Question

Figure shows a wire sliding on two parallel, conducting rails placed at a separation l. A magnetic field B exists in a direction perpendicular to the plane of the rails. What force is necessary to keep the wire moving at a constant velocity v ?

Answer 1

Because the force exerted by the magnetic field on the rod is given by F_magnetic = ilB, the direction of this force is opposite to that of the motion of the rod.
Now, let the external force on it be F.
Because the velocity is constant, the net force acting on the wire must be zero.
Thus, F = F_magnetic = ilB is acting in the direction of the velocity.