A straight rod of mass m and length l can slide on two parallel plastic rails kept in a horizontal plane with separation d. The coefficient of friction between the wire and the rails is μ. If the wire carries a current i, what minimum magnetic field should exist in space in order to slide the wire on the rails.

Let us consider the Magnetic field is B. Then The force on the wire due to magnetic field is F = ilB If the wire does not slide on the rails, the force of friction by the rails should be equal to F If B be the minimum Magnetic field which can prevent sliding, this force is also equal to frictional force miyu*mg. Thus, Miyu*mg = ilB B = Miyu*mg/il