I shouldn't answer for the physicists, but I'll have a go. The simplest first principle explanation is that the needle of the compass points according to the magnetic field/lines of force at that point. Statistically, this centers on the magnetic pole as located geographically in the vicinity of Ellesmere island, looking just at the direction relative to the surface. The situation is a little more complicated by the occurance of magnetic anomalies that cause some perturbation, usually a small deviation. The compass is constructed to not respond to the vertical component of magnetic field.
http://en.wikipedia.org/wiki/Earth's_magnetic_field
Over geologic history, the magnetic pole of the earth has moved, and even flipped poles. This is evidenced in the magnetic polarization 'frozen' into contemporaneously deposited magnetically active igneous rock. Some examples are in rock on the floor of the Atlantic, in bands parallel to the spreading Atlantic ridge. This is something like a giant magnetic tape, that records the movement and direction of the magnetic pole over geologic time.
It seems that in Murmansk the nothern lights are visible. Were I was in Manitoba was probably very lucky to see the bright kind of aurora, usually need to be more to north. Sky was absolutely clear, very cold, dry, 2 AM. I just about jumped out of skin, because I wasn't expecting it, and didn't know what it was at first. There was no city close by so it could not have been reflected city light.



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