As depicted in the figure, a current generator I_g drives a constant current i through the circuit. A wire ab , having mass m and length l , is capable of sliding along the smooth horizontal rails linked to I_g . The complete arrangement is positioned within a vertical magnetic field B . Determine the velocity of the wire as a function of time t .

Step-by-step solution

From the given circuit diagram, the constant current i flows through the wire ab from a to b . The uniform magnetic field B is directed into the plane of the paper. The magnetic force acting on the current-carrying wire ab is given by F = i( l B ) . The magnitude of this force is F = ilB (90^ ) = ilB . Using the right-hand rule or Fleming's left-hand rule, the direction of this force is towards the right, which is away from the generator. Since the horizontal rails are smooth, the net force on the wire is F = ilB .