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The magnetization $\mathbf{M}$ is magnetic dipole moment per unit volume. In magnetostatics it producesThe magnetic field intensity $\mathbf{H}=\mathbf{B}/{\mu }_0-\mathbf{M}$ obeysso $\mathbf{H}$ isolates free currents while $\mathbf{M}$ accounts for bound currents. For a linear isotropic material, $\mathbf{B}=\mu \mathbf{H}$.

Ampere's law for a circular loop around the free line current givesin both media. ThereforeAt $r=R$, the net bound surface-current density isHence its magnitude isand for a positive current along $+{\mathbf{e}}_z$ it points along $-{\mathbf{e}}_z$ when ${\mu }_1>{\mu }_2$, reversing when ${\mu }_1<{\mu }_2$.