Dielectric effects confined inside the dielectric material?

In summary, the conversation revolves around the polarization effects of a dielectric material and how they remain confined inside the material itself. The equations for a LIH dielectric state that the electric field inside the material is reduced by \epsilon_r, but outside the material, the electric field is back to normal. This is only a good approximation if the dielectric is small compared to its thickness. The discussion also touches upon how this conflicts with Maxwell's equations for dielectrics and the possibility of using numerical simulations to calculate the effects of polarization density outside the dielectric's volume.
  • #1
Ocirne94
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Hi all,
I am wondering how is it possible that the polarization effects of a dielectric material remain confined inside the material itself.
That is: for a LIH dielectric, the equations state that the electric field inside the material is reduced by [itex]\epsilon_r[/itex]. But outside the material, no matter how close to it, the electric field is back to normal.
Now consider a dielectric such as the one in the image: there is a net [itex]\sigma_p > 0[/itex] on the right face and a net [itex]-\sigma_p < 0[/itex] on the left one, and there is no net charge (free or polarization) between the two faces.
If we measure the electric field at the position of the [itex]\sigma_p[/itex] label to the right, how can it be unaffected by the near positive charge density? I would instead say - by Coulomb's theorem - that the [itex]\sigma_p[/itex] produces an electrical field [itex]E_p = \frac{\sigma_p}{\epsilon_0}[/itex] which should be summed to the external field. And, if the dielectric is wide enough, the effects of the charged left side are negligible. But this conflicts with Maxwell's equations for dielectrics.
Where is the mistake?
Thank you in advance for your patience and your time,
Ocirne
polarized-dielectric-amounts-induced-surface.gif
 
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  • #2
Ocirne94 said:
That is: for a LIH dielectric, the equations state that the electric field inside the material is reduced by [itex]\epsilon_r[/itex]. But outside the material, no matter how close to it, the electric field is back to normal.
Which equations say that? It is not true, but it could be a good approximation.

Ocirne94 said:
If we measure the electric field at the position of the [itex]\sigma_p[/itex] label to the right, how can it be unaffected by the near positive charge density? I would instead say - by Coulomb's theorem - that the [itex]\sigma_p[/itex] produces an electrical field [itex]E_p = \frac{\sigma_p}{\epsilon_0}[/itex] which should be summed to the external field. And, if the dielectric is wide enough, the effects of the charged left side are negligible.
Only if the dielectric is small compared to its thickness.
But this conflicts with Maxwell's equations for dielectrics.
How?
 
  • #3
mfb said:
Which equations say that? It is not true, but it could be a good approximation.

Consider this setup:

Dielectric.png


I was told that here the fields are
[itex]E_1=\frac{\sigma}{\epsilon_0}=E_3[/itex] (outside the dielectric),
[itex]E_2=\frac{\sigma}{\epsilon_0 \epsilon_r}[/itex] inside it.
The fields outside the dielectric are the same as if there were no dielectric: they ignore any possible contribution from the surface polarization densities.
Is it because the field's expression comes from the infinite plane approximation ([itex]E=\frac{\sigma}{2\epsilon_0}[/itex]), which could imply that the dielectric's thickness is negligible?
 
  • #4
That is an approximation for infinite size of the plates and the dielectric (or a very narrow gap). It does not stay valid if you consider other shapes.
Ocirne94 said:
Is it because the field's expression comes from the infinite plane approximation (##E=\frac{\sigma}{2\epsilon_0})##, which could imply that the dielectric's thickness is negligible?
Right.
 
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Likes Ocirne94
  • #5
Thank you.
So for other setups without this approximation the polarization density does indeed affect the electric field outside the dielectric's volume, which likely means some double integral to calculate these effects...
 
  • #6
Or even messier methods like numerical simulations, yes.
 

Related to Dielectric effects confined inside the dielectric material?

1. What is a dielectric material?

A dielectric material is an insulating material that can store and/or transmit electric charge. It is typically made up of non-conductive materials such as rubber, glass, or plastic, and is often used to separate or insulate conductive materials in electrical components.

2. What are dielectric effects?

Dielectric effects refer to the changes in the behavior of an electric field when it passes through a dielectric material. These effects can include polarization, energy storage, and changes in the dielectric constant, which is a measure of a material's ability to store electric energy.

3. How are dielectric effects confined inside the dielectric material?

Dielectric effects are confined inside the dielectric material because of its high resistivity. This means that the material does not allow electric charges to flow through it easily, causing them to become trapped and creating an electric field inside the material.

4. What are some practical applications of dielectric effects confined inside a dielectric material?

Dielectric materials and their effects are used in a variety of practical applications, such as in capacitors for energy storage, in insulating materials for electrical wiring, and in electronic devices for signal transmission and filtering.

5. How do temperature and frequency affect dielectric effects confined inside a dielectric material?

Temperature and frequency can both have an impact on the dielectric effects inside a material. Generally, dielectric materials have a higher dielectric constant at lower temperatures, meaning they have a greater ability to store electric energy. Additionally, the dielectric constant can vary with frequency, which is important to consider in applications where the frequency of the electric field may change.

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