Consider the possibility of a new design for an electric train. The train is driven by a force of the vertical component of the Earth's magnetic field (~50uT) on a conducting axle 3.0 m long. The current passes through one rail, up a conducting wheel, through the axle, down the other wheel, and through the other rail back to the power supply at the end of the rail line.
  1. What current is needed to provide a 10 kN force?
  2. How much power is lost (to heating) for each Ohm of resistance in the rails and the axle?
  3. Is such a design realistic?