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I think the confusion arises because of poor understanding of the dipolar field.vanhees71 said:It's much clearer, not to mention the Earth and compass needles first but just use magneto statics a la Ampere and define everything in terms of vectors (magnetic field, B→, and, if you want to deal with permanent magnets, magnetization).
People know that two bar magnets line up [S-N] [S - N]. They would then assume that if we model the Earth as a bar magnet, we will also have [Earth] [Compass needle] ⇒ [S - N] [S - N] failing to realize that this happens only at the magnetic poles. It is natural to assume that the Earth's magnetic field, just like its gravitational field, has a non-zero divergence. I too had that misconception until I learned some physics.