  In this work, we use structure and dynamics in sedimentation equilibrium, in
the presence of gravity, to examine, $via$ confocal microscopy, a Brownian
colloidal system in the presence of an external electric field. The zero field
equation of state (EOS) is hard sphere without any re-scaling of particle size,
and the hydrodynamic corrections to the long-time self-diffusion coefficient
are quantitatively consistent with the expected value for hard spheres. Care is
taken to ensure that both the dimensionless gravitational energy, which is
equivalent to a Peclet number $Pe_g$, and dipolar strength $\Lambda$ are of
order unity. In the presence of an external electric field, anisotropic
chain-chain clusters form; this cluster formation manifests itself with the
appearance of a plateau in the diffusion coefficient when the dimensionless
dipolar strength $\Lambda \sim 1$. The structure and dynamics of this
chain-chain cluster state is examined for a monodisperse system for two
particle sizes.
