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We know that the direction of compass needle always points towards the magnetic north pole. If we take the compass to the site of magnetic north pole, which direction will the compass needle point?

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    $\begingroup$ It will point straight up or down. $\endgroup$ – mmesser314 Aug 13 '15 at 13:12
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If the Earth's magnetic field were a perfect dipole, the compass needle would float aimlessly. Or it might point in the last direction it was facing before you stepped over the magnetic north pole. If you have magnetized metal in your pockets, it might point there. If you tilt the compass from horizontal, it will point toward the low side. If you started it spinning, it would continue spinning until friction slowed and stopped it. Earth's magnetic field lines would be vertical at the magnetic north pole if the magnetic north pole coincided exactly with the geomagnetic north pole. So a compass held horizontally there would have no preferred direction.

But the Earth's magnetic field is not a perfect dipole. The north pole of the Earth's magnetic field does not fall exactly at the geomagnetic north pole (geomagnetic is the north antipodal point of a theoretical perfect dipole that extends through the center of the Earth), so the field lines are not exactly vertical. A horizontal compass will be erratic and unreliable at the geomagnetic north pole, and may exhibit all the behavior in the paragraph above.

The magnetic pole and the geomagnetic pole are constantly in motion due to fluid movements in the Earth's core. They wander many miles each year, but on average they hover around the Earth's rotation axis. Here is a link which explains the movement of the geomagnetic pole: https://en.wikipedia.org/wiki/Geomagnetic_pole.

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