# Dielectric effects confined inside the dielectric material?

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1. Feb 20, 2015

### Ocirne94

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 $\epsilon_r$. 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 $\sigma_p > 0$ on the right face and a net $-\sigma_p < 0$ 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 $\sigma_p$ 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 $\sigma_p$ produces an electrical field $E_p = \frac{\sigma_p}{\epsilon_0}$ 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?
Ocirne

2. Feb 20, 2015

### Staff: Mentor

Which equations say that? It is not true, but it could be a good approximation.

Only if the dielectric is small compared to its thickness.
How?

3. Feb 21, 2015

### Ocirne94

Consider this setup:

I was told that here the fields are
$E_1=\frac{\sigma}{\epsilon_0}=E_3$ (outside the dielectric),
$E_2=\frac{\sigma}{\epsilon_0 \epsilon_r}$ 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 ($E=\frac{\sigma}{2\epsilon_0}$), which could imply that the dielectric's thickness is negligible?

4. Feb 21, 2015

### Staff: Mentor

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.
Right.

5. Feb 21, 2015

### Ocirne94

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. Feb 21, 2015

### Staff: Mentor

Or even messier methods like numerical simulations, yes.