Problem 4. Consider a sphere with radius a carrying uniform magnetization M in the z-direction. Outside the sphere is a spherical layer of linear material with inner radius a and outer radius b. The permeability of the material is μ. The H field inside the sphere, inside the layer, and outside in vacuum are H§, Hɩ, and Hv, respectively. There is no free current in the system. μlo Hv HS μ Σ H₂ (a) Show that the volume bound current density Jb is zero in all regions. (b) Obtain the surface bound current density Kb at the two interfaces in terms of M, Hs, H, Hv, Áo and A. V (c) Write down the boundary condition of the parallel component of H field at the inner interface. (d) Write down the boundary condition of the perpendicular component of H field at the inner interface, in terms of M and μ. (f) Write down the boundary condition of the perpendicular component of H field at the outer interface, in terms of μ and μo. (e) Write down the boundary condition of the parallel component of H field at the outer interface.