  We report Brownian Dynamics simulation results for the relative permittivity
of electrorheological (ER) fluids in an applied electric field. The relative
permittivity of an ER fluid can be calculated from the Clausius-Mosotti (CM)
equation in the small applied field limit. When a strong field is applied,
however, the ER spheres are organized into chains and assemblies of chains in
which case the ER spheres are polarized not only by the external field but by
each other. This manifests itself in an enhanced dielectric response, e.g., in
an increase in the relative permittivity. The correction to the relative
permittivity and the time dependence of this correction is simulated on the
basis of a model in which the ER particles are represented as polarizable
spheres. In this model, the spheres are also polarized by each other in
addition to the applied field. Our results are qualitatively similar to those
obtained by Horv\'ath and Szalai experimentally (\textit{Phys. Rev. E},
\textbf{86}, 061403, 2012). We report characteristic time constants obtained
from bi-exponential fits that can be associated with formation of pairs and
short chains as well as with aggregation of chains. The electric field
dependence of the induced dielectric increment reveals the same qualitative
behavior that experiments did: three regions with different slopes
corresponding to different aggregation processes are identified.
