1. The problem statement, all variables and given/known data A solid conducting sphere of radius R and carrying charge +q is embedded in an electrically neutral nonconducting spherical shell of inner radius R and outer radius 2 R . The material of which the shell is made has a dielectric constant of 3.0. Relative to a potential of zero at infinity, what is the potential at the center of the conducting sphere? 2. Relevant equations V = ∫Edr = kq/r + C Gauss's law in dielectrics: ∫KEdA = q/ε0 3. The attempt at a solution I've made a few assumptions. The field in a conducting sphere is zero, which means the potential in a conducting sphere is constant. Looking at just the sphere alone, potential at the center relative to infinity should be kq/R (positive because I'm going against electric field?). With the dielectric in place to still take zero at infinity I need to take into account the potential difference across the dielectric (I think?) Edielectric = q/KAε0 V(R->2R) = -∫Edielectric*dr (negative because I'm going in direction of electric field?) = -kq/Kr [2R - R] = -kq/2KR + kq/KR = kq/2KR I know that a dielectric will decrease the electric potential, so I thought V = Vsphere - Vdielectric = kq*((1/R) - (1/6R)). This is not correct and I'm not sure where I messed up.