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Capacitance - Dielectric Constant Relation?

  1. Sep 28, 2008 #1
    Hi,

    Does anyone know if there is a relation between a materials capacitance (C) and its dielectric constant (K)?

    Thanks,
     
  2. jcsd
  3. Sep 28, 2008 #2
    So I think I may have figured it out, and for people reading the post here is my attempt at the answer:
    [tex]K_{e}=1+\chi_{e}=1+\frac{\epsilon-\epsilon_{0}}{\epsilon_{0}}=1+\frac{\epsilon_{r}\epsilon_{0}-\epsilon_{0}}{\epsilon_{0}}=1+\epsilon_{r}-1=\epsilon_{r}
    [/tex]
    [tex]
    \epsilon_{r}=\frac{C_{x}}{C_{0}}
    [/tex]
    So
    [tex]
    K_{e}=\frac{C_{x}}{C_{0}}
    [/tex]

    where

    [tex]K_{e}[/tex] - dielectric constant
    [tex]\chi_{e}[/tex] - electric susceptibility
    [tex]\epsilon[/tex] - permittivity of the dielectric material
    [tex]\epsilon_{r}[/tex] - relative permittivity
    [tex]\epsilon_{0}[/tex] - permittivity of free space
    [tex]C_{x}[/tex] - capacitance of the dielectric material
    [tex]C_{0}[/tex] - capacitance of vacuum

    Please feel free to correct me.
     
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