4) (4 points) Faraday\'s Law for a train Consider a train traveling down a railr

Question

4) (4 points) Faraday's Law for a train Consider a train traveling down a railroad track at a speed of 60 miles per hour. Assume that the front wheels and axle of the train act like a wire to electrically connect the two rails. In the United States, the two rails of the track are separated by 4 feet, 8.5 inches. A 1000-ohm resistor is also connected between the two rails of the track. To simplify this problem, assume that the Earth's field points perpendicular to the ground with a strength of B = 0.5 Gauss, and assume that the rails, wheels, and axle are all perfect conductors. a) (+1) Make a clear sketch. b) (+3) Calculate the current induced through the 1000-ohm resistor due to Faraday's Law.

Explanation / Answer

We have 2 parallel rails, and a resistor perpendicular to these rails. The resistor is moving at 60 mph parallel to the rails.

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The induced emf is

emf = B L v

as B = 0.5E-4 T
L = 1.4351 m
v = 60 mph = 26.8167 m/s

Thus,

emf = 1.924*10^-3 V

Thus,

I = emf / R

I = 1.92*10^-6 A or 1.92 microAmpreres   [ANSWER]

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