Introduction to Electrodynamics 5th Edition – David Griffiths (2023) - eTextbook

Introduction To Electrodynamics Etextbook
By David Griffiths


5th Edition

, Contents


Preface Xii

Advertisement Xiv

1 Vector Analysis 1
1.1 Vector Algebra 1
1.1.1 Vector Operations 1
1.1.2 Vector Algebra: Component Form 4
1.1.3 Triple Products 7
1.1.4 Position, Displacement, And Separation Vectors 8
1.1.5 How Vectors Transform 10
1.2 Differential Calculus 13
1.2.1 “Ordinary” Derivatives 13
1.2.2 Gradient 13
1.2.3 The Del Operator 16
1.2.4 The Divergence 17
1.2.5 The Curl 18
1.2.6 Product Rules 20
1.2.7 Second Derivatives 22
1.3 Integral Calculus 24
1.3.1 Line, Surface, And Volume Integrals 24
1.3.2 The Fundamental Theorem Of Calculus 29
1.3.3 The Fundamental Theorem For Gradients 29
1.3.4 The Fundamental Theorem For Divergences 31
1.3.5 The Fundamental Theorem For Curls 34
1.3.6 Integration By Parts 36
1.4 Curvilinear Coordinates 38
1.4.1 Spherical Coordinates 38
1.4.2 Cylindrical Coordinates 43
1.5 The Dirac Delta Function 45
1.5.1 The Divergence Of ˆR/R 2 45
1.5.2 The One-Dimensional Dirac Delta Function 46
1.5.3 The Three-Dimensional Delta Function 50

V

,Vi Contents

1.6 The Theory Of Vector Fields 52
1.6.1 The Helmholtz Theorem 52
1.6.2 Potentials 53


2 Electrostatics 59
2.1 The Electric Field 59
2.1.1 Introduction 59
2.1.2 Coulomb’s Law 60
2.1.3 The Electric Field 61
2.1.4 Continuous Charge Distributions 63
2.2 Divergence And Curl Of Electrostatic Fields 66
2.2.1 Field Lines, Flux, And Gauss’s Law 66
2.2.2 The Divergence Of E 71
2.2.3 Applications Of Gauss’s Law 71
2.2.4 The Curl Of E 77
2.3 Electric Potential 78
2.3.1 Introduction To Potential 78
2.3.2 Comments On Potential 80
2.3.3 Poisson’s Equation And Laplace’s Equation 83
2.3.4 The Potential Of A Localized Charge Distribution 84
2.3.5 Boundary Conditions 88
2.4 Work And Energy In Electrostatics 91
2.4.1 The Work It Takes To Move A Charge 91
2.4.2 The Energy Of A Point Charge Distribution 92
2.4.3 The Energy Of A Continuous Charge Distribution 94
2.4.4 Comments On Electrostatic Energy 96
2.5 Conductors 97
2.5.1 Basic Properties 97
2.5.2 Induced Charges 99
2.5.3 Surface Charge And The Force On A Conductor103
2.5.4 Capacitors 105


3 Potentials 113
3.1 Laplace’s Equation 113
3.1.1 Introduction 113
3.1.2 Laplace’s Equation In One Dimension 114
3.1.3 Laplace’s Equation In Two Dimensions 115
3.1.4 Laplace’s Equation In Three Dimensions 117
3.1.5 Boundary Conditions And Uniqueness Theorems 119
3.1.6 Conductors And The Second Uniqueness Theorem 121

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