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 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
| 
