Author(s): Daniel Fleisch
Publisher: Cambridge University Press
Date : 2008
Pages : 144
Format : PDF
OCR :
Quality :
Language : English
ISBN-10 : 0521701473 |
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.
Contents:
Preface page 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
v
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 the Ampere–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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