Introduction to Electrodynamics - D.J.Griffiths, Prentice Hall, 1999.pdf

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Introduction to Electrodynamics
David
1.
Griffiths
Reed College
Prentice
Hall
Prentice Hall
Upper Saddle River, New Jersey 07458
Library of Congress (::ataloging-in-Publication Data
Griffiths, David
1.
(David Jeffrey)
Introduction to electrodynamics / David J. Griffiths - 3rd ed.
p. em.
Includes biqliographical references and index.
ISBN
0-13-805326-X
I.
Electrodynamics.
I.
Title.
OC680.G74 1999
537.6---<1c21
98-50525
CIP
Executive Editor:
Alison Reeves
Production Editor:
Kim Dellas
Manufacturing Manager:
Trudy Pisciotti
Art Director:
Jayne Conte
Cover Designer:
Bruce Kenselaar
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Gillian Keiff
Composition:
PreTEx' Inc.
•
ISBN
©
1999,1989, 1981 by Prentice-Hall, Inc.
Upper Saddle River, New Jersey 07458
All rights reserved. No part of this book may be
reproduced, in any form or by any means,
without permission in writing from the publisher.
Reprinted with corrections September, 1999
Printed in the United States of America
1098765
0-13-805326-X
Prentice-Hall International (UK) Limited,
London
Prentice-Hall of Australia Pty. Limited,
Sydney
Prentice-Hall Canada Inc.,
Toronto
Prentice-Hall Hispanoamericana, S.A.,
Mexico City
Prentice-Hall of India Private Limited,
New Delhi
Prentice-Hall of Japan, Inc.,
Tokyo
Prentice-Hall Asia Pte. Ltd.,
Singapore
Editora Prentice-Hall do Brasil, Ltda.,
Rio de Janeiro
Contents
Preface
Advertisement
1
Vector Analysis
1.1
Vector Algebra . . . . . . . . . . . . . . .
1.1.1 Vector Operations. . . . . . . . . .
1.1.2 Vector Algebra: Component Form .
1.1.3 Triple Products . . . . . . . . . . .
1.1.4 Position, Displacement, and Separation Vectors
1.1.5 How Vectors Transform
1.2 Differential Calculus . . . . .
1.2.1 "Ordinary" Derivatives
1.2.2 Gradient.....
1.2.3 The Operator V .
1.2.4 The Divergence .
1.2.5 The Curl . . . .
1.2.6 Product Rules . .
1.2.7 Second Derivatives
1.3 Integral Calculus . . . . .
1.3.1 Line, Surface, and Volume Integrals
1.3.2 The Fundamental Theorem of Calculus
1.3.3 The Fundamental Theorem for Gradients
1.3.4 The Fundamental Theorem for Divergences
1.3.5 The Fundamental Theorem for Curls.
1.3.6 Integration by Parts
.
1.4 Curvilinear Coordinates.
.
1.4.1 Spherical Polar Coordinates
1.4.2 Cylindrical Coordinates
1.5 The Dirac Delta Function . . . . . .
1.5.1 The Divergence of
f /
r
2 . .
1.5.2 The One-Dimensional Dirac Delta Function.
ix
xi
1
1
1
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46
111
IV
CONTENTS
1.5.3 The Three-Dimensional Delta Function
The Theory of Vector Fields ..
1.6.1 The Helmholtz Theorem
1.6.2 Potentials........
50
52
52
53
58
1.6
2
Electrostatics
2.1 The Electric Field
2.1.1 Introduction...
2.1.2 Coulomb's Law.
2.1.3 The Electric Field.
2.1.4 Continuous Charge Distributions.
2.2 Divergence and Curl of Electrostatic Fields
2.2.1 Field Lines, Flux, and Gauss's Law
2.2.2 The Divergence of E . . . .
2.2.3 Applications of Gauss's Law
2.2.4 The Curl of E . . . . . .
2.3 Electric Potential . . . . . . . .
2.3.1 Introduction to Potential
2.3.2 Comments on Potential.
2.3.3 Poisson's Equation and Laplace's Equation
2.3.4 The Potential of a Localized Charge Distribution
2.3.5 Summary; Electrostatic Boundary Conditions
2.4 Work and Energy in Electrostatics . . . . . . . . .
2.4.1 The Work Done to Move a Charge . . . . . .
2.4.2 The Energy of a Point Charge Distribution. .
2.4.3 The Energy of a Continuous Charge Distribution
2.4.4 Comments on Electrostatic Energy.
2.5 Conductors . . . . . . .
2.5.1 Basic Properties
.
2.5.2 Induced Charges
.
2.5.3 Surface Charge and the Force on a Conductor
2.5.4 Capacitors
.
Special Techniques
3.1 Laplace's Equation
.
3.1.1 Introduction
.
3.1.2 Laplace's Equation in One Dimension
3.1.3 Laplace's Equation in Two Dimensions
3.1.4 Laplace's Equation in Three Dimensions
3.1.5 Boundary Conditions and Uniqueness Theorems
3.1.6 Conductors and the Second Uniqueness Theorem
3.2 The Method of Images . . . . . . .
3.2.1 The Classic Image Problem
3.2.2 Induced Surface Charge ..
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3
110
110
III
112
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121
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