A conducting rod MN of mass m and length \'l\' is placed on parallel smooth conducting rails connect

A conducting rod MN of mass m and length \'l\' is placed on parallel smooth conducting rails connected to an uncharged capacitor of capacitance C and a battery of emf `epsilon` as shown. A uniform magnetic field B is existing perpendicular to the plane of the rails. The steady state velocity acquired by the conducting rod MN after closing switch S is (neglect the resistance of the parallel rails and the conducting rod)