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 P: 27 1. The problem statement, all variables and given/known data An infinite cylindrical shell of radius b is placed inside a constant field B which points along the upwards z-axis. A second cylindrical shell of radius ar>a is filled with a paramagnetic material of permeability u. Find the magnetic field everywhere. 2. Relevant equations H = B/(u_0) + M H = -grad W Laplacian W = -grad M W is continuous over all boundaries. The change in dW/dr over a boundary is equal to the negative change in Magnetization over the boundary. Cylindrical laplace equation solution (From my undergraduate E+M notebook) W(r, phi) = D_0 + A_0*(a+b*phi) + $\EPSILON$ [r^n + (A_n*r^-n)]*[B_n*cos(n*phi)+C_n*sin(n*phi)] Another version of this equation can be found here http://www.cord.edu/faculty/gealy/ph...SepVarsCyl.pdf on page two. Summed from n = 1 to infinity 3. The attempt at a solution Since there's no free current in this situation, I tried using magnetic scalar potential to solve this problem. Unfortunately, I end up with too many variable in the proposed Laplace equation solutions that I need to create to use the boundary conditions. In my main attempt I had four boundary conditions and seven types of variables. My main problem is that I need to find the H field to find the B-field, but in order to find the H-field, I also need a function for the paramagnetic material's Magnetization density M. The forum wants me to post my attempts, but I've already filled three pages of notebook paper with failed algebra and I doubt that that would be constructive. I'm not really looking for an exact solution, I really just need general guidance.