A student's guide to Maxwell's equations

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 the Ampere-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