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

• happyparticle

#### 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}## ?

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?

Last edited: