{I} uniform external magnetic field Bext : _B[)2 Figure 3: A spherical shell made of magnetically susceptible material, placed in a uniform external magnetic eld. (a) (5 points) Consider the auxiliary eld H(r). Explain why in this problem it is possible to introduce a single scalar potential function W(r) which satises H = V W. (b) (5 points) Write down the equation W satises in each of the three regions: r b. (c) (10 points) At each of the two surfaces, r = a and r = I), write down a set of two appropriate boundary conditions, one for the value of W itself, and another for its normal derivative