The polarization charge density ##\rho##p in a charged dialectric

[happyparticle]

Homework Statement

The polarization charge density $\rho$p in a charged dialectric

Relevant Equations

$\rho p = - \nabla\cdot \vec{P}$
$\vec{P} = \epsilon_0 \chi_e \vec{E}$

Hi,

I have a dialectric cube and inside the center of the cube I have a part where we have Introduced evenly electrons.

I have to find the polarization charge density in the 3 regions.
I know outside the cube is the vacuum, thus $\vec{P} = 0$ and inside the dialectric (non charged part) $\vec{P} = \epsilon_0 \chi_e \vec{E}_{tot}$

However, in the charged part of the dialectric is it $\vec{P} = \epsilon_0 \chi_e \vec{E}_{tot}$ ?

 

[kuruman]

I have a dialectric cube and inside the center of the cube I have a part where we have Introduced evenly electrons.

What does this "part" inside the cube look like? Is it a finite volume like a smaller cube, or a sphere or what? Where are its boundaries?

Maybe you can write down that inside the dielectric is $\vec{P} = \epsilon_0 \chi_e \vec{E}_{tot}$ in principle, but you don't know $\vec{E}_{tot}$. You need to find that in terms of the amount of charge at the center of the cube.

What does the subscript $tot$ for the electric field mean anyway? Is it a total of some kind? What is being added to get it? I think you mean the field as a function of position $\vec E(\vec r)$.

How does this problem differ from the one you posted here
bound-charges-of-a-block-top-and-bottom-surface.1011665
other than it is more vague?