Charge on a nonconducting rod with a conducting shell

[reising1]

A charge of uniform linear density 2.20 nano Coulombs per meter is distributed along a long, thin, nonconducting rod. The rod is coaxial with a long conducting cylindrical shell (inner radius = .0600 m, outer radius = .104 m). The net charge on the shell is zero.

a) What is the magnitude (in N/C) of the electric field at distance r = 16.4 cm from the axis of the shell.
b) What is the charge density on the inner surface of the shell?
c) What is the charge density on the outer surface of the shell?

So that is the full question.
I just need help with part C. I figured out the answer to part a and b. Any insight on part C. I'm thinking it might be 0, but I'm not sure. Any help would be appreciated.

 

[Doc Al]

The net charge on the shell is zero.

What does that tell you?

 

[reising1]

Does this mean the charge on the inside of the shell is equal but opposite to the charge on the outside of the shell? So that the answer to C would be the same as B except negated?

 

[Doc Al]

Does this mean the charge on the inside of the shell is equal but opposite to the charge on the outside of the shell?

Yes.

So that the answer to C would be the same as B except negated?

No. Beware: They are asking for the charge density (charge per unit area), not the charge.

 

[reising1]

But what about the fact that the radius is different on the outer surface. To compute letter B, the charge on the inside, I used the radius.

 

[reising1]

Specifically, for letter B, I computed the surface charge density as

total charge = -(2)(pi)(r)(surface charge density)
2.20 micro Coloumbs = (2)(pi)(.060 m)(surface charge density)
thus,
surface charge density on the inner surface = -5.835E-9

So, would I do this same thing to calculate the surface charge density on the outer surface, except use (.104 m) as the radius?

 

[Doc Al]

So, would I do this same thing to calculate the surface charge density on the outer surface, except use (.104 m) as the radius?

Exactly.

 

[reising1]

That is exactly what I did. But the answer is wrong. Should the answer be negative or positive?

I got -3.36673918E-9 C/M^2

 

[reising1]

Just to clarify the computation, I did:

surface charge density = (-2.0E-9 C/m) / (2*pi*.104 m)
That is how I got the -3.36673918E-9 C/M^2

But the answer is wrong.

 

[Doc Al]

That is exactly what I did. But the answer is wrong. Should the answer be negative or positive?

Positive. The inner surface charge is negative to balance out the rod's positive charge. The charge per unit length on the inner and outer surfaces must add to zero, since the shell has zero net charge.