  We construct relativistic models of charged dust thick disks for a particular
conformastatic spacetime through a Miyamoto-Nagai transformation used in
Newtonian gravity to model disk like galaxies. Two simple families of thick
disk models and a family of thick annular disks based on the field of an
extreme Reissner-Nordstr\"om black hole and a Morgan-Morgan-like metric are
considered. The electrogeodesic motion of test particles around the structures
are analyzed. Also the stability of the particles against radial perturbation
is studied using an extension of the Rayleigh criteria of stability of a fluid
in rest in a gravitational field. The models built satisfy all the energy
conditions.
