Airplanes and trains move through the earth's magnetic field at rather high speeds, so it is reasonable to wonder if our planet's magnetic field can have a substantial effect on them. We shall use a typical value of 0.500G for the earth's field.
a) The French TGV train and Japanese "bullet train" reach speeds of up to 180 with wheels moving on tracks about 1.50 apart. If these trains could move at top speed at right angles to the earth's magnetic field, what potential difference would be induced across the tracks where the wheels roll?
b) Does this potential difference seem large enough to cause noticeable effects?
c) The Boeing 747-400 series of aircraft has a wingspan of 64.4 and a cruising speed of 565 . If there is no wind blowing (so that this is also their speed relative to the ground), what is the maximum potential difference that could be induced between the opposite tips of the wings of such a plane?
d) Does this potential difference seem to be large enough to cause problems with the airplane?