Real magnetic field is inversely proportional to the distance cubed. But the imaginary Earth's magnetic field measured near the poles is 0.65 gauss and near the equator is 0.2 gauss.
A compass floating on water would point toward the imaginary Earth's magnetic poles, but would not move toward them.
A compass floating on water in a real magnetic field will move and point toward the magnetic poles.
The fact is sun's rays move westward around the Earth, creating a weak electric current that constantly moves around the Earth. That induces compasses point north also creates polar lights at night.
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