A Student's Guide to Maxwell's Equations

Gauss's law for electric fields, Gauss's law for magnetic fields, Faraday's law, and the Ampere-Maxwell law are four of the most influential equations in science. 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. This book is a wonderful resource for undergraduate and graduate courses in electromagnetism and electromagnetics. A website hosted by the author at www.cambridge.org/9780521701471 contains interactive solutions to every problem in the text as well as audio podcasts to walk students through each chapter.

Daniel Fleisch is Associate Professor in the Department of Physics at Wittenberg University, Ohio.

Preface	p. vii
Acknowledgments	p. ix
Gauss's law for electric fields	p. 1
The integral form of Gauss's law	p. 1
The electric field	p. 3
The dot product	p. 6
The unit normal vector	p. 7
The component of E normal to a surface	p. 8
The surface integral	p. 9
The flux of a vector field	p. 10
The electric flux through a closed surface	p. 13
The enclosed charge	p. 16
The permittivity of free space	p. 18
Applying Gauss's law (integral form)	p. 20
The differential form of Gauss's law	p. 29
Nabla - the del operator	p. 31
Del dot - the divergence	p. 32
The divergence of the electric field	p. 36
Applying Gauss's law (differential form)	p. 38
Gauss's law for magnetic fields	p. 43
The integral form of Gauss's law	p. 43
The magnetic field	p. 45
The magnetic flux through a closed surface	p. 48
Applying Gauss's law (integral form)	p. 50
The differential form of Gauss's law	p. 53
The divergence of the magnetic field	p. 54
Applying Gauss's law (differential form)	p. 55
Faraday's law	p. 58
The integral form of Faraday's law	p. 58
The induced electric field	p. 62
The line integral	p. 64
The path integral of a vector field	p. 65
The electric field circulation	p. 68
The rate of change of flux	p. 69
Lenz's law	p. 71
Applying Faraday's law (integral form)	p. 72
The differential form of Faraday's law	p. 75
Del cross - the curl	p. 76
The curl of the electric field	p. 79
Applying Faraday's law (differential form)	p. 80
The Ampere-Maxwell law	p. 83
The integral form of the Ampere-Maxwell law	p. 83
The magnetic field circulation	p. 85
The permeability of free space	p. 87
The enclosed electric current	p. 89
The rate of change of flux	p. 91
Applying the Ampere-Maxwell law (integral form)	p. 95
The differential form of the Ampere-Maxwell law	p. 101
The curl of the magnetic field	p. 102
The electric current density	p. 105
The displacement current density	p. 107
Applying the Ampere-Maxwell law (differential form)	p. 108
From Maxwell's Equations to the wave equation	p. 112
The divergence theorem	p. 114
Stokes' theorem	p. 116
The gradient	p. 119
Some useful identities	p. 120
The wave equation	p. 122
Maxwell's Equations in matter	p. 125
Further reading	p. 131
Index	p. 132
Table of Contents provided by Ingram. All Rights Reserved.

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A Student's Guide to Maxwell's Equations

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