  The purpose of the present work is to extend the earlier results for
asymptotically flat vacuum space-times to asymptotically flat solutions of the
Einstein-Maxwell equations. Once again, in this case, we get a class of
asymptotically shear-free null geodesic congruences depending on a complex
world-line in the same four-dimensional complex space. However in this case
there will be, in general, two distinct but uniquely chosen world-lines. One of
which can be assigned as the complex center-of- charge while the other could be
called the complex center of mass. Rather than investigating the situation
where there are two distinct complex world-lines, we study instead the special
degenerate case where the two world-lines coincide, i.e., where there is a
single unique world-line. This mimics the case of algebraically special
Einstein-Maxwell fields where the degenerate principle null vector of the Weyl
tensor coincides with a Maxwell principle null vector. Again we obtain
equations of motion for this world-line - but explicitly found here only in an
approximation. Though there are ambiguities in assigning physical meaning to
different terms it appears as if reliance on the Kerr and charged Kerr metrics
and classical electromagnetic radiation theory helps considerably in this
identification. In addition, the resulting equations of motion appear to have
many of the properties of a particle with intrinsic spin and an intrinsic
magnetic dipole moment. At first order there is even the classical
radiation-reaction term 2/3{q^{2}}{c^{-3}}ddot{v}, now obtained without any use
of the Lorentz force law but obtained directly from the asymptotic fields
themselves. One even sees the possible suppression, via the Bondi mass loss, of
the classical runaway solutions due to the radiation reaction force.
