In Chris Van Allsburg\'s story The Polar Express, a boy takes a magical train ri
ID: 1682730 • Letter: I
Question
In Chris Van Allsburg's story The Polar Express, a boy takes a magical train ride to the North Pole. Near the pole, assume the strength of the Earth's magnetic field is 5.02×10-5 T and the field lines are vertical (as they actually are at the nearby magnetic south pole). Also assume that at the end of the track, the two steel rails are connected by a conducting wire. Each axled pair of steel wheels on the train closes a circuit with the end of the track. The width of the track is the standard US/Canadian gauge, 1.44 m, and the train is moving at 26.0 m/s.(a) What emf is generated in the rails ahead of the train? (answer in A)
(b) In part a, you are not told how many pairs of wheels the train has. Why don't you need to know?
Explanation / Answer
It pretty much reduces down to EMF = B L v where B is the magnetic field, L is the track width, v is the velocity, as the question says all 3 of these vectors are perpendicular. So we plug the numbers in and get EMF = 1.88 mV The EMF is induced across each axle, perpendicular to the track, so there is no additive effect of the voltages as you move parallel to the track down further sets of wheels.