My understanding of magnetic fields was that the strength of the field was "path dependent". I.E. the $\mathbf{B}$ field decreased more when it went through materials with relative permeability close to 1 as compared to ferrous materials with much higher relative permeability. (I.E. magnet -> wood -> some point in space would have a lower B field than magnet -> iron -> some point in space). I guess I got this idea because outside of electromagnetism permeability means "the state or quality of a material or membrane that causes it to allow liquids or gases to pass through it." So I assumed it was the way the magnetic field passed through a material, and how the magnetic field turned out on the other side of that material.

But then I started reading https://www.maxwells-equations.com, and now my whole world is turned upside down. Specifically because of this line: "In Equation [1], permeability is the permeability of the medium (material) *where we are measuring the fields.*" (emphasis added). So it doesn't matter what is between the magnet and the point? It only depends on the distance and the material itself?

[This][1] Question and answer seem to indicate the magnetic field is indeed "path dependent". But I'm not sure if they're talking about the H field or the B field.


  [1]: https://physics.stackexchange.com/questions/67728/magnetic-field-insulators?rq=1