A Student's Guide to Maxwell's Equations
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A guide for undergraduate and graduate courses in electromagnetism and electromagnetics.
Preface viiAcknowledgments ix1 Gauss's law for electric fields 11.1 The integral form of Gauss's law 1The electric field 3The dot product 6The unit normal vector 7The component of E normal to a surface 8The surface integral 9The flux of a vector field 10The electric flux through a closed surface 13The enclosed charge 16The permittivity of free space 18Applying Gauss's law (integral form) 201.2 The differential form of Gauss's law 29Nabla - the del operator 31Del dot - the divergence 32The divergence of the electric field 36Applying Gauss's law (differential form) 382 Gauss's law for magnetic fields 432.1 The integral form of Gauss's law 43The magnetic field 45The magnetic flux through a closed surface 48Applying Gauss's law (integral form) 502.2 The differential form of Gauss's law 53The divergence of the magnetic field 54Applying Gauss's law (differential form) 553 Faraday's law 583.1 The integral form of Faraday's law 58The induced electric field 62The line integral 64The path integral of a vector field 65The electric field circulation 68The rate of change of flux 69Lenz's law 71Applying Faraday's law (integral form) 723.2 The differential form of Faraday's law 75Del cross - the curl 76The curl of the electric field 79Applying Faraday's law (differential form) 804 The Ampere-Maxwell law 834.1 The integral form of the Ampere-Maxwell law 83The magnetic field circulation 85The permeability of free space 87The enclosed electric current 89The rate of change of flux 91Applying the Ampere-Maxwell law (integral form) 954.2 The differential form of theAmpere-Maxwell law 101The curl of the magnetic field 102The electric current density 105The displacement current density 107Applying the Ampere-Maxwell law (differential form) 1085 From Maxwell's Equations to the wave equation 112The divergence theorem 114Stokes' theorem 116The gradient 119Some useful identities 120The wave equation 122Appendix Maxwell's Equations in matter 125Further reading 131Index 132
