  We have solved the Einstein-Maxwell equations for a class of isotropic
metrics with constant spatial curvature in the presence of magnetic fields. We
consider a slight modification of the Tolman averaging relations so that the
energy-momentum tensor of the electromagnetic field possesses an anisotropic
pressure component. This inhomogeneous magnetic universe is isotropic and its
time evolution is guided by the usual Friedmann equations. In the case of flat
universe, the space-time metric is free of singularities (except the well-known
initial singularity at t = 0). It is shown that the anisotropic pressure of our
model has a straightforward relation to the Weyl tensor. We also analyze the
effect of this new ingredient on the motion of test particles and on the
geodesic deviation of the cosmic fluid.
