# Concentric cylindrical insulator and conductor

1. Jul 1, 2012

### pilotguy

1. The problem statement, all variables and given/known data

A line charge λ is surrounded by a long cylindrical insulator with a linear charge density 2λ and radius a. This is surrounded by a concentric conductor cylinder of radius b. Use Gauss’s Law to find the charge density on the surface per unit length at r = a just inside the conductor and the charge density per unit length at r = b just inside the conductor. Plot E as a function of r. What is the change of potential from the center of the cylinder to b? Draw a figure of the situation.

2. Relevant equations

Gauss's Law, $\phi$E=$\oint$E*dA=qenc/$\epsilon$0

3. The attempt at a solution

I'm not sure of my reasoning.

Because the inner cylinder is an insulator, wthe net flux on it will be zero, so the charge on the surface of the conductor must cancel out the charge o the insulator:

qc,in/ε + qline/ε + qc,out/ε = 0

2λa2$\pi$ + λ + qc,out = 0
qc,out=-λ(2a2$\pi$+1), the charge density per unit length at r=a

Uncertain. And now I'm not sure how to proceed with finding the charge density at r=b.