∂Fz ___ ∂x

∂Fy ____ ∂x

- ∂Fx ____ ∂y

] (not applicable)

Unidirectional( W F = Fz z )

infinite flat plate (both W E and W B )infinite solenoid ( W B )

W ∇ · W F = ∂Fz ___ ∂z

W ∇ × W F =

[

∂Fz ___ ∂y

- ∂Fz ___

∂x

0

] GS: rectangular solid

AL: rectangle

Axial( W F = Fs s )

infinite cylindrically symmetric object ( W E ) W ∇ · W F = 1 __

s ∂ ___ ∂s

(sFs) W ∇ × W F = 0 (identically)GS: cylindrical canAL: (not applicable)

Radial( W F = Fr r )

spherically symmetric object ( W E ) W ∇ · W F = 1 __

r 2 ∂ ___ ∂r

(r 2 Fr) W ∇ × W F = 0 (identically)GS: sphereAL: (not applicable)

Circular( W F = Fϕ ϕ )

infinite cylindrically symmetric situation where current flows parallel to its axis ( W B ) or where ∂ W B /∂t is parallel to the axis ( W E )

W ∇ · W F = 0 (identically) W ∇ × W F =

[

[ W ∇ × W F ] u

[ W ∇ × W F ] ϕ

[ W ∇ × W F ] z ]

=

[

- ∂Fϕ

____ ∂z

0

1 __ u

∂ ___ ∂u

(uFϕ) ]

GS: (not applicable)AL: circle


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Six Ideas That Shaped

Physics

Third Edition

Thomas A. Moore

Unit E: Electric and Magnetic Fields are Unified


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SIX IDEAS THAT SHAPED PHYSICS, UNIT E:ELECTRIC AND MAGNETIC FIELDS ARE UNIFIED, THIRD EDITION

Published by McGraw-Hill Education, 2 Penn Plaza, New York, NY 10121. Copyright © 2017 by McGraw-Hill Education. All rights reserved. Printed in the United States of America. Previous editions © 2003, and 1998. No part of this publication may be reproduced or distributed in any form or by any means, or stored in a database or retrieval system, without the prior written consent of McGraw-Hill Education, including, but not limited to, in any network or other electronic storage or transmission, or broadcast for distance learning.

Some ancillaries, including electronic and print components, may not be available to customers outside the United States.

ISBN 978-0-07-760092-1MHID 0-07-760092-4

Senior Vice President, Products & Markets: Kurt L. StrandVice President, General Manager, Products & Markets: Marty LangeVice President, Content Design & Delivery: Kimberly Meriwether DavidManaging Director: Thomas TimpBrand Manager: Thomas M. Scaife, Ph.D. Product Developer: Jolynn KilburgMarketing Manager: Nick McFaddenDirector of Development: Rose KoosDigital Product Developer: Dan WallaceDirector, Content Design & Delivery: Linda AvenariusProgram Manager: Faye M. HerrigContent Project Managers: Melissa M. Leick, Tammy Juran, Sandy SchneeDesign: Studio Montage, Inc.Content Licensing Specialists: Deanna DausenerCover Image: NASACompositor: SPi Global

Dedication

To Joyce, the light of my life.

All credits appearing on page or at the end of the book are considered to be an extension of the copyright page.

The Internet addresses listed in the text were accurate at the time of publication. The inclusion of a website does not indicate an endorsement by the authors or McGraw-Hill Education, and McGraw-Hill Education does not guarantee the accuracy of the information presented at these sites.

Library of Congress Cataloging-in-Publication DataNames: Moore, Thomas A. (Thomas Andrew), author.Title: Six ideas that shaped physics. Unit E, Electric and magnetic fields are unified/Thomas A. Moore.Other titles: Electric and magnetic fields are unifiedDescription: Third edition. | New York, NY : McGraw-Hill Education, [2016] | 2017 | Includes index.Identifiers: LCCN 2015048199| ISBN 9780077600921 (alk. paper) | ISBN 0077600924 (alk. paper)Subjects: LCSH: Electromagnetic fields—Textbooks.Classification: LCC QC665.E4 M66 2016 | DDC 537—dc23 LC record available at http://lccn.loc.gov/2015048199

www.mhhe.com


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v

Contents: Unit EElectric and Magnetic Fields Are Unified

About the Author ix

Preface xi

Introduction for Students xviii

Chapter E1 2Electric Fields 2

Chapter Overview 2E1.1 Introduction to the Unit 4E1.2 Charge 5E1.3 Electric Force 7E1.4 The Field Concept 8E1.5 Defining the Electric Field 9E1.6 The Field of a Single Particle 11E1.7 The Superposition Principle 12

TWO-MINUTE PROBLEMS 14HOMEWORK PROBLEMS 15ANSWERS TO EXERCISES 17

Chapter E2 18Charge Distributions 18

Chapter Overview 18E2.1 Introduction 20E2.2 The Dipole 20E2.3 Electrical Polarization 22E2.4 Other Important Charge Distributions 24E2.5 The Field of an Infinite Line 27E2.6 The Field of an Infinite Plane 28


Chapter E3 38Electric Potential 38

Chapter Overview 38E3.1 Introduction 40E3.2 Review of Energy Concepts 41E3.3 Potential Energy and Electrical Potential 43E3.4 From Field to Potential 45E3.5 From Potential to Field 49


Chapter E4 56Static Equilibrium 56

Chapter Overview 56E4.1 Conductors and Insulators 58E4.2 Static Charges on Conductors 59E4.3 Capacitance 62E4.4 The Parallel-Plate Capacitor 63E4.5 The Electric Field as a Form of Energy 66


Chapter E5 72Current 72

Chapter Overview 72E5.1 Introduction 74E5.2 A Model of Current Flow 74E5.3 Current Density 77E5.4 Flux 79E5.5 Electrical Current 82



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Table of Contents

E9.6 Creating Currents in Moving Loops 154TWO-MINUTE PROBLEMS 156HOMEWORK PROBLEMS 157ANSWERS TO EXERCISES 163

Chapter E10 164Currents Create Magnetic Fields 164

Chapter Overview 164E10.1 The Magnetic Field of a Moving Charge 166E10.2 The Magnetic Field of a Wire Segment 169E10.3 The Magnetic Field of an Infinite Wire 170E10.4 The Magnetic Field of a Circular Loop 172E10.5 All Magnets Involve Circulating Currents 174


Chapter E11 182The Electromagnetic Field 182

Chapter Overview 182E11.1 A Mystery 184E11.2 Relativity and the Electromagnetic Field 184E11.3 How the Fields Transform 188E11.4 The Mystery Is Solved! 191E11.5 The Electromagnetic Field of a Moving Particle 192


Chapter E12 200Gauss’s Law 200

Chapter Overview 200E12.1 What Is a Field Equation? 202E12.2 Divergence 202E12.3 The Divergence as a Derivative 204E12.4 Gauss’s Law 205E12.5 Tools For Applying Gauss’s Law 205E12.6 Applications 209


Chapter E13 218Ampere’s Law 218

Chapter Overview 218E13.1 Curl 220

Chapter E6 88Dynamic Equilibrium 88

Chapter Overview 88E6.1 A Simple Model for a Battery 90E6.2 Implications of Equilibrium 92E6.3 Surface Charges Direct the Flow 93E6.4 Potentials in a Simple Circuit 96E6.5 Resistance and Power 98E6.6 Discharging a Capacitor 99


Chapter E7 108Analyzing Circuits 108

Chapter Overview 108E7.1 Circuit Diagrams 110E7.2 Kirchhoff’s Laws 112E7.3 Circuit Elements in Series 114E7.4 Circuit Elements in Parallel 115E7.5 Analyzing Complex Circuits 116E7.6 Realistic Batteries 118E7.7 Electrical Safety Issues 118


Chapter E8 126Magnetic Fields 126

Chapter Overview 126E8.1 The Phenomenon of Magnetism 128E8.2 The Definition of the Magnetic Field Direction 128E8.3 Magnetic Forces on Moving Charges 130E8.4 A Review of the Cross Product 132E8.5 Defining the Field’s Magnitude 133E8.6 A Free Particle in a Magnetic Field 135


Chapter E9 144Currents Respond to Magnetic Fields 144

Chapter Overview 144E9.1 The Magnetic Force on a Wire 146E9.2 The Magnetic Torque on a Loop 147E9.3 Current Loops Behave Like Bar Magnets 149E9.4 The Potential Energy of an Oriented Loop 151E9.5 Electric Motors 152


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Table of Contents

Chapter E17 286Induction 286

Chapter Overview 286E17.1 Self-Induction 288E17.2 “Discharging” an Inductor 290E17.3 The Energy in a Magnetic Field 291E17.4 LC Circuits 292E17.5 Transformers 294


Chapter E18 302Electromagnetic Waves 302

Chapter Overview 302E18.1 An Electromagnetic Disturbance 304E18.2 Properties of Electromagnetic Waves 306E18.3 Intensity of an Electromagnetic Wave 308E18.4 Waves from a Charged Particle 309E18.5 Maxwell’s Rainbow 311E18.6 Why the Sky Is Blue 313


Appendix EA 318The Electromagnetic Transformation Law 318

EA.1 Introduction 318EA.2 The Reverse Transformation for the Field 318EA.3 The Case of the Transverse Particle 319EA.4 Concluding Unrelativistic Postscript 321

EXERCISE ANSWERS 321

Appendix EB 322Radiation from an Accelerating Particle 322

EB.1 Introduction 322EB.2 The Derivation 322

Index 324

Periodic table 333

Short Answers to Selected Problems 334

E13.2 The Curl as a Derivative 221E13.3 Ampere’s Law 222E13.4 Tools for Applying Ampere’s Law 223E13.5 Applications 226


Chapter E14 236Integral Forms 236

Chapter Overview 236E14.1 Introduction 238E14.2 Integrating Gauss’s Law 238E14.3 Using the Integral Form of Gauss’s Law 239E14.4 Integrating Ampere’s Law 242E14.5 Using the Integral Form of Ampere’s Law 243E14.6 Which Form Is Better? 246


Chapter E15 252Maxwell’s Equations 252

Chapter Overview 252E15.1 Correcting Ampere’s Law 254E15.2 Gauss’s Law Needs No Correction 256E15.3 Gauss’s Law for the Magnetic Field 257E15.4 Faraday’s Law 258E15.5 Maxwell’s Equations 261E15.6 A Short History of Maxwell’s Equations 262


Chapter E16 268Faraday’s Law 268

Chapter Overview 268E16.1 Applying Faraday’s Law 270E16.2 Magnetic Flux and Induced EMF 271E16.3 Lenz’s Law 274E16.4 Some Example Applications 275E16.5 Superconductivity and Magnetic Flux 278



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ix

About the Author

Thomas A. Moore graduated from Carleton College (magna cum laude with Distinction in Physics) in 1976. He won a Danforth Fellowship that year that supported his graduate education at Yale University, where he earned a Ph.D. in 1981. He taught at Carleton College and Luther College before taking his current position at Pomona College in 1987, where he won a Wig Award for Distinguished Teaching in 1991. He served as an active member of the steering committee for the national Intro-ductory University Physics Project (IUPP) from 1987 through 1995. This textbook grew out of a model curric-ulum that he developed for that project in 1989, which was one of only four selected for further development and testing by IUPP. He has published a number of articles about astro-physical sources of gravitational waves, detection of gravitational waves, and new approaches to teaching physics, as well as a book on general relativity entitled A General Relativity Workbook (University Science Books, 2013). He has also served as a reviewer and as an associate editor for American Journal of Physics. He currently lives in Claremont, California, with his wife Joyce, a retired pastor. When he is not teaching, doing research, or writing, he enjoys reading, hiking, calling contradances, and playing Irish traditional fiddle music.


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xi

Preface

Introduction

This volume is one of six that together comprise the text materials for Six Ideas That Shaped Physics, a unique approach to the two- or three-semester calculus-based introductory physics course. I have designed this curriculum (for which these volumes only serve as the text component) to support an introductory course that combines two elements that rarely appear together: (1) a thoroughly 21st-century perspective on physics (including a great deal of 20th-century physics), and (2) strong support for a student-centered class-room that emphasizes active learning both in and outside of class, even in situations where large-enrollment sections are unavoidable. This course is based on the premises that innovative metaphors for teaching basic concepts, explicitly instructing students in the processes of constructing physical models, and active learning can help students learn the subject much more effectively. In the course of executing this project, I have completely rethought (from scratch) the presentation of every topic, taking advantage of research into physics education wherever possible. I have done nothing in this text just because “that is the way it has always been done.” Moreover, because physics education research has consistently underlined the importance of active learning, I have sought to provide tools for pro-fessors (both in the text and online) to make creating a coherent and self- consistent course structure based on a student-centered classroom as easy and practical as possible. All of the materials have been tested, evaluated, and rewritten multiple times. The result is the culmination of more than 25 years of continual testing and revision. I have not sought to “dumb down” the course to make it more accessible. Rather, my goal has been to help students become smarter. I have intention-ally set higher-than-usual standards for sophistication in physical thinking, but I have also deployed a wide range of tools and structures that help even average students reach this standard. I don’t believe that the mathemati-cal level required by these books is significantly different than that in most university physics texts, but I do ask students to step beyond rote think-ing patterns to develop flexible, powerful, conceptual reasoning and model-building skills. My experience and that of other users is that normal students in a wide range of institutional settings can (with appropriate support and practice) meet these standards. Each of six volumes in the text portion of this course is focused on a single core concept that has been crucial in making physics what it is today. The six volumes and their corresponding ideas are as follows:

Unit C: Conservation laws constrain interactions Unit N: The laws of physics are universal (Newtonian mechanics) Unit R: The laws of physics are frame-independent (Relativity) Unit E: Electric and Magnetic Fields are Unified Unit Q: Particles behave like waves (Quantum physics) Unit T: Some processes are irreversible (Thermal physics)


xii

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Preface

I have listed the units in the order that I recommend they be taught, but I have also constructed units R, E, Q, and T to be sufficiently independent so they can be taught in any order after units C and N. (This is why the units are lettered as opposed to numbered.) There are six units (as opposed to five or seven) to make it possible to easily divide the course into two semesters, three quarters, or three semesters. This unit organization therefore not only makes it possible to dole out the text in small, easily-handled pieces and provide a great deal of flexibility in fitting the course to a given schedule, but also carries its own important pedagogical message: Physics is organized hierarchically, structured around only a handful of core ideas and metaphors. Another unusual feature of all of the texts is that they have been designed so that each chapter corresponds to what one might handle in a single 50- minute class session at the maximum possible pace (as guided by years of experience). Therefore, while one might design a syllabus that goes at a slower rate, one should not try to go through more than one chapter per 50-minute session (or three chap-ters in two 70-minute sessions). A few units provide more chapters than you may have time to cover. The preface to such units will tell you what might be cut. Finally, let me emphasize again that the text materials are just one part of the comprehensive Six Ideas curriculum. On the Six Ideas website, at

𝚠𝚠𝚠𝚙𝚑𝚢𝚜𝚒𝚌𝚜𝚙𝚘𝚖𝚘𝚗𝚊𝚎𝚍𝚞/𝚜𝚒𝚡𝚒𝚍𝚎𝚊𝚜/

you will find a wealth of supporting resources. The most important of these is a detailed instructor’s manual that provides guidance (based on Six Ideas users’ experiences over more than two decades) about how to construct a course at your institution that most effectively teaches students physics. This manual does not provide a one-size-fits-all course plan, but rather exposes the important issues and raises the questions that a professor needs to con-sider in creating an effective Six Ideas course at their particular institution. The site also provides software that allows professors to post selected prob-lem solutions online where their students alone can see them and for a time period that they choose. A number of other computer applets provide expe-riences that support student learning in important ways. You will also find there example lesson plans, class videos, information about the course phi-losophy, evidence for its success, and many other resources. There is a preface for students appearing just before the first chapter of each unit that explains some important features of the text and assumptions behind the course. I recommend that everyone read it.

Comments about the Current Edition

My general goals for the current edition have been to correct errors, improve the presentation in some key areas, make the book more flexible, and espe-cially to improve the quality and range of the homework problems, as well as significantly increase their number. Users of previous editions will note that I have split the old “Synthetic” homework problem category into “Model-ing” and “Derivations” categories. “Modeling” problems now more specifi-cally focus on the process of building physical models, making appropriate approximations, and binding together disparate concepts. “Derivation” problems focus more on supporting or extending derivations presented in the text. I thought it valuable to more clearly separate these categories. The “Basic Skills” category now includes a number of multipart prob-lems specifically designed for use in the classroom to help students practice basic issues. The instructor’s manual discusses how to use such problems. I have also been more careful to give instructors more choice about what to cover, making it possible for them to omit chapters without a loss of conti-nuity. See the unit-specific part of this preface for more details.


xiii

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Preface

Users of previous editions will also note that I have dropped the menu-like chapter location diagrams, as well as the glossaries and symbol lists that appeared at the end of each volume. There was no evidence that these were actually helpful to students. Units C and N still instruct students very care-fully on how to construct problem solutions that involve translating, mod-eling, solving, and checking, but examples and problem solutions for the remaining units have been written in a more flexible format that includes these elements implicitly but not so rigidly and explicitly. Students are rather guided in Unit N to start recognizing these elements in more generally for-matted solutions, something that I think is an important skill. The only general notation change is that now I use W v exclusively and universally for the magnitude of a vector W v . I still think it is very important to have notation that clearly distinguishes vector magnitudes from other sca-lars, but the old mag( W v ) notation is too cumbersome to use exclusively, and mixing it with using just the simple letter has proved confusing. Unit C con-tains some specific instruction about the commonly used notation that most texts by other authors use (as well as discussing its problems). Finally, at the request of many students, I now include short answers to selected homework problems at the end of each unit. This will make students happier without (I think) significantly impinging on professors’ freedom.

Specific Comments About Unit E

This unit has been completely rewritten for this edition, almost from scratch. My goals, based on feedback from users and students, have been to greatly reduce this unit’s pace, increase flexibility, adjust the lengths of several chap-ters to better fit the 50-minute target, and improve the homework problems. I have therefore cut about 20% of the material in the previous edition, and spread the remaining material over 18 chapters instead of 16, yielding a pace that is about 30% gentler than before. I think that everyone will find that this unit now has a pace more comparable to the other units. In spite of the new chapters, the text is actually a few pages shorter than previous editions. The cuts are mostly at the level of details and tangents, though certain omissions may appear more obvious than others. For example, I have omit-ted a discussion of sticky-tape electrostatics, not because it is not extremely valuable (it is) but because it is better to explore it in class than summa-rize it in the text. This material now appears online in the form of a les-son plan. Another important cut was that (generally) I have reduced the focus on calculating electric fields of charge configurations. Professors who still wish to build students’ skills in this regard may allot more time and use problems in the text to provide examples and/or activities. I have also reduced the time spent on symmetry arguments: my theoretician’s focus on making them precise in previous editions has, I think, been an unnecessary distraction. After much rumination and feedback, I have decided to keep the emphasis on the differential forms of Maxwell’s equations, for reasons both theoretical and pedagogical. I remain convinced that the differential forms are not only more fundamental but simpler than the integral forms for students familiar with elementary calculus but not vector calculus. The kinds of problems that one can solve with either are virtually identical, and (when appropriately presented) require roughly the same number of steps and level of sophistication, but the differential method better prepares stu-dents for future work. I also find that when appropriately prepared stu-dents are given the choice of which method to use, the majority select the differential approach.


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Preface

With the help of student feedback, I have streamlined this presentation greatly in this edition, and given more explicit and straightforward guidance on how to use the differential forms (based on recognizing standard field patterns). The integral forms now appear in an optional chapter, which also provides a greatly simplified and more informal (that is, less rigorous) dis-cussion of how they are linked to the differential forms. Even so, I have also better laid the groundwork for the integral forms, explicitly discussing line integrals in the context of potential and flux in the context of current, so students will see these concepts developed (in contexts where they are less abstract) even if the chapter on integral forms is omitted. These concepts are also very helpful in the chapter on Faraday’s law. I have included many new problems, some especially designed to be used as class activities. In particular, problems E12M.1, E13M.1, and E15M.1 now provide students with essential guided practice in using the differen-tial versions of Maxwell’s equations. I have found from experience that such activities can make students much more comfortable with these equations. At the request of many users, I have elected to stick with standard SI units and notation (including using ε0 and µ0 instead of k and c) throughout. B-bar (now denoted W @ B ) only appears in a few places where it really makes a difference, and even then in parallel to the usual notation. I am also using standard notation for divergence and curl (my previous notation made more sense in the first edition than it does now). In other places, I have made my notation more consistent with Griffiths’ E&M text. I have combined the first two chapters by de-emphasizing Coulomb’s law and the calculation of complicated electric fields, and moving the mate-rial on dipoles to chapter E2. I have split what was previously two chapters of material on current and circuits into three chapters (the last of which is optional). I have also split the exploration of the unity of the electromagnetic field and the derivation of the time-dependent terms in Maxwell’s equations into two chapters, and the treatment of inductance into two chapters. The chapter on waves (the old chapter E15) has been moved to unit Q, and the chapter on electromagnetic waves no longer requires it. That chapter now includes a description of the field created by an accelerated point particle, and an appendix provides the equivalent of Purcell’s famous derivation of the electric field created by an accelerating charge (but without using field lines). In summary, here is a commented list of chapters in the new edition.

E1: Electric Field (combines old E1 and E2) E2: Charge Distributions (sections 2.5 and 2.6 are optional) E3: Potential (includes line integrals) E4: Static Equilibrium (includes capacitors) E5: Current (includes flux) E6: Dynamic Equilibrium (covers simple circuits) E7: Analyzing Circuits (now optional) E8: Magnetic Fields E9: Currents Respond to Magnetic Fields E10: Currents Create Magnetic Fields E11: The Electromagnetic Field (the unit could end here!) E12: Gauss’s law (greatly simplified) E13: Ampere’s law (greatly simplified) E14: Integral forms (now optional) E15: Maxwell’s Equations E16: Faraday’s Law (not really needed for E18) E17: Induction (not really needed for E18) E18: Electromagnetic Waves


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Preface

One can now give students a a basic introduction to electric and magnetic fields in either 10 or 11 class sessions by ending with chapter E11 (in such a case, section E11.5 can be omitted, because it is only relevant to chapters E15 and E18). There is still a distinct (though reduced) step up in sophistication starting in chapter E12. In a treatment that ends with E18, one could also omit chapters E16 and E17, though I think these chapters are important for other reasons. By omitting chapters E7 and E14 (or by omitting E16 and E17), Six Ideas users who need to present the unit in 16 class sessions can still do so. In the recommended unit sequence, this unit follows unit R. Unit E, since it takes a 21st-century perspective on electricity and magnetism, does refer to relativistic arguments, particularly in chapter E11. However, I have been deliberate in arranging things so that students only need to know (1) the principle of relativity, (2) that c is the ultimate speed limit, and (3) the fact that moving objects are Lorentz contracted. These are simple enough to take on faith, so I do not think that Unit R is truly a prerequisite. Finally, I recommend carefully considering your expectations with regard to homework. When teaching most units, I assign mostly M and R problems for homework, but in this unit, problems of this level can be pretty challeng-ing, so assigning more B problems might be appropriate. (Some D and A problems are more for the benefit of instructors than for students.)

Appreciation

A project of this magnitude cannot be accomplished alone. A list including everyone who has offered important and greatly appreciated help with this project over the past 25 years would be much too long (and such lists appear in the previous editions), so here I will focus for the most part on people who have helped me with this particular edition. First, I would like to thank Tom Bernatowicz and his colleagues at Washington University (particularly Marty Israel and Mairin Hynes) who hosted me for a visit to Washingtion University where we discussed this edition in detail. Many of my decisions about what was most important in this edition grew out of that visit. Bruce Sherwood and Ruth Chabay always have good ideas to share, and I appre-ciate their generosity and wisdom. Benjamin Brown and his colleagues at Marquette University have offered some great suggestions as well, and have been working hard on the important task of adapting some Six Ideas prob-lems for computer grading. Pomona College and the Wig Fund supported a sabbatical in 2012 during which I did most of the writing on unit E. I’d like to thank Michael Lange at McGraw-Hill for having faith in the Six Ideas project and starting the push for this edition, and Thomas Scaife for con-tinuing that push. Eve Lipton and Jolynn Kilburg have been superb at guiding the project at the detail level. Many others at McGraw-Hill, including Melissa Leick, Ramya Thirumavalavan, Kala Ramachandran, David Tietz, and Deanna Dausener, were instrumental in proofreading and producing the printed text. I’d also like to thank Wei Jia Ong, and Loredana Vetere for reviewing this unit, and my students in Physics 72 at Pomona College (especially Gail Gallaher, Alex Hof, Asher Abrahms and Jonah Grubb) for helping me track down errors in the manuscript form and offering useful feedback. Finally a very special thanks to my wife Joyce, who sacrificed and supported me and loved me dur-ing this long and demanding project. Heartfelt thanks to all!

Thomas A. MooreClaremont, California


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SmartBook is the first and only adaptive reading experience designed to change the way students read and learn. It creates a personalized reading experience by highlighting the most impactful concepts a student needs to learn at that moment in time. As a student engages with SmartBook, the read-ing experience continuously adapts by highlighting content based on what the student knows and doesn’t know. This ensures that the focus is on the content he or she needs to learn, while simultaneously promoting long-term retention of material. Use SmartBook’s real-time reports to quickly identify the concepts that require more attention from individual students–or the entire class. The end result? Students are more engaged with course content, can better prioritize their time, and come to class ready to participate.

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Continually evolving, McGraw-Hill Connect® has been redesigned to pro-vide the only true adaptive learning experience delivered within a simple and easy-to-navigate environment, placing students at the very center.

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• Personalized Learning – Squeezing the most out of study time, the adap-tive engine in Connect creates a highly personalized learning path for each student by identifying areas of weakness, and surfacing learning resources to assist in the moment of need. This seamless integration of reading, practice, and assessment, ensures that the focus is on the most important content for that individual student at that specific time, while promoting long-term retention of the material.

Preface


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Introduction for Students

Introduction

Welcome to Six Ideas That Shaped Physics! This text has a number of features that may be different from science texts you may have encountered previ-ously. This section describes those features and how to use them effectively.

Why Is This Text Different?

Research into physics education consistently shows that people learn physics most effectively through activities where they practice applying physical rea-soning and model-building skills in realistic situations. This is because phys-ics is not a body of facts to absorb, but rather a set of thinking skills acquired through practice. You cannot learn such skills by listening to factual lectures any more than you can learn to play the piano by listening to concerts! This text, therefore, has been designed to support active learning both inside and outside the classroom. It does this by providing (1) resources for various kinds of learning activities, (2) features that encourage active reading, and (3) features that make it as easy as possible to use the text (as opposed to lectures) as the primary source of information, so that you can spend class time doing activities that will actually help you learn.

The Text as Primary Source

To serve the last goal, I have adopted a conversational style that I hope you will find easy to read, and have tried to be concise without being too terse. Certain text features help you keep track of the big picture. One of the key aspects of physics is that the concepts are organized hierarchically: some are more fundamental than others. This text is organized into six units, each of which explores the implications of a single deep idea that has shaped physics. Each unit’s front cover states this core idea as part of the unit’s title. A two-page chapter overview provides a compact summary of that chapter’s contents to give you the big picture before you get into the details and later when you review. Sidebars in the margins help clarify the purpose of sections of the main text at the subpage level and can help you quickly locate items later. I have highlighted technical terms in bold type (like this) when they first appear: their definitions usually appear nearby. A physics formula consists of both a mathematical equation and a con-ceptual frame that gives the equation physical meaning. The most important formulas in this book (typically, those that might be relevant outside the cur-rent chapter) appear in formula boxes, which state the equation, its purpose (which describes the formula’s meaning), a description of any limitations on the formula’s applicability, and (optionally) some other useful notes. Treat everything in a box as a unit to be remembered and used together.

Active Reading

Just as passively listening to a lecture does not help you really learn what you need to know about physics, you will not learn what you need by simply

Why active learning is crucial

Features that help you use the text as the primary source of information

What is active reading?


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scanning your eyes over the page. Active reading is a crucial study skill for all kinds of technical literature. An active reader stops to pose internal ques-tions such as these: Does this make sense? Is this consistent with my experi-ence? Do I see how I might be able to use this idea? This text provides two important tools to make this process easier. Use the wide margins to (1) record questions that arise as you read (so you can be sure to get them answered) and the answers you eventually receive, (2) flag important passages, (3) fill in missing mathematical steps, and (4) record insights. Writing in the margins will help keep you actively engaged as you read and supplement the sidebars when you review. Each chapter contains three or four in-text exercises, which prompt you to develop the habit of thinking as you read (and also give you a break!). These exercises sometimes prompt you to fill in a crucial mathematical detail but often test whether you can apply what you are reading to realistic situ-ations. When you encounter such an exercise, stop and try to work it out. When you are done (or after about 5 minutes or so), look at the answers at the end of the chapter for some immediate feedback. Doing these exercises is one of the more important things you can do to become an active reader. SmartBook (TM) further supports active reading by continuously mea-suring what a student knows and presenting questions to help keep students engaged while acquiring new knowledge and reinforcing prior learning.

Class Activities and Homework

This book’s entire purpose is to give you the background you need to do the kinds of practice activities (both in class and as homework) that you need to genuinely learn the material. It is therefore ESSENTIAL that you read every assignment BEFORE you come to class. This is crucial in a course based on this text (and probably more so than in previous science classes you have taken). The homework problems at the end of each chapter provide for differ-ent kinds of practice experiences. Two-minute problems are short concep-tual problems that provide practice in extracting the implications of what you have read. Basic Skills problems offer practice in straightforward appli-cations of important formulas. Both can serve as the basis for classroom activities: the letters on the book’s back cover help you communicate the answer to a two-minute problem to your professor (simply point to the let-ter!). Modeling problems give you practice in constructing coherent mental models of physical situations, and usually require combining several formu-las to get an answer. Derivation problems give you practice in mathemati-cally extracting useful consequences of formulas. Rich-context problems are like modeling problems, but with elements that make them more like realistic questions that you might actually encounter in life or work. They are especially suitable for collaborative work. Advanced problems chal-lenge advanced students with questions that involve more subtle reasoning and/or difficult math. Note that this text contains perhaps fewer examples than you would like. This is because the goal is to teach you to flexibly reason from basic prin-ciples, not slavishly copy examples. You may find this hard at first, but real life does not present its puzzles neatly wrapped up as textbook examples. With practice, you will find your power to deal successfully with realistic, practical problems will grow until you yourself are astonished at how what had seemed impossible is now easy. But it does take practice, so work hard and be hopeful!

Features that support develop-ing the habit of active reading

Read the text BEFORE class!

Types of practice activities provided in the text


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