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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.)

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    $\begingroup$ Is this linear, i.e. can we extrapolate this to 100% of the current field? $\endgroup$ – Paŭlo Ebermann Apr 27 at 12:40
  • $\begingroup$ I think so, although you may have to make the rings bigger to keep things safely under the superconduction limits. $\endgroup$ – Anders Sandberg Apr 27 at 15:24
  • $\begingroup$ Also, if mankind is ever going to terraform Mars, we definitely need an equatorial magnetizer! ;-) $\endgroup$ – cmaster Apr 27 at 18:42
  • $\begingroup$ @cmaster - One can put coils in the L1 point to deflect the solar wind at Mars: medium.com/our-space/… $\endgroup$ – Anders Sandberg Apr 27 at 19:55
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    $\begingroup$ @beppe9000 - The game is the boardgame Terraforming Mars. $\endgroup$ – Anders Sandberg Apr 28 at 2:45

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