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/Classes/Fall2011/2212GHJ/main/quiz_help/200908/q2s.pdf

 

[rude man]

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

 

[magnifik]

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

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]

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

but why not Rin to Rout?

 

[rude man]

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