  The presence of dust grains profoundly affects the diffusion of the magnetic
field in molecular clouds. When the electrons and ions are well coupled to the
magnetic field and charged grains are only indirectly coupled, emergent Hall
diffusion may dominate over all the other non ideal magnetohydrodynamic (MHD)
effects in a partially ionized dusty cloud. The low frequency, long wavelength
(0.01 t0 1 pc) dispersive MHD waves will propagate in such a medium with the
polarization of the waves determined by the dust charge density or the dust
size distribution. In the presence of shear flows, these waves may become
Kelvin Helmholtz (KH) unstable with the dust charge density or the grain size
distribution operating as a switch to the instability. When Hall diffusion time
is long (compared to the time over which waves are sheared), the growth rate of
the instability in the presence of sub Alfvenic flow increases with the charge
number Z on the grain, while it is quenched in the presence of Alfvenic or
super Alfvenic flows. However, when Hall diffusion is fast, the growth rate of
the instability depends on the dust charge only indirectly.
