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 cambridge.org/9780521701471 contains interactive solutions to every problem in the text as well as audio podcasts to walk students through each chapter.

Preface
Acknowledgments
1 Gauss's law for electric fields
1.1 The integral form of Gauss's law
The electric field
The dot product
The unit normal vector
The component of E normal to a surface
The surface integral
The flux of a vector field
The electric flux through a closed surface
The enclosed charge
The permittivity of free space
Applying Gauss's law (integral form)
1.2 The differential form of Gauss's law
Nabla - the del operator
Del dot - the divergence
The divergence of the electric field
Applying Gauss's law (differential form)
2 Gauss's law for magnetic fields
2.1 The integral form of Gauss's law
The magnetic field
The magnetic flux through a closed surface
Applying Gauss's law (integral form)
2.2 The differential form of Gauss's law
The divergence of the magnetic field
Applying Gauss's law (differential form)
3 Faraday's law
3.1 The integral form of Faraday's law
The induced electric field
The line integral
The path...Preface
Acknowledgments
1 Gauss's law for electric fields
1.1 The integral form of Gauss's law
The electric field
The dot product
The unit normal vector
The component of E normal to a surface
The surface integral
The flux of a vector field
The electric flux through a closed surface
The enclosed charge
The permittivity of free space
Applying Gauss's law (integral form)
1.2 The differential form of Gauss's law
Nabla - the del operator
Del dot - the divergence
The divergence of the electric field
Applying Gauss's law (differential form)
2 Gauss's law for magnetic fields
2.1 The integral form of Gauss's law
The magnetic field
The magnetic flux through a closed surface
Applying Gauss's law (integral form)
2.2 The differential form of Gauss's law
The divergence of the magnetic field
Applying Gauss's law (differential form)
3 Faraday's law
3.1 The integral form of Faraday's law
The induced electric field
The line integral
The path integral of a vector field
The electric field circulation
The rate of change of flux
Lenz's law
Applying Faraday's law (integral form)
3.2 The differential form of Faraday's law
Del cross - the curl
The curl of the electric field
Applying Faraday's law (differential form)
4 The Ampere-Maxwell law
4.1 The integral form of the Ampere-Maxwell law
The magnetic field circulation
The permeability of free space
The enclosed electric current
The rate of change of flux
Applying the Ampere-Maxwell law (integral form)
4.2 The differential form of theAmpere-Maxwell law
The curl of the magnetic field
The electric current density
The displacement current density
Applying the Ampere-Maxwell law (differential form)
5 From Maxwell's Equations to the wave equation
The divergence theorem
Stokes' theorem
The gradient
Some useful identities
The wave equation
Appendix Maxwell's Equations in matter
Further reading
Index