Polarized Dielectric and Charge Density.

[supratim1]

Homework Statement

A long round dielectric cylinder is polarized so that the vector P = ar, where 'a' is a +ve constant & 'r' is the distance from the axis.find the space density rho` of bound charge as a function of distance r from the axis.

Homework Equations

Gauss Law.

The Attempt at a Solution

I actually can't make out how to link polarization with charge density.

I am thinking of using Gauss' Law, taking a Gaussian surface of same radius as of cylinder and a length 'dh' and integrate it to full length. But I am not sure what to do.

 

[ideasrule]

Bound charge density is just negative the divergence of the polarization. This is analogous to the Maxwell's law that says free charge density is the divergence of the electric displacement field, D.

 

[supratim1]

thank you. but how do i find the divergence of polarization?

 

[ideasrule]

See the last equation here: http://hyperphysics.phy-astr.gsu.edu/hbase/diverg.html

It isn't pretty, but notice that the polarization has no dependence on either angle. This means only the first term is non-zero, and you can just evaluate that term.

 

[supratim1]

thank you very much.