For electromagnetic wave propagation, we can typically characterize a medium by conductivity $\sigma$, permeability $\mu$, and permittivity $\epsilon$. Consider if this material had current passing through it. Would it possibly change the permeability $\mu$? So if you had a rod of mu-metal for example, you know the permeability $\mu$ but does that change if you induce current through the rod?
Update: So I understand that B-H the relationship has a point where the material saturates, and increasing the incident field only causes a small increase in the induced field, and effectively reduces permeability $\mu$. However, in the above example, assume that the incident H field is small enough that it does not reach saturation. What I am talking about is if you connected wires at the 2 ends of the rod and connected it to a current source (AC or DC), does that change the permeability $\mu$?
Perhaps you guys already understood this but let me know if your answer changes.