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Homework Help: Laplace equation in an annulus with Neumann BCs

  1. Oct 4, 2009 #1
    1. The problem statement, all variables and given/known data

    Solve Laplace's equation inside a circular annulus (ring) (a < r < b) subject to the BCs:



    2. Relevant equations


    I also believe because of the physics of a ring, we have additional BCs:



    3. The attempt at a solution

    I have used separation of variables to arrive at a general solution:


    This solution takes into account the periodic boundary conditions specified above under "Relevant Equations", but I am struggling to correctly apply the Neumann BCs specified by the problem in order to arrive at equations for the arbitrary constants.

    I try to take the partial derivative of u(r,theta) with respect to r and arrive at:


    I don't know how I can apply Fourier series (assuming that is what I'm supposed to do) to solve for each of the coefficients (A,B,C,D).
  2. jcsd
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