How Do You Find the Field Inside a Polarized Cylinder?

[shaun_chou]

Homework Statement

This problem is at Griffiths 4.13. A very long cylinder of radius a with a uniform polarization perpendicular to the axis. The question is to solve for the field inside the cylinder.

Homework Equations

$$\rho_b=P\cdot\hat{n}$$ and $$\sigma_b=-\nabla\cdot P$$

The Attempt at a Solution

I can't find a good solution using above equations. Can anyone help me? Thanks a lot!

 

[jdwood983]

I don't think you need those two equations for this problem. You should be looking at Gauss's Law inside and outside the cylinder.

 

[jdwood983]

Also, $\rho_b$ and $\sigma_b$ are the bound charges (volume and surface respectively) and are not the electric field.

Is your professor suggesting you solve the problem using them, or did you assume you should since the question by Griffiths is right after the section on the bound charges?