Hi Everyone - I have a classical E&M physics problem that I've been tearing my hair out over. It relates to how ferromagnetic materials boost the field strength of a non-uniform magnetic field. My takeaway from college physics class was that (assuming there's no saturation in the material) the field inside a magnetic material is boosted linearly by a multiplicative constant. So if the field vector at any point in free space p is B(p), if that point in space is enclosed within a magnetic material, the field vector will be αB(p), where α is the relative permeability of the material. But based on some measurements I did, this doesn't appear that my takeaway was correct. It appears instead that there's some sort of "spatial averaging" going on inside the magnetic material, leaving me totally confused. Please see attached for a detailed description of my problem, with images, etc. Can any one explain what's going on here? Thanks in advance.