A bar of mass m, length L, and resistance R slides without friction on parallel rails shown in the figure. A battery that maintains a constant emf ɛ is connected between the rails, and a constant magnetic field B is directed perpendicularly into the plane of the page. If the bar starts from rest at t = 0, (a) Find the current in the bar when it is moving at a speed v. (b) Write down the equation of motion of the bar (from F = ma), with v(t) of the bar as the unknown function of time. %3D (c) As t→ o, the speed v of the bar approaches a constant value vm. What is the value of vm?

A bar of mass m, length L, and resistance R slides without friction on parallel rails shown in the figure. A battery that maintains a constant emf ɛ is connected between the rails, and a constant magnetic field B is directed perpendicularly into the plane of the page. If the bar starts from rest at t = 0, (a) Find the current in the bar when it is moving at a speed v. (b) Write down the equation of motion of the bar (from F = ma), with v(t) of the bar as the unknown function of time. %3D (c) As t→ o, the speed v of the bar approaches a constant value vm. What is the value of vm?