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If we were to hypothetically place a magnet to the right of the magnet above with the North pole of the right magnet next to the South pole of the left magnet, from real-life experience, I know that the magnets will move in a straight line toward each other along the magnetic field. However, shouldn't the magnetic force the magnets experience be perpendicular to the magnetic field lines, causing the magnets to deflect each other?

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A bar magnet is not a point charge, and does not follow $q\vec{v} × \vec{B} $ , sort of.

For example, the force on a current loop in a non uniform field, is 'in the direction of the field lines'.

Its a bit confusing since we are saying that yes, the individual force on each $\rho dv$ element is perpendicular to the B field, but the SUM of these forces on some FIXED distribution, is not.

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