The figure shows a portion of an infinitely long, concentric cable in cross section. The inner conductor carries a charge of 6 nC/m and the outer conductor is uncharged.
(part 5 of 6)
What is the surface charge density inside the hollow cylinder?
Answer in units of nC/m^2.
Central solid conducting cylinder of radius 0.013 m and charge 6 nC/m.
Inner radius of cylindrical shell = 0.0475 m
Outer radius of cylindrical shell = 0.067 m
Charge of shell = 0 nC/m
Qenc = Q1 + Qin
(sigma) = Q/A
Flux = EA = Qenc/E0
The Attempt at a Solution
I constructed a Gaussian Cylinder between the outer and inner parts of the shell. I know that E inside the shell is zero (since it is a conductor), so Qenc/E0 = 0, which means Qenc = 0.
However, Qenc = Q1 + Qin, where Qin is the charge on the inside surface of the shell.
The charge density (sigma) relies on Qin, and (sigma) = Qin/A
However, A = 2(pi)rL, and L is not given; rather, L is infinite! I know r = 0.0475 m. Help!