Application: Motional emf as a motion detector mechanism. Suppose you want to know if a train is moving on a rail but it is too far to see. Assume the rails are a distance d apart and are insulated from each other. To check for motion of the train, you measure the potential difference between the two rails.

(a) Calculate the velocity of the train assuming that the magnetic field of the Earth is equal to Bo and is perpendicular to the surface of the Earth, pointing downward. The potential difference measured is V with its positive pole on the top rail in Figure 10.37.

(b) In which direction is the train moving?

(c) If the resistance per meter of the rails is known (continuous rail), calculate the distance from the measurement point to the train. How can this distance be found by a simple measurement at the point where the observer is located?

(d) Can these measurements be used to avoid collision of trains?