  In this paper we apply the techniques which have been developed over the last
few decades for generating nontrivially new solutions of the Einstein-Maxwell
equations from seed solutions for simple spacetimes. The simple seed spacetime
which we choose is the "magnetic universe" to which we apply the Ehlers
transformation. Three interesting non-singular metrics are generated. Two of
these may be described as "rotating magnetic universes" and the third as an
"evolving magnetic universe." Each is causally complete - in that all timelike
and lightlike geodesics do not end in a finite time or affine parameter. We
also give the electromagnetic field in each case. For the two rotating
stationary cases we give the projection with respect to a stationary observer
of the electromagnetic field into electric and magnetic components.
