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?
[Physics] What happens when a compass is taken to the site of magnetic pole of earth
earthgeomagnetismmagnetic fields
Related Solutions
Earth's magnetic field isn't really a dipole, but a dynamic field due to the convection occurring in the planet's core (consists of molten iron). The model below shows a simulation of the magnetic field (blue is pointing towards the core while yellow points away), the cluster of curves in the middle is the planet's core.
The geomagnetic pole is the location of the pole if earth's magnetic field were a simple dipole (no convection-driven fields).
Note also that, in your image, the geomagnetic pole hasn't moved much in the last century while the magnetic pole has. This is because every several thousand years, the magnetic poles flip sides (a non-constant rate of reversal, so we can't really say a definitive time-frame).
If possible do as @AccidentalFourierTransform explained in a comment, namely:
Get a standard compass. Clean off the paint in one end of the needle, and pain the other one. Congrats, now you have a compass that is attracted to the South Pole!
Be aware, that some compasses are embedded in an oil capsule, so disassembling will destroy them mostly.
Also remember that the needle uses always both poles, as the magnetic field influences the structure of the needle as a whole. Otherwise it wouldnt't work, so the easiest is to use your imagination.
Perhaps you meant the declination which must be adjusted on the compass, which can influence the way you've got to take, when hiking close to the north or south? Navigation 101
Best Answer
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.