It seems based on the magnetic field of ring magnets like the magnetic field lines of a bar magnet actually runs from N to S also inside the magnet, yet schematic images tend to show the field lines running from N to S outside the magnet, then through south pole up to north pole inside magnet. That seems wrong, like it contradicts the behaviour of for example this axially magnetised ring magnet -->
Magnetic field lines are always continuous loops. And divergence of magnetic field would imply the presence of a magnetic monopole, which despite extensive search for their presence, have not been found.
Some confusion may arise because permanent magnets are often modelled mathematically using a distribution of magnetic monopoles; because it makes the math easier (scalar vs vector potential), and one can achieve the same fields outside the magnet with such an approach as with the more physically correct current loop distribution. But this is just a mathematical convenience, and at best confusing when trying to answer questions about the field inside the magnet.
TLDR: In the absence of physical magnetic monopoles, field lines are always continuous loops.
The field lines run south to north. The magnet lends magneto-motive force, which drives the field to increase as it goes through the magnet.
Magnetic field lines have only been used to topographically illustrate the magnetic field area surrounding magnets. Some illustrations show lines inside the magnet, and these are the more accurate because the large magnetic field of a magnet is formed from a combination of all the smaller magnetic fields of each similarly aligned molecule in the magnet. The stronger areas nearest the magnet are illustrated with lines close together. The further from the magnet, the weaker the field and this is illustrated with lines further apart. But, despite the theoretical presence of magnetic field lines, also known as flux lines, they have never actually been found to exist. The magnetic field would better be illustrated and understood as being a fog of magnetised Space strongest at the magnets core, and reducing intensity farther from the magnet.
Supporting information: https://www.eia.gov/energyexplained/electricity/magnets-and-electricity.php
According to Theoria Apotheosis on YouTube who is supposed to be a doctor of physics states that magnetic force is literally like an helix at the centrifugal point. The lines of force form a torus as seen by his invention that shows the exact field lines.
Currently accepted understanding is flawed which I have witnessed to be inaccurate in comparison.
