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As far as I am concerned, the compass is facing along the magnetic field lines on the Earth's surface which in turn points towards the North pole by its design. But for a magnet, the field lines go from north to south on the surface (outside the magnet). Does this mean that Earth's geographic North pole is the magnetic South pole?

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It is. The geographic North is close to the Magnetic South. They're not absolutely coincident, and the magnet is slightly moving continuously due to Earth's dynamics. However, the geographic North pole is well stablished.

However, remember that names are just a convention.

We call it North because the compass points there. That's the reason for the name. Then, if you start thinking, yes: that means a magnetic South inside the Earth, but the name was there before.

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    $\begingroup$ Slightly backwards, I think. The direction North was named before the magnetic convention was adopted. The magnetic North is named because it points North on a compass, so the geographic North pole is a magnetic South pole. $\endgroup$ Jan 9 at 20:01
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    $\begingroup$ Note also that there is no misnomer here. The geographic North Pole was not named by reference to magnetic phenomena, but because the direction of North was already established (etymologically it means "to the left of the rising sun"), and the North Pole is the Pole which is found to the North. If the poles of a compass magnet are then named according to which pole they orient towards, then the magnetic poles themselves must logically be the opposite. (1/2) $\endgroup$
    – Steve
    Jan 10 at 1:59
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    $\begingroup$ There is no system of naming that can make all three names consistent, because magnetic principles involve an attraction of opposites, whereas the linguistic desire is to express association by giving the same name to the Pole as to the side of the magnet which orients towards it (rather than the side which flees from it). (2/2) $\endgroup$
    – Steve
    Jan 10 at 2:07
  • $\begingroup$ When I read your comments I was stranged because I tought that's exactly what I said. But reading it again, it's true that it might be confusing. What I meant is: "The direction where the compass points to is called North", but that was like this before people knew WHY a compass does that. I was trying to say the same as the immediately previous comment, but it seems I failed haha. Of course the name could have been given even before. It's the direction of the Polar star, the direction of the moss in rocks, etc. $\endgroup$
    – FGSUZ
    Jan 10 at 10:53

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