# How do they know Magnetic Field Lines run from South to North inside a magnet?

I get how they can plot the field lines outside the magnet, but how do they know how it runs inside the magnet to form a closed loop? Isn't the direction fo the field lines the direction of the force acting on a north pole placed at that point in the field? Then what would be the direction of the force acting on a hypothetical North Pole at the center of the magnet. Thanks!:(Image Attached)

There are two (2) kinds of field inside a magnetic material $$\mathbf B$$ and $$\mathbf H$$. The one that has continuous loops is $$\mathbf B$$ field and it is "surface thing" by which is meant that if you cut a thin disk, a crevasse as Thomson called it, out of the material whose normal is parallel with the direction of $$\mathbf B$$ then this field across the slit is continuous. On the contrary, if you cut a thin cylinder, a needle out of the material that is parallel with $$\mathbf H$$ field then $$\mathbf H$$ is continuous across the needle. Here $$\mathbf B = \mu_0(\mathbf H + \mathbf M)$$, where $$\mathbf M$$ is the local magnetization density of the material. Inside a long permanent magnet the fields $$\mathbf B$$ and $$\mathbf H$$ are in opposite direction, the field lines of $$\mathbf B$$ are closed continuous loops but that of $$\mathbf H$$ are not closed originate but start at one pole and end at the other.
Within the crevasses, disks or needles, one can measure the local fields. If you place a wire loop in the disk you can measure the induced voltage when changing the $$\mathbf B$$ and its flux rate $$\Phi$$ in time, and thus both field magnitude and direction can be ascertained.
If you place a magnetic needle inside the thin cylinder carved out of the magnetic material then $$\mathbf H$$ will exert a torque and force that can be measured from which the field magnitude and its direction can be deduced.