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

AI Thread Summary
The discussion focuses on determining the polarization charge density in a dielectric cube containing a region with evenly distributed electrons. It clarifies that outside the cube, the polarization vector is zero, while inside the non-charged part, it is defined as ##\vec{P} = \epsilon_0 \chi_e \vec{E}_{tot}##. The key question arises regarding the polarization in the charged region, with uncertainty about the total electric field ##\vec{E}_{tot}## and its dependence on the charge distribution. Participants seek clarification on the geometry of the charged region and the meaning of the "total" electric field. The conversation highlights the need for a clearer understanding of the problem's parameters and their implications for calculating polarization.
happyparticle
Messages
490
Reaction score
24
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}## ?
 
Physics news on Phys.org
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:
Kindly see the attached pdf. My attempt to solve it, is in it. I'm wondering if my solution is right. My idea is this: At any point of time, the ball may be assumed to be at an incline which is at an angle of θ(kindly see both the pics in the pdf file). The value of θ will continuously change and so will the value of friction. I'm not able to figure out, why my solution is wrong, if it is wrong .
Thread 'Trying to understand the logic behind adding vectors with an angle between them'
My initial calculation was to subtract V1 from V2 to show that from the perspective of the second aircraft the first one is -300km/h. So i checked with ChatGPT and it said I cant just subtract them because I have an angle between them. So I dont understand the reasoning of it. Like why should a velocity be dependent on an angle? I was thinking about how it would look like if the planes where parallel to each other, and then how it look like if one is turning away and I dont see it. Since...
Thread 'Voltmeter readings for this circuit with switches'
TL;DR Summary: I would like to know the voltmeter readings on the two resistors separately in the picture in the following cases , When one of the keys is closed When both of them are opened (Knowing that the battery has negligible internal resistance) My thoughts for the first case , one of them must be 12 volt while the other is 0 The second case we'll I think both voltmeter readings should be 12 volt since they are both parallel to the battery and they involve the key within what the...
Back
Top