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I know that if you increase permeability, you get smaller skin depth. The same happens with increase of electrical conductivity of material. But WHY is the point to my question.

And what happens if I have a layer of material on order of a micron, while calculated skin depth is 500 microns? Most of the magnetic field just flies trough the conductor layer I guess. But how does the permeability effect it now? Does more field fly trough if I increase the permeability or decrease it?

EDIT: My thinking is that the higher the magnetic permeability of the material is, the more it increases the total field inside the material once an outside field enters it.

So if material has a high permeability, the total field is higher, so more eddy currents are induced in the first layers of atoms. This eddy current creates more magnetic field that is in opposite direction and so decreasing the magnetic field that is then going trough the next layers of atoms. So the skin depth decreases. But if material has very low permeability, then less eddy currents are induced in the first layers and so the magnetic field penetrates longer. And if material is very thin, it just shoots trough. But having less permeability is still better if you want the magnetic field to get trough.

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