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I learn some basic information about the relative permittivity. I can understand that when the relative permittivity $\epsilon_r \to \infty$ that material is a perfect conductor. On the other hand, for any finite value of $\epsilon_r$, that material is a perfect dielectric.

However, I need help to obtain an intuitional or qualitative understanding of a specific physical setting, that is, two-layer different materials, a dielectric (diel_A) and a vacuum, between two plates (electrodes) with a fixed external electric field. In this case, what is the actual physical effect, or what happens if the relative permittivity of "diel_A" increases? Thank you in advance!

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  • $\begingroup$ A perfect conductor has permittivity of negative infinity. $\endgroup$
    – Gilbert
    Feb 15 at 11:30
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For a parallel plate capacitor without any dielectric material $$C_0=\frac{\epsilon_0 A}{s}$$

Now consider a simple situation where you have a capacitor with a half-filled dielectric with dielectric constant $\kappa$ (same as relative permittivity). $$\frac{1}{C_s}=\frac{1}{C_v}+\frac{1}{C_d}$$ Putting $C_v=A\epsilon_0/(s/2)$ and $C_d=A\kappa \epsilon_0/(s/2)$ will give $$C_s=\frac{2\kappa }{\kappa +1}C_0$$ $$\lim_{\kappa\rightarrow -\infty}C_s=2C_0$$ The explanation for this can be understood from here. It's clear that if $s\rightarrow s/2$ so that $C_0\rightarrow 2C_0$.

Edit: The notation is as follows

  • $s$ stands for the distance between the plate.
  • $C_s$ is the combined capacitance.
  • $C_v$ is the capacitance of the vacuum part.
  • $C_d$ is the capacitance of the dielectric part.
  • $\epsilon_0$ is the permittivity of free space.
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  • $\begingroup$ thank you for the help, could you explain the notations? For example, what is $\epsilon_0$ and $s$? $\endgroup$
    – Nobody
    Feb 15 at 10:20
  • $\begingroup$ I added notations. :) $\endgroup$ Feb 15 at 11:46

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