  It is known that the anomalous Hall conductivity (AHC) in a disordered two
dimensional electron system with Rashba spin-orbit interaction and finite
ferromagnetic spin-exchange energy is zero in the metallic weak-scattering
regime because of the exact cancellation of the bare-bubble contribution by the
vertex correction. We study the effect of inhomogeneous longitudinal electric
field on the AHC in such a system. We predict that AHC increases from zero (at
zero wavenumber), forms a peak, and then decreases as the wavenumber for the
variation of electric field increases. The peak-value of AHC is as high as the
bare-buble contribution. We find that the wave number, q, at which the peaks
occur is the inverse of the geometric mean of the mean free path of an electron
and the spin-exchange length scale. Although the Rashba energy is responsible
for the peak-value of AHC, the peak position is independent of it.
