A Student's Guide to Maxwell's Equations

A Student's Guide to Maxwell's Equations

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by Daniel Fleisch
     
 

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ISBN-10: 052187761X

ISBN-13: 9780521877619

Pub. Date: 01/28/2008

Publisher: Cambridge University Press

Maxwell's Equations are four of the most influential equations in science: Gauss's law for electric fields, Gauss's law for magnetic fields, Faraday's law, and the Ampere-Maxwell law. In this guide for students, each equation is the subject of an entire chapter, with detailed, plain-language explanations of the physical meaning of each symbol in the equation, for

Overview

Maxwell's Equations are four of the most influential equations in science: Gauss's law for electric fields, Gauss's law for magnetic fields, Faraday's law, and the Ampere-Maxwell law. In this guide for students, each equation is the subject of an entire chapter, with detailed, plain-language explanations of the physical meaning of each symbol in the equation, for both the integral and differential forms. The final chapter shows how Maxwell's Equations may be combined to produce the wave equation, the basis for the electromagnetic theory of light.

Product Details

ISBN-13:
9780521877619
Publisher:
Cambridge University Press
Publication date:
01/28/2008
Pages:
146
Sales rank:
382,135
Product dimensions:
5.98(w) x 8.98(h) x 0.51(d)

Table of Contents

Preface vii

Acknowledgments ix

1 Gauss's law for electric fields 1

1.1 The integral form of Gauss's law 1

The electric field 3

The dot product 6

The unit normal vector 7

The component of E normal to a surface 8

The surface integral 9

The flux of a vector field 10

The electric flux through a closed surface 13

The enclosed charge 16

The permittivity of free space 18

Applying Gauss's law (integral form) 20

1.2 The differential form of Gauss's law 29

Nabla - the del operator 31

Del dot - the divergence 32

The divergence of the electric field 36

Applying Gauss's law (differential form) 38

2 Gauss's law for magnetic fields 43

2.1 The integral form of Gauss's law 43

The magnetic field 45

The magnetic flux through a closed surface 48

Applying Gauss's law (integral form) 50

2.2 The differential form of Gauss's law 53

The divergence of the magnetic field 54

Applying Gauss's law (differential form) 55

3 Faraday's law 58

3.1 The integral form of Faraday's law 58

The induced electric field 62

The line integral 64

The path integral of a vector field 65

The electric field circulation 68

The rate of change of flux 69

Lenz's law 71

Applying Faraday's law (integral form) 72

3.2 The differential form of Faraday's law 75

Del cross - the curl 76

The curl of the electric field 79

Applying Faraday's law (differential form) 80

4 The Ampere-Maxwell law 83

4.1 The integral form of the Ampere-Maxwell law 83

The magnetic field circulation 85

The permeability of free space 87

The enclosed electric current 89

The rate of change of flux 91

Applying the Ampere-Maxwell law (integral form) 95

4.2 The differential form of theAmpere-Maxwell law 101

The curl of the magnetic field 102

The electric current density 105

The displacement current density 107

Applying the Ampere-Maxwell law (differential form) 108

5 From Maxwell's Equations to the wave equation 112

The divergence theorem 114

Stokes' theorem 116

The gradient 119

Some useful identities 120

The wave equation 122

Appendix Maxwell's Equations in matter 125

Further reading 131

Index 132

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