I guess the title says it all. How big of an electromagnet would you need to generate a magnetic field the same as Earth's? Like, what kind of amperes are we talking here? (Assuming a hypothetical superconducting magnet, of course.)
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You are in luck, since Osamu Motojima and Nagato Yanagi have already calculated it for you in their report Feasibility of Artificial Geomagnetic Field Generation by a Superconducting Ring Network. They conclude that producing 10% of the current field is feasible using "12 latitudinal high-temperature superconducting rings, each carrying 6.4 MA current with a modest 1 GW of power requirement".
(The motivation for the report is the concern about the consequences of Earth losing its field during a geomagnetic reversal, but it doesn't look like those are particularly bad.)
Anders Sandberg
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