  We examine the dynamical consequences of homogeneous cosmological magnetic
fields in the framework of loop quantum cosmology. We show that a big-bounce
occurs in a collapsing magnetized Bianchi I universe, thus extending the known
cases of singularity-avoidance. Previous work has shown that perfect fluid
Bianchi I universes in loop quantum cosmology avoid the singularity via a
bounce. The fluid has zero anisotropic stress, and the shear anisotropy in this
case is conserved through the bounce. By contrast, the magnetic field has
nonzero anisotropic stress, and shear anisotropy is not conserved through the
bounce. After the bounce, the universe enters a classical phase. The addition
of a dust fluid does not change these results qualitatively.
