A neutral conducting cylindrical shell

[maxd23]

Homework Statement

A neutral conducting cylindrical shell with inner radius b and outer radius c surrounds a charged insulated cylinder of radius a at its center whose volume charge density varies radially away from the center as

ρ(r) = ρ0 (1− r / a) . A cross-sectional view is shown.

(a) Find the electric field as a function of r everywhere using Gauss’ Law for 4 regions: (i) 0 < r < a; (ii) a < r < b; (iii) b < r < c; (iv) r > c.

I'm Having trouble with the 4th part (iv) and what the charge on the inner surface of the conductor would be.

Homework Equations

E•dA = Qenc/E_0

The Attempt at a Solution

I have uploaded an image with my work

 

[BvU]

I have uploaded an image with my work

I like the clarity of your drawing (the $c$ is a bit dim), but the rest is rather difficult to read ...
Fortunately for part iv all you need to do is find the total charge and I suppose you did that ok?

 

[maxd23]

I like the clarity of your drawing (the $c$ is a bit dim), but the rest is rather difficult to read ...
Fortunately for part iv all you need to do is find the total charge and I suppose you did that ok?

From my professor: "if you consider a gaussian cylinder with r>c of length L, you will have some net charge within it that will produce an electric field. Since the cylindrical shell is neutral, the charge is that due to the inner cylinder within the gaussian cylinder of length L"
I'm a bit confused