I understand how the number of turns makes a difference, but I can’t find anywhere what happens(or why) if the core is not fully in. I also didn’t find any circuit diagrams that would at least explain it numerically
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Basically, having a material with high permeability gives a bonus to inductance, depending on how much of that material intersects with the actual magnetic field of your coil. Said magnetic field is a torus (donut) shape around your coil – the most effective shape for a ferromagnetic core is thus something like an [EI-frame](https://image.made-in-china.com/2f0j00dTERaAOFEGqm/Manufacturer-Ei-Frame-Transformer-Customized.jpg) that surrounds the coil in that donut shape and also reaches down through the center – the name comes from the shape of the metal laminations, one is an E-shaped piece and it meets a flat chunk, the I. If you have a setup where the center normally has a ferromagnetic core inserted, then pull the core partway out of the center, some of it is going to reach outside the donut and no longer significantly contribute to increasing the inductance because the magnetic field doesn’t reach it.
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