[solved] electric potential: point charge in a hollow charged conductor 1. The problem statement, all variables and given/known data A hollow spherical conductor, carrying a net charge +Q, has inner radius r1 and outer radius r2 = 2r1. At the center of the sphere is a point charge +Q/2. d) Determine the potential as a function of r for 0 < r < r1. 2. Relevant equations (π = pi) For r > r2, the electric field is (3Q)/(8πε0r2). For r1 < r < r2, the electric field is 0 (ie, field inside conductor is zero in static situations). For 0 < r < r1, the electric field is Q/(8πε0r2). The potential as a function of r for r > r2 (where voltage is taken to be 0 when r is infinite) is (3Q)/(8πε0r). The potential as a function of r for r1 < r < r2 is (3Q)/(16πε0r1). 3. The attempt at a solution My first instinct was to add the potential (3Q)/(16πε0r1) to Q/(8πε0r), which is the potential from infinity to r if the shell wasn't present. However, the answer is wrong. I also made many other fruitless attempts at this problem, but none of them very logical. Can someone tell me what I'm doing wrong, and how to find this potential when r is within the cavity of the conductor? I would greatly appreciate your help with this problem (and thank you in advance)!