Is it possible to exploit the magnetic field of Earth to obtain electricity?
In 1996, NASA experimented with such a thing. It used a tethered satellite (the tether containing metal and being 12.5 miles long), moving through the magnetosphere. It worked under the same principle as a dynamo, where a moving wire in a magnetic field would create electricity. One part of the circuit was the tether itself, where the other was the ionosphere, the distant, ionized region of our atmosphere. This effect is not without cost, however, as the magnetic field opposes the motion of the system, thus lessening its kinetic energy and degrading its orbit. The tether exploited about 1 ampere at 3500 volts of electricity.
See more about this experiment at:
Tethered Satellite System (TSS-1R) by NASA
Justin Clifford, High School Student, Alpine, Utah
'The mathematician's patterns, like the painter's or the poets, must be beautiful; the ideas, like the colours or the words, must fit together in a harmonious way. Beauty is the first test: there is no permanent place in the world for ugly mathematics.'