Wave generation associated with the expansion of a dust cloud into a background plasma across a magnetic field is studied by using numerical simulation and theoretical models. As the dust grains expand across the magnetic field into the background plasma and charge up, an ambipolar electric field develops across the boundary layer between the negatively charged dust cloud and the background plasma. A strongly sheared electron E × B flow develops along the boundary. Plasma irregularities develop in response to the sheared electron flow velocity. It is noted that these irregularities are observed in the dust grain charge as well as the background plasma electron and ion densities. The fluctuations in dust grain charge are interpreted to be a fundamental collective effect in the dusty plasma produced by the dust cloud expansion. A theoretical model for the shear-driven instability in the dust cloud boundary is presented. In general, the theoretical model predictions show good agreement with the numerical simulation results.