An infinite family of axisymmetric charged dust disks of finite extension is presented. The disks are obtained by solving the vacuum Einstein-Maxwell equations for conformastatic spacetimes, which are characterized by only one metric function. In order to obtain the solutions, a functional relationship between the metric function and the electric potential is assumed. It is also assumed that the metric function is functionally dependent on another auxiliary function, which is taken as a solution of the Laplace equation. The solutions for the auxiliary function are then taken as given by the infinite family of generalized Kalnajs disks recently obtained by Gonz\'alez and Reina [G. A. Gonz\'alez and J. I. Reina, Mon. Not. R. Astron. Soc. 371, 1873 (2006).], expressed in terms of the oblate spheroidal coordinates and corresponding to a family of well-behaved Newtonian axisymmetric thin disks of finite radius. The obtained relativistic thin disks have a charge density that is equal, except maybe by a sign, to their mass density, in such a way that the electric and gravitational forces are in exact balance. The energy density of the disks is everywhere positive and well behaved, vanishing at the edge. Accordingly, as the disks are made of dust, their energy-momentum tensor agrees with all the energy conditions.