1. The problem statement, all variables and given/known data A spherical shell of radius R0 has a non-uniform surface charge density: η=η0*cos(2θ), where θ is the angle measured from the positive z axis and η0 is a constant. This shell is inserted into another spherical shell (this one has a volume) with its inner lip at radius R1 and outer lip at radius R2 and in the volume between there is a perfect conducting material (denoted σ→∞). this outer shell is electrically neutral. The two spheres are concentric. Except for the volume between r=R1 and r=R2, the whole space is characterized by the vacuum constants, ε0 and μ0 What is the electric scalar potential everywhere? I attached a sketch of the problem. 2. Relevant equations Laplace Equation in spherical coordinates with azimutal symmetry (∂/∂[itex]\varphi[/itex]=0): [itex]\nabla[/itex]2ψ=0 3. The attempt at a solution In the regions r<R0 and R0<r<R1 I write the general solution for the laplace equation: ∑(Anrn+Bnr-n-1)Pn(cosθ), n goes from 0 to ∞ and Pn() are lagandere polynomials. In the region r<R0 i set Bn=0 so that the solution wont "explode" when r→0. I "stitch" the two potentials (from either side) at r=R0 through the continuity of the tangential electric field and the discontinuity of the normal electric field due to η. Here i got stuck. I think that I need to find the boundary conditions at r=R1 and r=R2 but I cant find it. Any help would be appreciated, Thanks!