Let us consider the following thought experiment. There is a magnetic field in free space produced by a steady current, hence solution of the (magnetostatic) Ampere's law Curl H = J. There is also a material with some parameters ε and μ and no currents, where the Ampere's law is Curl H = 0. Considering the usual interface conditions on the boundary between the auxiliary material and the free space, inside the material I expect to see a magnetic field generated by the change in permeability μ. On the other hand, if the material had the same parameters of the free space, ε0 and μ0, I expect to see no field inside: it is as if there were an invisible barrier which shields a region of the free space from the outside. Is my reasoning correct?