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EM (laplace equation)

  1. Apr 3, 2009 #1
    1. The problem statement, all variables and given/known data
    Hi, I've attached the question as I don't know how to write equations on here without them looking awful.


    2. Relevant equations
    Laplace -> del^2 V=0


    3. The attempt at a solution
    I've done the first bit (expression for Q0).

    For the next bit I tried to solve laplace's equation to find the potential in the gap. I called the general radius of a point u, as r is already taken. I was then going to use the boundary condition that
    -dV/du (at u=a) = charge density/permittivity of free space

    Which is from the boundary condition for perpendicular field components, and the field must be zero inside the solid sphere.

    I took delta to be along the z-axis, so the problem has azimuthal symmetry and we can use the usual general solution of

    V = sum[Pl(cost) (Al u^l + Bl u^-(l+1))]

    Where t is theta.

    Looking at the answer given for charge density, I thought this V would only include an l=0 and l=1 term. So I used them and then used the boundary conditions that

    V=0 at u=r=b + delta*cost
    V=V0 at u=a

    However this did not give me the result.

    Any help? Thanks
     

    Attached Files:

    Last edited: Apr 3, 2009
  2. jcsd
  3. Apr 3, 2009 #2

    turin

    User Avatar
    Homework Helper

    Did you try the method of images?
     
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