  We consider the two-body dynamical capture of black holes carrying U(1)
charge which can not only correspond to electric or magnetic charge but also
have other physical interpretations such as dark or hidden charge. In the
low-velocity and weak-field regime, we study gravitational and electromagnetic
radiations from point masses with U(1) charges in a hyperbolic orbit, and we
develop a formalism to derive the merger rate of charged black holes from the
two-body dynamical capture. We apply the formalism to find the effects of the
charge-to-mass ratio on the merger rate for possible different cases and
discover that the effects depend on the models.
