Here are presented experiments on fine particles levitating in low-pressure weakly ionized plasmas under a vertical magnetic field. The magnetic field is useful to provide a vertically long cylindrical column of fine-particle clouds, yielding even string-shaped vertically aligned fine particles, under the double-plasma configuration. Measurements show that fine-particle clouds rotate in the azimuthal direction on the horizontal plane even in such a weak magnetic field that positive ions are slightly magnetized. With an increase of the magnetic field, the rotation speed increases, being followed by subsequent saturation. The rotation speed and direction can be controlled by varying radial plasma potential and/or density profiles. The rotation is induced under the condition that the interparticle distance is small enough for the strong Coulomb coupling among fine particles. A mechanism of the rotation could be explained by effects of ion motions on fine particles, which are modified in the presence of the vertical magnetic field. (C) 2001 American Institute of Physics.