  In this paper we discuss global existence of the solution of the Maxwell and
Newton system of equations, describing the interaction of a rigid charge
distribution with the electromagnetic field it generates. A unique solution is
proved to exist (for regular charge distributions) on suitable homogeneous and
non-homogeneous Sobolev spaces, for the electromagnetic field, and on
coordinate and velocity space for the charge; provided initial data belong to
the subspace that satisfies the divergence part of Maxwell's equations.
