What if a compass is placed at the northernmost place on Earth?

The magnetic north pole is not the geographical north. If you are at the geographical north pole, the compass will point to the magnetic north pole, which is to the south, of course (from geographical north pole all directions are south).

If you are near the magnetic north pole, in theory the compass will point down into the ground. But the magnetic north pole is kind of diffuse and moves around daily.

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If you are at true North, the compass will still indicate magnetic North, because the magnetic and true North are in different locations.
If you go to magnetic North, then theoretically at least, if you move the compass around in a small horizontal circle, the needle will rotate.

that depends on its orientation
if needles axis is parallel to line joining north and south poles than either it will keep rotating because it will find north pole in all directions. or it might settle in a direction but if shacked settle in some new random direction.


on the other hand if axis is perpendicular to line joining north and south pole. needle will point downwards.

The compass would just spin around and around...