1. The problem statement, all variables and given/known data Not sure if I'm doing this problem correctly (no answer key for these practice problems). I just want to check with people that know this material well enough. A hollow spherical non-conducting shell of inner radius a and outer radius b carries charge density p = C/r^2 in the region a =< r =< b. Find the electric field in the following regions r < a a < r < b r > b 2. Relevant equations [tex] \varepsilon_0\int E \cdot dA = Qenc [/tex] 3. The attempt at a solution for r < a Qenc = 0 so E = 0 for a < r < b [tex] Qenc = \int _a^r pdV[/tex] Volume of a sphere with radius r [tex] 4/3 \pi r^3 [/tex] so then [tex] dV = 4\pi r^2 dr[/tex] which means [tex] Qenc = \int_a^r C/r^2 4\pi r^2 dr[/tex] or [tex] \int_a^r4C \pi dr [/tex] Solving I get [tex] Qenc = 4\pi C (r-a) [/tex] Now that I have Qenc I can use [tex] \varepsilon_0\int E \cdot dA = Qenc [/tex] using a gaussian surface of a sphere with radius r, I do [tex] \varepsilon_0EA = 4\pi C (r-a) [/tex] A = 4\pi r^2 so that leaves me with [tex] E = C(r-a)/r^2\varepsilon_0 [/tex] for r > b I used a similar process except I did [tex] Qenc = \int _a^b pdV[/tex] making [tex] Qenc = 4\pi C (b-a) [/tex] so then [tex] E = C(b-a)/r^2\varepsilon_0[/tex] while my answers make sense to me, I'd like to make sure I'm not making any mistakes because this question is harder than anything ive done so far!