Not sure if this is advanced. Highly doubt it but oh well 1. The problem statement, all variables and given/known data Consider an infinitely long charged cylinder of radius R, carrying a charge whose density varies with radius as ρ(r) = ρo r. Derive expressions for the electric field (a) inside the cylinder (i.e. r<R), and (b) outside the cylinder (i.e. r>R). 2. Relevant equations Gauss's Law q=ρ δτ 3. The attempt at a solution (a) E inside cylinder I sketched a Gaussian surface inside of the cylinder. I believe that E is parallel to ds ( E⃗ ||ds⃗ ) So, gauss's law becomes E∮ds = q/ϵ for the side I believe the integral of ds is 2π r L (L being the length of the cylinder even though it is infinite. And q = ρo r π r2 L derived from q=ρ δτ So we have E (2π r L) = ρo r π r2 L /ϵ Simplifying to E = ρo r2/ 2ϵ Is this correct for (a)? And for (b) would it be the same idea but with a gaussian surface outside of R? Thanks!