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nemuritai

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Similarly, a compass near a wire traces out the magnetic field lines ie North/South.

My question is how do I reconcile the fact that the force of a magnet on another magnet is along the field lines whereas for two wires it is perpendicular? The latter is from the fact that the lorentz force is perpendicular to v and B, but why is the force of two magnets alongside the magnetic field instead of perpendicular?

Is the force alongside the B field in one and perpendicular in the other? What error have I made?