A coaxial cable consists of two concentric cylindrical conductors as shown here: http://puu.sh/luFZx/7f3e1ccb07.png . The inner cylinder has a linear charge density of +λ1, meaning that each meter of the cable will have λ C of charge on the inner cylinder. The outer cylinder has a linear charge density of +λ2. Various regions of this structure are labelled as follows: (1) inside the inner cylinder, (2) within the inner conductor, (3) between the cylinders, (4) within the outer conductor, and (5) outside the cable.
a. Find an expression for the electric field in each of the five regions as a function of the distance from the center of the cable, r.
b. If the inner cylinder has a charge density of +10 nC/m and the outer cylinder has a charge density of +15 nC/m, what is the magnitude of the electric field at 30 mm from the center? (Assume that r=30 mm is located in section #3).
***This is in electrostatic equilibrium btw.
E = λ/(2πrϵ0)
3. The Attempt at a Solution
For part A, I tried drawing a Gaussian surface and using equations.. but then I realized it was a conductor in electrostatic equilibrium. We were taught a week or two ago that the electric field of a conductor in electrostatic equilibrium would always equal 0, as would any holes in it. So why don't the first four regions have E = 0?
I was waiting to do part B til I finish part A.