A long, thin straight wire w/ linear charge density lambda runs down the center of a thin, hollow metal cylinder of radius R. The cylinder has net linear charge density of 2lambda. Assume lambda is positive. Find an expression for the electric field strength inside the cylinder.
I used a cylinder of length L for my gaussian surface:
the charge inside is lambda * L
E*2pir*L = lambda * L / permittivity constant
E= lambda/ (2pi*r*permittivity constant)
This is correct, but the thing I don't see is how the electric field from the metal cylinder cancels inside the cylinder. Wouldn't it only cancel at the very center?