  Astrophysical fluids may acquire non-zero electrical charge because of strong
irradiation or charge separation in a magnetic field. In this case,
electromagnetic and gravitational forces may act together and produce new
equilibrium configurations, which are different from the uncharged ones.
Following our previous studies of charged test particles and uncharged perfect
fluid tori encircling compact objects, we introduce here a simple test model of
a charged perfect fluid torus in strong gravitational and electromagnetic
fields. In contrast to ideal magnetohydrodynamic models, we consider here the
opposite limit of negligible conductivity, where the charges are tied
completely to the moving matter. This is an extreme limiting case which can
provide a useful reference against which to compare subsequent more complicated
astrophysically-motivated calculations. To clearly demonstrate the features of
our model, we construct three-dimensional axisymmetric charged toroidal
configurations around Reissner-Nordstr\"om black holes and compare them with
equivalent configurations of electrically neutral tori.
