TABLE OF CONTENTS We will now construct a relativistic theory of electric interactions. This means that we will take the nonrelativistic electrostatic equations of Chapter 2 and ask how these equations must be generalized to satisfy the Principle of Relativity. It turns out that this question has a unique answer: there is one and only one set of relativistic equations that reduces to the electrostatic equations in the static limit. As a by-product of our investigations, we will discover that the electric field is insufficient for describing the interactions among charges. An extra field the magnetic field is needed whenever we deal with charges in motion.
In the electrostatic case, the charge density ? is time independent, and the current density j is zero. Under these conditions, the equations in Chapter 2 give us a complete description of the electric interactions in terms of a single function of space: the potential ?. If j is not zero, then this potential function is insufficient to describe the electric interactions. The following simple example will make this clear.
Consider a long straight wire carrying a uniform current density but no charge density. For a concrete picture, we may think of the wire as carrying a flow of conduction electrons whose negative contribution to the charge density is compensated by a positive contribution from the positive ions of the crystal lattice of the wire. Consider, next, a point charge q that is moving with velocity v parallel to...
