Would a magnetic rod through Mars shield it from solar wind?

Would a magnetic rod going all the way through Mars shield it from solar wind?

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Theoretically yes.

It would have to produce a magnetic field of sufficient strength of course.

The Earth's magnetic field at the Earth's surface ranges from 25 to 65 µT. Given that Mars is approximately 50% smaller than the Earth a smaller field would probably be sufficient.

The benefits of the shielding would be:

1. The level of radiation at the surface would be greatly reduced thus making Mars a safer place to live.
2. Mars would be able to hold a thicker atmosphere than it has now. One of the reasons that Mar's atmosphere is so thin is due to the solar wind actually stripping away the atmospheric gases.

If such a rod could be built and installed it would be a constant strength and would do a better job of protecting Mars than Earth's field does of protecting the Earth as that fluctuates and is "due" for one of it's periodic reversals.

However, it's probably beyond our current technologies to build such a rod.

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You needn't necessarily run a rod all the way through. A wire wrapped around the circumference of Mars would do the job as well.

Since a magnetic dipole (which is basically what a bar magnet is) can be thought of as a current loop, wrapping a wire around Mars would achieve the same thing.

I have to point out though, that this solution is not very feasible at all. The magnetic field produced by a current through a loop is given by $$B = \frac{\mu _0 I }{2 \pi r} \text{Tesla}$$ Therefore for a magnetic field of ~ $1 \mu T$ and the radius of Mars being $3397$ $km$, we'd need a current of about $100000000$ $A$ ($10^8$ $A$) which is a massive amount of current to generate and sustain.

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