# Bound Charges Due to Polarization

1. Mar 25, 2007

### azone

1. The problem statement, all variables and given/known data
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)

2. Relevant equations
Find the bound surface charge density and volume charge density.

3. 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.

2. Mar 25, 2007

### siddharth

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.

Yes, that seems correct.

Last edited: Mar 26, 2007