1. The problem statement, all variables and given/known data 2 concentric conducting spherical shells, with radii a and 2a, have charge +Q and -Q respectively. The space between the shells is filled with a linear dielectric with permittivity ε(r) = (ε0*a)/(1.5*a - 0.5*r), which varies with distance r. a) Use Gauss's law to determine the displacement field between the shells b) Determine the bound surface and volume charge between the shells c) Determine the total energy of the system d) Determine the capacitance 2. Relevant equations D = ε0E+P D = εE 3. The attempt at a solution I already did part a and got the following equation for D: D = Q/4πr2 in the radial direction For part b I rearranged the equation, D=εE to get an expression for E which was: E=(Q(1.5a-0.5r))/4πr2ε0a in the radial direction Then I used the equation D = ε0E+P to solve for P, giving me the following: P=(Q/4πr2)(1 - ((1.5a - 0.5r)/a)) in the radial direction Now that I had an expression for P I tried to find the surface and volume bound charge, this is where my confusion starts. For the volume bound charge I found the negative of the divergence of P and ended up getting an expression that depended on r. Volume bound charge = Q/8πar2 It doesn't make sense to me that the volume bound charge depends on r so now I'm wondering if I did something wrong when I found the expression for P. Can anyone tell me if I've made a mistake somewhere? The other question that I have is regarding part c, is there an electric field outside the outer sphere because of the bound charges? The charge from the 2 spherical shells cancel out so Gauss's law should give 0 field outside the outer shell, but if the bound charge contributes to the field then it will be non-zero and I'll have to include it in my calculation of the total energy. Any help is appreciated.