  It has been shown that magnetic fields play an important role in the
stability of molecular clouds, mainly perpendicularly to the field direction.
However, in the parallel direction the stability is a serious problem still to
be explained. Interstellar turbulence may allow the generation of Alfv\'en
waves that propagate through the clouds in the magnetic field direction. These
regions also present great amounts of dust particles which can give rise to new
wave modes, or modify the pre-existing ones. The dust-cyclotron damping affects
the Alfv\'en wave propagation near the dust- cyclotron frequency. On the other
hand, the clouds present different grain sizes, which carry different charges.
In this sense, a dust particle distribution has several dust-cyclotron
frequencies and it will affect a broad band of wave frequencies. In this case,
the energy transfer to the gas is more efficient than in the case where the
ion-cyclotron damping is considered alone. This effect becomes more important
if a power law spectrum is considered for the wave energy flux, since the major
part of the energy is concentrated in low-frequency waves. In this work we
calculate the dust- cyclotron damping in a dusty and magnetized dwarf molecular
cloud, as well as determine the changes in the Alfv\'en wave flux. Then, we use
these results to study the gravitational stability of the cloud. We show that,
considering the presence of charged dust particles, the wave flux is rapidly
damped due to dust-cyclotron damping. Then the wave pressure acts in a small
length scale, and cannot explain the observable cloud sizes, but can explain
the existence of small and dense cores.
