Answer the following question regarding earth’s magnetism:

In which direction would a compass free to move in the vertical plane point to, if located right on the geomagnetic north or south pole?

The compass will get aligned in vertical direction (up-down) if is held vertically at the North Pole. This is due to the fact that magnetic field is perpendicular at the Poles and the magnetic needle of the compass aligns to it.

Note: There will be no predictable motion in horizontal plane due to very weak horizontal component of magnetic field.