# Electric field in a hollow cylinder

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/Rout 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 qinside, 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

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rude man
Homework Helper
Gold Member
Just use Gauss' theorem. The surface has radius r, and
q(inside) is whatever's inside!

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
Homework Helper
Gold Member
It doesn't. It integrates from Rin to r.

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

but why not Rin to Rout?

rude man
Homework Helper
Gold Member
Because ity asks for the field at Rin < r < Rout, not AT Rout.