The paper reports on the dynamics of a 3-dimensional dusty plasma in a strong magnetic field. An electrostatic potential well created by a conducting or non-conducting ring in the rf discharge confines the charged dust particles. In the absence of the magnetic field, dust grains exhibit a thermal motion about their equilibrium position. As the magnetic field crosses a threshold value (B $>$ 0.02 T), the edge particles start to rotate and form a vortex in the vertical plane. At the same time, the central region particles either exhibit thermal motion or $vec{E} times vec{B}$ motion in the horizontal plane. At B $>$ 0.15 T, the central region dust grains start to rotate in the opposite direction resulting in a pair of counter-rotating vortices in the vertical plane. The characteristics of the vortex pair change with increasing the strength of the magnetic field (B $sim$ 0.8 T). At B $>$ 0.8 T, dust grains exhibit very complex motion in the rotating torus. The angular frequency variation of rotating particles indicates a differential or sheared dust rotation in a vortex. The angular frequency increases with increasing the magnetic field from 0.05 T to 0.8 T. The ion drag force and dust charge gradient along with the E-field are considered as possible energy sources for driving the edge vortex flow and central region vortex motion, respectively. The directions of rotation also confirm the different energy sources responsible for the vortex motion.
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