The theme of this chapter is the way in which electric charge causes electromagnetic fields. It is thus complementary to chapter 15, which deals with the forces on charged particles caused by electromagnetic fields.
The basic experimental law is Coulomb's law, which gives us the force between two stationary charged particles as a function of their charge and the distance between them. This force is conservative, and therefore has a potential energy. From this we get the scalar potential.
Since Coulomb's law is a ``one over R-squared'' law like Newton's law of gravitation, a version of Gauss's law applies to the part of the electric field derived from the scalar potential. (Gauss's law actually applies to the part derived from the time derivative of the vector potential as well, but we don't particularly need this fact.) We use Gauss's law to get the electric field produced by lines and sheets of stationary electric charge.
A version of Gauss's law also applies to magnetic fields with the simplification that there is no ``magnetic charge'' -- i. e., the magnetic flux out of a closed surface is always zero.
The scalar potential is the timelike component of the four-potential. For a stationary charge the spacelike part of the four-potential, i. e., the vector potential, is zero. (Symmetry demands this -- which way would the vector potential point if it were non-zero?)
Using what we know about relativity and four-vectors, we can immediately infer the scalar and vector potentials for a moving charged particle. We can therefore also compute the electric and magnetic fields for a moving charge. (The details are a bit complicated for a point charge, but can be understood qualitatively without too much effort.)
Computing the scalar and vector potentials, and hence the electric and magnetic fields, for moving lines and sheets of charge is actually easier than for a single point charge. We use the results of our earlier Gauss's law calculations to get the electric and magnetic fields due to these moving sheets and lines.
The emphasis shifts back to the theme of chapter 15 when we get to generators and Faraday's law, namely, the effect of electric and magnetic fields on particles. In this case we study the effect of time-variable vector potentials. Such fields create non-conservative electric forces. Electric generators work via this mechanism. The example studied in the text is generalized into Faraday's law, which states that the EMF around a closed loop equals minus the time rate of change of magnetic flux through the loop. The EMF is the work per unit charge done on a charge particle moving around a closed loop by the non-conservative part of the electric force.
The fact that real photons are massless gives us the dispersion relation for electromagnetic waves. The four-potential is in effect the wave function for photons. The electric and magnetic fields in an electromagnetic wave are perpendicular to the wave direction and to each other, but oscillate in phase. Electromagnetic radiation is created when charged particles accelerate.