  A rotating particle in electrorheological (ER) fluid leads to a displacement
of its polarization charges on the surface which relax towards the external
applied field ${\bf E}_0$, resulting in a steady-state polarization at an angle
with respect to ${\bf E}_0$. This dynamic effect has shown to affect the ER
fluids properties dramatically. In this paper, we develop a dynamic effective
medium theory (EMT) for a system containing rotating particles of finite volume
fraction. This is a generalization of established EMT to account for the
interactions between many rotating particles. While the theory is valid for
three dimensions, the results in a special two dimensional configuration show
that the system exhibits an off-diagonal polarization response, in addition to
a diagonal polarization response, which resembles the classic Hall effect. The
diagonal response monotonically decreases with an increasing rotational speed,
whereas the off-diagonal response exhibits a maximum at a reduced rotational
angular velocity $\omega_0$ comparing to the case of isolated rotating
particles. This implies a way of measurement on the interacting relaxation
time. The dependencies of the diagonal and off-diagonal responses on various
factors, such as $\omega_0$, the volume fraction, and the dielectric contrast,
are discussed.
