Some fish species use electric sense to navigate efficiently in the turbid waters of confined spaces. This paper presents a first attempt to use this sense to control a group of nonholonomic rigid underwater vehicles navigating in a cooperative way. A leader whose motion is unknown to the others serves as an active agent for its passive neighbor, which perceives the leader's electric field via current measurements and moves in order to follow a trajectory relative to it. Then, this passive agent, becomes in its turn the leader for the next agent and so on. Sufficient conditions of convergence of the control law are derived for electric current servoing. This is achieved without the explicit knowledge of the location of the agents. Some limits on the possible motion of the leader along with the importance of the choice of controlled outputs are demonstrated. Switching between different group configurations by following a virtual agent is also described. Simulation and experimental results illustrate the theoretical study.