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While reading Griffith's Electrodynamics, I didn't quite understand how magnetic fields were introduced.

Electric Fields were introduced as an intermediary calculation to finding the electrostatic force, and their detection makes sense in a way, because the Field and Force are in the same direction. Specifically, the electric field (a physical entity of its own right) is the force per unit charge.

However, magnetic fields were introduced as 'that which is detected by bar magnets'. We used the bar magnet to infer that the magnetic field outside a straight current carrying wire makes concentric circles, and then brought another current carrying wire to see the direction of the 'force'. We then inferred that the force law must be of the form $q(v \times B)$.

My question is this: How did we conclude that the bar magnet detects the field and not the force, and how does it detect the field and not the force? What is the difference between what happens in a current carrying wire and a bar magnet in the presence of a magnetic field?

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So like, when we say bar magnet it is useful to remind ourselves that the earliest examples of these were compasses. Compasses were known to point North, but the exact reason why they pointed North was a bit mysterious. One can reasonably infer a strange field pointed in the north-south direction.

There is technically no reason that it couldn't work the way in electric dipole will orient in an electric field, I suppose. I think therefore the question is answered only by appeal to the absence of detected magnetic monopoles and the fact that every magnet appears to have both a North and South Pole. Like, when you chop a bar magnet in half you do not get just a North Pole and a South Pole separately, you get two smaller bar magnets. This makes it much much harder to argue that the force is coming from one side of the magnet being pulled towards the North Pole and the other side being pulled towards the South Pole by direct forces.

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