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A rod of length $L$ and mass $m$ slides on frictionless conducting guides down vertical rails, connected at the bottom, that enclose a uniform magnetic field of magnitude $B$ as shown, starting at rest at $t = 0$. The loop formed by the rod and rails has a total resistance of $R$. Gravity makes the rod fall. Find:

a) The current $I(v)$ induced in the rod when the speed of the rod is $v$ (down). Indicate the direction on the figure above.

b) The net force on the rod as a function of $v$.

c) For extra credit, solve the resulting equations of motion for $v(t)$ and/or determine the terminal velocity of the rod.