Perfectly conducting loop of wire moving through a uniform and stationary magnetic field

A conductive loop of wire moving with constant velocity in a magnetic field is one of the most used examples in physics textbooks in connection to the Faraday-Lenz law, highlighting the consistency of electromagnetism with the principle of conservation of energy. It is frequently concluded that currents are not induced in a perfectly conducting loop because an induced current would have to be infinite and therefore would violate the principle of energy conservation. In this paper we discuss this problem and show that a model that includes the loop self-inductance prevents the divergence of the current and leads to results compatible with the conservation of energy.