Introduction to Electricity and Magnetism

271 Pages·2018·4.476 MB·English

by  John Dirk Walecka

Introduction to
Electricity
and
Magnetism
TTTThhhhiiiissss ppppaaaaggggeeee iiiinnnntttteeeennnnttttiiiioooonnnnaaaallllllllyyyy lllleeeefffftttt bbbbllllaaaannnnkkkk
Introduction to
Electricity
and
Magnetism
John Dirk Walecka
College of William and Mary, USA
World Scientific
Published by
World Scientific Publishing Co. Pte. Ltd.
5 Toh Tuck Link, Singapore 596224
USA office: 27 Warren Street, Suite 401-402, Hackensack, NJ 07601
UK office: 57 Shelton Street, Covent Garden, London WC2H 9HE
Library of Congress Cataloging-in-Publication Data
Names: Walecka, John Dirk, 1932– author.
Title: Introduction to electricity and magnetism / John Dirk Walecka
(College of William and Mary, USA).
Description: New Jersey : World Scientific, 2018. |
Includes bibliographical references and index.
Identifiers: LCCN 2018029050| ISBN 9789813272064 (hardcover : alk. paper) |
ISBN 9789813273108 (pbk. : alk. paper)
Subjects: LCSH: Electricity. | Magnetism.
Classification: LCC QC522 .W35 2018 | DDC 537--dc23
LC record available at https://lccn.loc.gov/2018029050
British Library Cataloguing-in-Publication Data
A catalogue record for this book is available from the British Library.
Copyright © 2019 by World Scientific Publishing Co. Pte. Ltd.
All rights reserved. This book, or parts thereof, may not be reproduced in any form or by any means,
electronic or mechanical, including photocopying, recording or any information storage and retrieval
system now known or to be invented, without written permission from the publisher.
For photocopying of material in this volume, please pay a copying fee through the Copyright Clearance
Center, Inc., 222 Rosewood Drive, Danvers, MA 01923, USA. In this case permission to photocopy
is not required from the publisher.
For any available supplementary material, please visit
https://www.worldscientific.com/worldscibooks/10.1142/11036#t=suppl
Printed in Singapore
For John and Ann
TTTThhhhiiiissss ppppaaaaggggeeee iiiinnnntttteeeennnnttttiiiioooonnnnaaaallllllllyyyy lllleeeefffftttt bbbbllllaaaannnnkkkk
Preface
The present author has published several physics textbooks: a graduate
nuclear theory book [Walecka (2004)], a modern physics series [Walecka
(2008); Walecka (2010); Walecka (2013)] that provides an introduction
to quantum mechanics and twentieth-century physics ranging from the
undergraduate to the advanced graduate levels, two graduate books on
statistical mechanics [Walecka (2000); Walecka (2011)], and a graduate-
level introduction to general relativity [Walecka (2007)]. There are also
problem solutions manuals for two of the latter texts [Walecka (2017);
Walecka (2017a)]. Published in collaboration, there are graduate texts
on classical mechanics and many-body theory [Fetter and Walecka (2003);
Fetter and Walecka (2003a); Fetter and Walecka (2006)] and a set of solu-
tions manuals for the modern physics series [Amore and Walecka (2013);
AmoreandWalecka(2014);AmoreandWalecka(2015)]. Allofthesebooks
are based on courses taught at either Stanford, where the author was on
the faculty from 1960-1986,or at the College of William and Mary, where
he served from 1992-2003.
There is one other course that I taught at Stanford in the spring of
1986 for which I have a good set of notes. This was the calculus-based
freshman physics course, Physics 53, on electricity and magnetism. It was
a big course with over 400 students, taught in two lecture sections, with
additional problem sessions taught by many good graduate teaching assis-
tants, overseen by an excellent head TA, Janet Tate.1 It was one of the
most enjoyable courses I ever taught, and what made it such fun was the
lecture demonstrations prepared by that master, Kurt Machein. I would
go in each night before a lecture and practice the demonstrations for the
1Physics 54was anoptional one-credit lab, graded P/NC,that went along withthe
course.
vii
viii Preface
next day under Kurt’s watchful eye. They always went well and really
enhanced and solidified the material. I vividly remember that Kurt and I
received a standing ovation after a particularly compelling final story and
demonstration.
There is an abundance of good introductory and more advanced elec-
tricity andmagnetismtexts. The one I usedwas [Ohanian(1985)], but see
also, for example, [Halliday and Resnick (2013); Freedman et al. (2013);
Purcell and Morin (2013); Griffiths (2017); Slater and Frank (2011);
Schwarz (1987); Abraham and Becker (1949); Stratton (2008); Panofsky
and Phillips (2005); Jackson (2009)], etc. The existence of all of these
texts, and the inability to include the wonderful demonstrations, made me
very reluctant to consider publishing these lectures.
On the other hand, these lectures do provide what in my opinion is a
clear,self-contained,calculus-basedintroductiontoasubjectthattogether
with classical mechanics, quantum mechanics, and modern physics lies at
the heart of today’s physics curriculum. A good introduction, even at the
costofsomerepetition,doesallowonetoapproachthemoreadvancedtexts
and monographs with better understanding and a deeper sense of appreci-
ation. Furthermore,these lectures,althoughrelativelyconcise,do takeone
from Coulomb’s law to Maxwell’s equations and special relativity in what
to me is a lucid and logical fashion. The principles of electromagnetism
have such an astonishing range of applicability. So, to round out the set
of physics texts,2 and for my own enjoyment, I have proceeded to convert
thoselecturesintothepresentbook. Ihopethatinusingthistext,students
and teachers alike can share some of the pleasure I took in writing it.
I would, once again, like to thank Dr. K. K. Phua, Executive Chair-
man of World Scientific Publishing Company, and my editor Ms. Lakshmi
Narayanan,for their help and support on this project.
Williamsburg, Virginia John Dirk Walecka
April 30, 2018 Governor’s Distinguished CEBAF
Professor of Physics, emeritus
College of William and Mary
2I was invited some time ago by my co-author Sandy Fetter to collaborate on a
graduate-level E&M text, based on a course he had taught so successfully many times
atStanford,andforwhichhehadagooddraftmanuscript. AsIhadnevertaughtthat
particulargraduatecoursemyself,Ireluctantlydeclinedtheinvitation.
Contents
Preface vii
Electricity 1
1. Introduction 3
1.1 Physics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
1.2 Newton’s Laws . . . . . . . . . . . . . . . . . . . . . . . . . 4
1.3 Gravitational Force . . . . . . . . . . . . . . . . . . . . . . . 4
1.4 Electrical Forces . . . . . . . . . . . . . . . . . . . . . . . . 5
1.4.1 Electrostatics . . . . . . . . . . . . . . . . . . . . . . 5
1.4.2 Electromagnetism . . . . . . . . . . . . . . . . . . . . 6
1.5 Electric Charge . . . . . . . . . . . . . . . . . . . . . . . . . 6
2. Coulomb’s Law 7
2.1 Electrostatics . . . . . . . . . . . . . . . . . . . . . . . . . . 7
2.2 Strength . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
3. The Electric Field 11
3.1 Superposition . . . . . . . . . . . . . . . . . . . . . . . . . . 11
3.2 Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
3.2.1 Point Charge . . . . . . . . . . . . . . . . . . . . . . 12
3.2.2 Lines of Force . . . . . . . . . . . . . . . . . . . . . . 13
3.2.3 Dipole Field . . . . . . . . . . . . . . . . . . . . . . . 13
3.2.4 Sheet of Charge . . . . . . . . . . . . . . . . . . . . . 15
3.2.5 Extension . . . . . . . . . . . . . . . . . . . . . . . . 17
ix
x Introduction toElectricity and Magnetism
3.3 Electric Flux . . . . . . . . . . . . . . . . . . . . . . . . . . 17
4. Gauss’ Law 21
4.1 Gauss’ Law Coulomb’s Law . . . . . . . . . . . . . . . . 22
⇒
4.2 Coulomb’s Law Gauss’ Law . . . . . . . . . . . . . . . . 22
⇒
4.3 Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
4.3.1 Sheet of Charge . . . . . . . . . . . . . . . . . . . . . 24
4.3.2 Line of Charge . . . . . . . . . . . . . . . . . . . . . 25
4.3.3 Conductors . . . . . . . . . . . . . . . . . . . . . . . 26
4.3.4 Charged Conducting Sphere . . . . . . . . . . . . . . 27
4.4 Charged Particle Motion . . . . . . . . . . . . . . . . . . . . 28
5. The Electrostatic Potential 31
5.1 Work Done by a Force . . . . . . . . . . . . . . . . . . . . . 31
5.2 Point Charge q . . . . . . . . . . . . . . . . . . . . . . . . . 32
5.2.1 Another Path . . . . . . . . . . . . . . . . . . . . . . 33
5.2.2 Closed Path . . . . . . . . . . . . . . . . . . . . . . . 34
5.3 Collection of Charges. . . . . . . . . . . . . . . . . . . . . . 35
5.4 Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
5.4.1 Sheet of Charge . . . . . . . . . . . . . . . . . . . . . 36
5.4.2 Line of Charge . . . . . . . . . . . . . . . . . . . . . 36
5.5 Charged-ParticleMotion . . . . . . . . . . . . . . . . . . . . 37
5.6 Properties of Potential . . . . . . . . . . . . . . . . . . . . . 37
5.7 Some Calculus . . . . . . . . . . . . . . . . . . . . . . . . . 39
5.7.1 Single-Variable Function . . . . . . . . . . . . . . . . 39
5.7.2 Multi-Variable Function . . . . . . . . . . . . . . . . 39
5.8 Gradient . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
5.9 Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
5.9.1 Sheet of Charge . . . . . . . . . . . . . . . . . . . . . 41
5.9.2 Point Charge . . . . . . . . . . . . . . . . . . . . . . 41
5.9.3 Collection of Charges . . . . . . . . . . . . . . . . . . 42
5.10Surface of Conductor an Equipotential . . . . . . . . . . . . 42
6. Electric Energy 45
6.1 Pair of Charges . . . . . . . . . . . . . . . . . . . . . . . . . 45
6.2 Collection of Charges. . . . . . . . . . . . . . . . . . . . . . 46
6.3 Charged Conductors . . . . . . . . . . . . . . . . . . . . . . 47
6.4 Charged Parallel Plates . . . . . . . . . . . . . . . . . . . . 48