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)
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.