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## Homework Statement

An infinitely long solid conducting cylindrical shell of radius a = 3.1 cm and negligible thickness is positioned with its symmetry axis along the z-axis as shown. The shell is charged, having a linear charge density λinner = -0.49 μC/m. Concentric with the shell is another cylindrical conducting shell of inner radius b = 15.6 cm, and outer radius c = 18.6 cm. This conducting shell has a linear charge density λ outer = 0.49μC/m.

1.What is V(c) – V(a), the potential difference between the the two cylindrical shells?

2. What is C, the capacitance of a one meter length of this system of conductors?

## Homework Equations

E = Q/(2πr^2εo)

Q = λSa where Sa = 2πr^2

## The Attempt at a Solution

For the first question, I did the integral

∫E.dA = q/εo

E(2πr^2) = q/εo

E = Q/(2πr^2εo)

Then I integrated that between upper bound a and lower bound b to get:

ΔV = -Q/(2πεo) ∫dr/(r^2)

= Q/(2πεo)*(1/r) or Q/(2πεo)*((1/a)-(1/b))

However, my answer was incorrect. I am just learning integrals, so I'm not sure if I set up the integral incorrectly. The Q I used is the inner charge, calculated with Q = λ*(2πr^2), which, with values, is Q = (-0.49 μC/m)*(2π*0.031^2).

I've done a couple of problems with concentric insulators and conductors inside, but the whole idea is very confusing for me and I don't really understand concepts. I find myself just plugging numbers into random equations to find answers.

For the second question, would I just take the total Q and divide that by the potential difference?

Any help is appreciated. Thanks!