Propagation of a quasi-neutral plasma beam or cloud across a magnetic field is considered for the case where the transverse dimension of the beam or cloud is sufficiently small compared to ion gyroradii. This situation commonly arises for active experiments in near-earth space. Two mechanisms are presented for transverse deflection of a beam or cloud in the -v0¿B0 direction where v0 is the velocity relative to the ambient medium. In the first, asymmetric escape of ions from an electrically polarized beam or cloud causes transverse deflection by means of a rocket effect. The transverse deflection distance is estimated to be a few times the initial transverse dimension of the beam or cloud. Dissipation occurs within a few times the thermal ion transverse crossing time. In the second mechanism, asymmetric charging results from localized accumulation of incident ions from the ambient medium. This excess positive charge distorts electric equipotentials and drives electron Hall currents that maintain an asymmetric compressed magnetic field region. The asymmetry of the magnetic stress contributes to transverse deflection with the same sign as the rocket effect. The asymmetric magnetic field also focuses incident ions to yield the localized charge accumulation. These ideas are qualitatively consistent with observations of the Active Magnetospheric Particle Tracer Explorers artificial comet releases.