We have so far in this book regarded the sources ρ, J of the electromagnetic field as given. However, the charges and currents in material media are themselves driven by the fields, so that we need to describe the electrical and magnetic responses of materials to an electromagnetic field. At the atomic level, the Coulomb forces between electrons and atomic nuclei are responsible for their binding into atoms and molecules, and the large scale structure of materials. A description at this level involves the complicated quantum mechanics of the constituent particles of the materials, and is the province of condensed matter physics and material science. For the most part, we shall rather be concerned with the macroscopic electrical and magnetic properties of materials, which can often be described phenomenologically by a small number of parameters, such as the electrical conductivity. These parameters are usually obtained by direct experiment on the material concerned.

We begin in this chapter with a description of conductors in electrostatic equilibrium.

Electrostatic equilibrium

A conductor is a material in which there are electrons, or ions, free to migrate and transport charge in response to an electric field. In a metal or semiconductor the charge carriers are electrons. The principal property of any homogeneous conductor in electrostatic equilibrium is that the electric field E(r) = 0 at all interior points r. If E(r) were not zero, the mobile charge carriers would move in response to the mean Coulomb force, until a charge distribution was established for which the condition held.