As shown in the figure, a wire slides on two parallel, conducting rails positioned at a separation l . A magnetic field B is directed perpendicular to the plane of the rails. What force is needed to keep the wire moving at a constant velocity v ?

Step-by-step solution

As the wire moves in the uniform magnetic field, a motional emf is induced across its ends, given by = Bvl . However, the two parallel rails are not connected to each other to form a closed loop, meaning the circuit is open. Because the circuit is open, the induced current I flowing through the wire is zero. The magnetic force acting on a current-carrying wire in a magnetic field is given by F_m = IlB . Substituting I = 0 , we get F_m = 0 . To keep the wire moving at a constant velocity, the net force must be zero.