Assume I put a 1 inch square cube of some material into a 10 Gauss magnetic field, heat it up to the point where it almost melts, and then let it cool rapidly. The heating would make the magnetic dipoles free to move more, and then during the cooling they would tend to align with the external field.
In the limit that the materials permeability reaches infinity, would it then magnetize to 10 gauss?
Every material in the world has some finite permeability so in reality it would acquire a field of less than 10 gauss, correct?