1. The problem statement, all variables and given/known data A metal sphere with radius r_a is supported on an insulating stand at the center of a hollow, metal spherical shell with radius r_b. There is charge +q on the inner sphere and charge -q on the outer spherical shell. Take the potential V to be zero when the distance r from the center of the spheres is infinite. What is the equation V(r) that models the potential in the region r_a < r < r_b? 2. Relevant equations ΔV = -∫E(r)∂r ψ=Q/ε_0 E∫A = ψ; ∫A = 4πr^2 3. The attempt at a solution 1. V(∞) - V(r) = ∫E(r)∂r (from ∞ to r) = ∫E(r)∂r (from ∞ to r_b) + ∫E(r)∂r (from r_b to r); 2. ∫E(r)∂r (from ∞ to r_b) should evaluate to a constant since E(r) = 0 by Gauss' Law (Taking the Gaussian object to have r > r_b, the enclosed charge is -q + q = 0; Electric flux = 0 and therefore electrical field outside the r_b shell is 0.) 3. ∫E(r)∂r (from ∞ to r) = Constant + ∫E(r)∂r (from r_b to r) 4. ∫E(r)∂r (from r_b to r) evaluates to q/(ε_0*4*π)| (from r_b to r) V(r_a< r < r_b) = q/(ε_0*4*π)| (from r_b to r) is as far as I got. Did I make a wrong assumption?