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Equilibrium configurations of a circling electrically charged fluid surrounding a central static black hole endowed with a test electric charge and embedded in a large-scale asymptotically uniform magnetic field are presented. Various configurations of the fluid are influenced by the balance between the gravitational and electromagnetic actions; previous studies of the circling charged fluid configurations around a rotating black hole showed a strong dependence on the spin of the black hole. In this work, we focus on configurations centered in the equatorial plane taking shapes of single or double toroidal structures. Our interest is the existence of these structures, and how various actions, such as electromagnetic, gravitational and centrifugal, influence their shapes and physics.