electric field in a hollow cylinder

magnifik

An infinitely long thick hollow cylinder has inner radius Rin and outer radius Rout. It has a non-uniform volume charge density, ρ(r) = ρ₀r/R_out where r is the distance from the cylinder axis. What is the electric field magnitude as a function of r, for Rin < r < Rout?

for this problem, when you find q_inside, do you integrate from Rin to r or from Rin to Rout? i'm confused because i would have expected it to be the latter, but in the solutions they integrate from Rin to r. can someone please explain this?

also, if you try to find the e-field where r > Rout, do you integrate from r to Rout?

Solution is here (problem II):
http://www.physics.gatech.edu/~em92/...200908/q2s.pdf

rude man

Just use Gauss' theorem. The surface has radius r, and
q(inside) is whatever's inside!

magnifik

since in the example in the document it asks for Rin < r < Rout.. why does it integrate from Rout to r??

rude man

It doesn't. It integrates from Rin to r.

magnifik

but why not Rin to Rout?

rude man

Because ity asks for the field at Rin < r < Rout, not AT Rout.