Recent studies have demonstrated the benefits of using electrodynamic tethers (EDT) for the exploration of the inner region of the Jovian system. Intense planetary magnetic field and reasonable environmental plasma density make the electrodynamic interaction of the conductive tether with the plasmasphere strong. The interaction is responsible for a Lorentz force that can be conveniently used for propellantless maneuvers and extraction of electrical power for on board use. Jupiter and the four Galilean Moons represent an exceptional gravitational environment for the study of the orbital dynamics of an EDT. The dynamics of such a system was analyzed using a 3-body model, consisting of the planet plus one of its moons (Io in this work) and the EDT itself. New and interesting features appear, like for example the possibility to place the tether in equilibrium with respect to a frame co-rotating with the moon at points that do not coincide with the classical Lagrangian points for non-null electrodynamic forces.