Safari, the world’s most comprehensive technology and business learning platform.

Find the exact information you need to solve a problem on the fly, or go deeper to master the technologies and skills you need to succeed

Start Free Trial

No credit card required

O'Reilly logo
A Student's Guide to Maxwell's Equations

Book Description

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

Table of Contents

  1. Coverpage
  2. A Student’s Guide to Maxwell’s Equations
  3. Title page
  4. Copyright page
  5. Contents
  6. Preface
  7. Acknowledgments
  8. 1 Gauss’s law for electric fields
    1. 1.1 The integral form of Gauss’s law
    2. The electric field
    3. The dot product
    4. The unit normal vector
    5. The component of normal to a surface
    6. The surface integral
    7. The flux of a vector field
    8. The electric flux through a closed surface
    9. The enclosed charge
    10. The permittivity of free space
    11. Applying Gauss’s law (integral form)
    12. 1.2 The differential form of Gauss’s law
    13. Nabla – the del operator
    14. Del dot – the divergence
    15. The divergence of the electric field
    16. Applying Gauss’s law (differential form)
  9. 2 Gauss’s law for magnetic fields
    1. 2.1 The integral form of Gauss’s law
    2. The magnetic field
    3. The magnetic flux through a closed surface
    4. Applying Gauss’s law (integral form)
    5. 2.2 The differential form of Gauss’s law
    6. The divergence of the magnetic field
    7. Applying Gauss’s law (differential form)
  10. 3 Faraday’s law
    1. 3.1 The integral form of Faraday’s law
    2. The induced electric field
    3. The line integral
    4. The path integral of a vector field
    5. The electric field circulation
    6. The rate of change of flux
    7. Lenz’s law
    8. Applying Faraday’s law (integral form)
    9. 3.2 The differential form of Faraday’s law
    10. Del cross – the curl
    11. The curl of the electric field
    12. Applying Faraday’s law (differential form)
  11. 4 The Ampere–Maxwell law
    1. 4.1 The integral form of the Ampere–Maxwell law
    2. The magnetic field circulation
    3. The permeability of free space
    4. The enclosed electric current
    5. The rate of change of flux
    6. Applying the Ampere–Maxwell law (integral form)
    7. 4.2 The differential form of the Ampere–Maxwell law
    8. The curl of the magnetic field
    9. The electric current density
    10. The displacement current density
    11. Applying the Ampere–Maxwell law (differential form)
  12. 5 From Maxwell’s Equations to the wave equation
    1. The divergence theorem
    2. Stokes’ theorem
    3. The gradient
    4. Some useful identities
    5. The wave equation
  13. Appendix: Maxwell’s Equations in matter
  14. Further reading
  15. Index