A very long train whose metal wheels are separated by a distance of 4 ft. 9 in.

Question

A very long train whose metal wheels are separated by a
distance of 4 ft. 9 in. is traveling at 55 mi/hr on a level track.The
vertical component of the magnetic field of the Earth is 6.2 x10^-5
T.
a) What is the induced emf between the right wheels and the
left wheels?
b) The wheels are in contact with the rails, and the rails are
connected by metal cross ties which close the circuit and
permit a current to flow from one rail to the other. Since the
number of cross ties is very large, their combined resistance
is nearly zero; most of the resistance of the circuit is within
the train. What is the current that flows in each axle of the
train? The axles are cylindrical rods of iron of diameter 3 in.
and length 4 ft 9 in.

Explanation / Answer

First, we need to convert to proper units.

55 mi/hr = 24.6 m/s

4 ft 9 in = 1.4478 m

3 inch diameter = .0762 m diameter = .0381 m radius

Part A)

The formula for induced EMF =

= BLv = (6.2 X 10-5)(1.4478)(24.6) = 2.01 X 10-3 V   = 2.01 mV

Part B)

The formula for resistance in the axle is

R = L/A

The resistivity of iron is 10 X 10-8 m

R = (10 X 10-8)(1.4478)/()(.0381)2

R = 3.17 X 10-5

The using V = IR, we can find I

I = (2.01 X 10-3)/(3.17 X 10-5) = 63 Amps

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