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So the Earth has a giant magnetic field we use to determine direction. The field roughly looks like a magnetic dipole, but because the field is generated by a turbulent liquid dynamo near the Earth's core, it's not a perfect dipole.

This leads me to believe that as you approach the magnetic north or south poles, your compass reading will become increasingly vague, and that there's probably a finite region near the pole where the compass direction rather randomly points some direction other than the pole itself.

Additionally, as you near the pole of a perfect dipole, the component of the magnetic field tangent to the surface approaches a magnitude of zero. Because real-world compasses have friction, imperfect magnets, and so forth, there's surely some minimum field strength required to accurately move the compass magnet.

Finally, I know that the pole has daily cycles as well as long-term movements. My guess is the daily cycles can be predicted with some kind of almanac or equation, and that travelers near the pole could receive periodic updates as to the center of the daily cycles so they could adjust their local declination accordingly. Still, there would be some kind of precision error here that might be significant.

Between the three effects above (and possibly others I don't know about), I'm guessing there's a real-world limit on how close you can get to the exact magnetic pole before a real-world compass can no longer be trusted.

How close can we get to the magnetic pole and still use a compass to determine direction?

To narrow the scope of the question, I'm thinking of a standard compass I can pick up at Walmart for like $10 (say, this one). However, answers regarding high-end compasses and very low-end compasses (like, a magnetized needle through a cork floating in water) would also be appreciated.

Additionally, my question relates to humans using compasses for navigation, so if the answer is less than a few hundred meters, that's close enough to "right on the pole" for my purposes. At that point, you could simply look at the building or other landmark you're trying to find. Conversely, if the answer is several hundred miles, that would make it impossible to use traditional compass-based navigation between settlements near the magnetic pole.

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    $\begingroup$ I didn't think the daily changes were predictable. I have seen aviation charts of northern Canada that have warnings about this issue, and I think that may be the major source of error. In that case it would be hard to define a precise area where compasses can not be trusted. $\endgroup$ – haresfur Aug 17 '17 at 3:28
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    $\begingroup$ No scientific answer, but I gave up using magnetic compasses about 1000km from the magnetic pole. Three different, high quality, compasses showed over 90 degrees difference, so we used the GPS instead. Solar compasses used to be popular in polar regions, but difficult to use in the field when it's cold and windy and dust and snow all over. However, 2000km or even a bit less from the magnetic pole, a magnetic field compass works rather good, but huge declination that is changing enough over the years so one need to update the bearings from e.g. old reports. $\endgroup$ – Tactopoda Aug 22 '17 at 3:34
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Regions where the strength of the horizontal component (H) of the magnetic field is small (i.e. where the field is close to vertical near the magnetic poles) define where a compass won't work reliably.

For example where H drops below 5000nT is considered unreliable for values of magnetic declination as per the error calculations in the World Magnetic Model 2015 report. I've seen aviation charts (of which I can't find an example) where 6000nT (also based on the WMM as that's the industry standard there too) is used to define where another navigation aid should be take preference.

You can get an idea of the geographic distances involved from this map of the 2015 horizontal field intensity over the northern hemisphere. The distance of a given field strength value to the pole isn't a fixed value as the field isn't exactly a dipole, so the south pole map looks quite different, but you get a realistic idea at least. Something like within 2,500km in the North, and a few hundred km in the South.

As @Tactopoda pointed out, declination can be very large within thousands of km of a magnetic pole, and the annual rate of change of H is also much greater than elsewhere, hence why a compass isn't very reliable, even where it can give a consistent reading.

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