A rod of length and mass slides on frictionless conducting guides down vertical rails, connected at the bottom, that enclose a uniform magnetic field of magnitude as shown, starting at rest at . The loop formed by the rod and rails has a total resistance of . Gravity makes the rod fall. Find:
a) The current induced in the rod when the speed of the rod is (down). Indicate the direction on the figure above.
b) The net force on the rod as a function of .
c) For extra credit, solve the resulting equations of motion for
and/or determine the terminal velocity of the rod.