  We prove there exists a charge solution to the 1-dimensional wave equation,
and a corresponding current, such that the pair satisfy the continuity
equation. We show that when they are extended to a smooth solution of the
continuity equation on a vanishing annulus containing the unit circle, with a
corresponding causal solution to Maxwell's equations, obtained from Jefimenko's
equations, the power radiated at infinity in a time cycle is zero.
