posted by David D. .
A long, thin straight wire with linear charge density -λ runs down the center of a thin, hollow metal cylinder of radius R. The cylinder has a net linear charge density 2λ. Assume λ is positive. Find expressions for the electric field at the following locations. Use lambda for λ, pi for π, epsilon_0 for ε0, r for r, and R for R.
(b) outside the cylinder, r > R
Use Gauss' law. Because of symmetry, the E field will be radially outward and a function of r only.
The product of E and the area of any imaginary concentric cylinder (Gauss' law surface) outside r = R is equal to the charge inside the cylinder, divided by epsilono. E will be inversely proportional to r.
Review or use Google look up Gauss' law if you are unfamiliar with it. Here is one good reference among many: