# Potential of Concentric Cylindrical Insulator and Conducting Shell

1. Feb 6, 2011

### hime

1. The problem statement, all variables and given/known data
An infinitely long solid insulating cylinder of radius a = 3.2 cm is positioned with its symmetry axis along the z-axis as shown. The cylinder is uniformly charged with a charge density ρ = 22 μC/m3. Concentric with the cylinder is a cylindrical conducting shell of inner radius b = 15 cm, and outer radius c = 20 cm. The conducting shell has a linear charge density λ = -0.41μC/m.

A) What is V(c) - V(a), the potentital difference between the outer surface of the conductor and the outer surface of the insulator?

B)Defining the zero of potential to be along the z-axis (x = y = 0), what is the sign of the potential at the surface of the insulator?

2. Relevant equations
E.dA=qenclosed/eo=2klambdatotal/r
V=-integral(E.dr)=2klambdatotal*ln(r)
lambda cylinder=7e-8C/m
lambda shell= -4.1e-6C/m
lambda total=lambdacylinder+lambdashell= -3.39e-7

3. The attempt at a solution

for part a: Vc-Va= 2klambdatotal*(ln(c)-ln(a)) = -8 056.39263

for part b: V(a) would be greater than zero because the there would be charge .41e-6 C/m accumulating on the outer surface of the insulating shell.