How scientists ensured this fundamental property of magnets?

[faheemahmed6000]

Firstly, please note that I am talking about the period BEFORE electricity and magnetism were unified. So I am NOT seeking for answers based on Ampere atomic current model of magnets.

I have read the following statement about the property of magnets at two different places. One from here:

and the other from Maxwell's treatise Vol II, Article 373:

It says that in the magnetic pole model, only the surfaces at the extremities (poles) act as centers of force and the rest of the magnet appears free from magnetic action.

How can we ensure this? For example, why cannot we have half of the magnet's volume being north pole and the other half volume being south pole? Why do we necessarily have the surfaces at the extremities as centers of force instead of volumes (analogous to the charge model)?

 

[mfb]

That is an approximation, you can calculate that it is usually a good approximation and you can use a magnetic field sensor (like a Hall probe) to measure it.

Imagine a solenoid as long chain of NS magnets in a row, partially overlapping: N S/N S/N S/N S where "X/Y" means both are at the same place. The net result is N ... S.

 

[Dale]

For example, why cannot we have half of the magnet's volume being north pole and the other half volume being south pole?

You certainly can. This is not a “fundamental property of magnets” in general, but a feature of a specific type of magnet: a uniformly magnetized cylinder. If you have a non-uniformly magnetized cylinder or a uniformly magnetized non-cylinder you can change that.