  We study the generalized $n$ component model of a driven diffusive system
with annealed random drive in the large $n$ limit. This non-equilibrium model
also describes conserved order parameter dynamics of an equilibrium model of
ferromagnets with dipolar interaction. In this limit, at zero temperature a
saddle point approximation becomes exact. The length scale in the direction
transverse to the driving field acquires an additional logarithmic correction
in this limit.
