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

• happyparticle
In summary, the conversation discusses finding the polarization charge density in different regions of a dielectric cube. The outside of the cube is vacuum, so the polarization charge density is zero. Inside the dielectric, the polarization charge density is equal to the product of the electric susceptibility and the total electric field. However, it is unclear how to find the total electric field, which is a function of position. The problem is similar to one previously posted, but with less specific information provided.
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}## ?

EpselonZero said:
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:

## What is the definition of polarization charge density?

The polarization charge density, denoted by ##\rho##p, is a measure of the amount of electric charge that is displaced within a dielectric material due to the presence of an external electric field.

## How is polarization charge density related to electric dipole moment?

The polarization charge density is directly proportional to the electric dipole moment of a dielectric material. This means that as the electric dipole moment increases, so does the amount of polarization charge density.

## What is the difference between free charge density and polarization charge density?

Free charge density refers to the amount of electric charge that is present in a material due to the presence of mobile charge carriers, such as electrons or ions. On the other hand, polarization charge density refers to the amount of charge that is displaced within a material due to the presence of an external electric field.

## How does the presence of a charged dielectric affect the electric field?

When a charged dielectric material is placed in an external electric field, it produces an internal electric field that is opposite in direction to the external field. This results in a decrease in the overall electric field within the material.

## What is the role of polarization charge density in dielectric materials?

Polarization charge density plays a crucial role in the behavior of dielectric materials. It affects the dielectric constant, or the ability of a material to store electric charge, as well as the overall electric field within the material. It is also responsible for the phenomenon of dielectric breakdown, where a material loses its insulating properties and allows electric current to flow.

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