  In this paper, we study fundamental aspects of electrostatics as a special
case in Stueckelberg-Horwitz electromagnetic theory. In this theory, spacetime
events $x^\mu(\tau)$ evolve in an unconstrained 8-dimensional phase space,
interacting through five $\tau$-dependent gauge fields induced by the current
densities associated with their evolutions. The chronological time $\tau$ was
introduced as an independent evolution parameter in order to free the
laboratory clock $x^0$ to evolve alternately 'forward' and 'backward' in time
according to the sign of the energy, thus providing a classical implementation
of the Feynman-Stueckelberg interpretation of pair creation/annihilation. The
resulting theory differs in its underlying mechanics from conventional
electromagnetism, but coincides with Maxwell theory in an equilibrium limit.
  After a brief review of Stueckelberg-Horwitz electrodynamics, we obtain the
field produced by an event in uniform motion and verify that it satisfies the
field equations. We study this field in the rest frame of the event, where it
depends explicitly on coordinate time $x^0$ and the parameter $\tau$, as well
as spatial distance $R$. Calculating with this generalized Coulomb field, we
demonstrate how Gauss's theorem and Stoke's theorem apply in 4D spacetime, and
obtain the fields associated with a charged line and a charged sheet. Finally,
we use the field of the charged sheet to study a static event in the vicinity
of a potential barrier. In all of these cases, we observe a small transfer of
mass from the field to the particle. It is seen that for an event in the field
of an oppositely charged sheet of sufficient density, the event can reverse
time direction, providing a specific model for pair phenomena.
