1. The problem statement, all variables and given/known data A sphere of radius a has a charge density which varies with distance r from the center according to http://img14.imageshack.us/img14/9577/wangsnessproblem594.gif [Broken] where A is a constant and http://img35.imageshack.us/img35/555/wangsnessproblem593.gif [Broken].[/URL] Find the scalar potential http://img35.imageshack.us/img35/9326/phi2.gif [Broken] at all points inside and outside the sphere by using the following formula: http://img17.imageshack.us/img17/4628/wangsnesseqn572.gif [Broken] Express your results in terms of the total charge Q of the sphere. 2. Relevant equations Volume of the Sphere: http://img10.imageshack.us/img10/8776/spherevolume.gif [Broken] Vector Capital R: (From Source to Point) http://img21.imageshack.us/img21/2586/captialr.gif [Broken] 3. The attempt at a solution I'm not sure if I'm over-simplifying this but I figured since the charge density is directly related and varies according to the volume, that is, that I can think of the sphere as containing a series of spheres layered on each other that are infinitely thin, I could take the integral and relate Q to the charge density and the volume. So: http://img197.imageshack.us/img197/5717/59work1.gif [Broken] Then: http://img197.imageshack.us/img197/3756/59work2.gif [Broken] Finding that: http://img197.imageshack.us/img197/5041/59work3.gif [Broken] Plugging that into the main formula above, I get: http://img197.imageshack.us/img197/9933/59work4.gif [Broken] And putting that in terms of Q: http://img180.imageshack.us/img180/7451/59work5.gif [Broken] So if I am reading the question correctly, this is the final formula it asks for. I am really suspicious that I missed something and am forgetting a concept that will make this problem more complex than I think it is. I might also be over-thinking things as well. Any insight would be appreciated. Thank you for your time in advance and I apologize about the pictures, as I am still learning MathType.