A very thin rod of length L and mass m slides without kinetic friction and without rolling along an inclined plane of angle theta so that its length is perpendicular to the sides of the plane. It is externally connected to a resistor R with flexible wires. There is a uniform, vertical magnetic field B that points downwards.
a. Find all the forces on the rod.
b. Derive a differential equation for the speed, v, of the rod and solve it to get v = v(t), assuming it starts from rest.
c. Find the coordinate x (parallel to the plane) of the rod assuming that at t = 0 it is located at x = 0.