How to Find Bound Charges in a Polarized Cylindrical Dielectric Shell?

[azone]

Homework Statement

We have a long cylindrical, dielectric shell in the z-axis with inner radius R1 and outer radius R2. The polarization is given by P=k/s^2 (in cylindrical coordinates, it is only in the shat direction, i.e. no zhat or phihat)

Homework Equations

Find the bound surface charge density and volume charge density.

The Attempt at a Solution

I know the general formula for surface charge is sigma=P.normal and for volume charge it is ro=-divergence of P. But I'm wondering if things are slightly altered because it is a shell and not a solid cylinder. Or can I just use the formula and then have a limit for s?
For the volume charge I'm thinking I can just use the formula which will give me ro=k/s^2. But for the surface charge I was thinking of doing two different ones for s=R1 and s=R2 to find inner surface charge and outer surface charge.
Any help would be appreciated.

 

[siddharth]

Or can I just use the formula and then have a limit for s?

What do you mean by a limit for s? Since the polarization is given as a function of s, you can find the volume charge density, which would also depend on s, from the divergence.

But for the surface charge I was thinking of doing two different ones for s=R1 and s=R2 to find inner surface charge and outer surface charge.
Any help would be appreciated.

Yes, that seems correct.