1. The problem statement, all variables and given/known data Two grounded spherical conducting shells of radii a and b (a < b) are arranged concentrically. The space between the shells carries a charge density ρ(r) = kr^2. What are the equations for the potential in each region of space? 2. Relevant equations Poisson's and LaPlace's in Spherical Coordinates 3. The attempt at a solution I solved Poisson's Equation for the space between the shells, in spherical coordinates, and arrived at: V(r) = (1/ε)kr^2/6 - (C1)/r + (C2) where C1 and C2 are the constants of integration. What would be the general solution for the potential in the other regions where ρ=0? Would I simply apply Laplace's equation in those regions, than apply the suitable boundary conditions?