1. The problem statement, all variables and given/known data Consider a two-layered cylindrical wire with inner-layer permeability μ1 and outer-layer permeability μ2. A line current I runs through the center in the z direction. Calculate the bound currents and the magnetic field produced by the bound currents. 2. Relevant equations  ∫ B⋅dl = Iμ0  ∫ H⋅dl = Ifree  B = μ0 (H+M)  B = μH  Jb = ∇x M  Kb = M x n 3. The attempt at a solution Using equation 2 and symmetry, I come up with H = I/(2πs) Using equation 4, I found the inner and outer material B fields. These point in the φ direction. B=Iμ1/(2πs) in the inner material B=Iμ2/(2πs) in the outer material. Plugging B and H into equation 3, I found the inner and outer material M fields. These point in the φ direction. M= I(μ1/μ0 - 1) / (2πs) in the inner material M= I(μ2/μ0 - 1) / (2πs) in the outer material Plugging M into equation 5, I calculate that Jb = 0 in both the inner and outer material. I expected some bound volume current, so this result is strange to me. If there is no bound volume current and I draw an amperian loop within the inner material, the enclosed total current must be equal to I. If that's the case, I should be able to use equation 1 to find that B = Iμ0/(2πs) but I already calculated a different inner B field above. How can I reconcile the different B values in this inner material?