  We investigate the thermodynamic and hydrodynamic properties of 4-dimensional
gauge theories with finite electric charge density in the presence of a
constant magnetic field. Their gravity duals are planar magnetically and
electrically charged AdS black holes in theories that contain a gauge
Chern-Simons term. We present a careful analysis of the near horizon geometry
of these black branes at finite and zero temperature for the case of a scalar
field non-minimally coupled to the electromagnetic field. With the knowledge of
the near horizon data, we obtain analytic expressions for the shear viscosity
coefficient and entropy density, and also study the effect of a generic set of
four derivative interactions on their ratio. We also comment on the attractor
flows of the extremal solutions.
