At school, we learned about the dynamo effect, where moving a magnet within an arrangement of copper coils generates an electrical current. The Earth's magnetic field shifts over time and this movement, in principle, can also induce a current in a sufficiently large loop of wire. But in practice, these shifts in magnetic field are too small for energy harvesting. A superconducting loop cooled to near absolute zero (-273°C) would help but the system would consume more energy than it produces.
Only a megawatt
Someone did the calculation for energy reception during solar-magnetic storms for a loop antenna the size of Sweden. A typical storm should give 1MW to 10MW: the output of just one large wind turbine. They also found that the maximum received power did not depend on the number of turns in the coil or the resistance.
"Harnessing celestial batteries" Am. J. Physics 77(7) Jul 2009