Maxwell's equations are four of the most influential equations in science. In this book, each equation is the subject of an entire chapter, making it a wonderful resource for undergraduate and graduate courses in electromagnetism and electromagnetics. Audio podcasts and solutions to the problems are available at www.cambridge.org/9780521701471. 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