Dielectric Constant (Relative Permittivity)

$epsilon_r = epsilon /epsilon_0$

$epsilon$

Brief Version

$epsilon_r$ is inversely proportional to how much stronger the electric field is in a given material compared to vacuum.

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Polarization ( $P$ ) is what happens when an electric field ( $E$ ) pushes on a material where the charges can move a little, but aren't fully free. You can think of it as the charges being shifted so that they may not cancel out in a given area. However, the charge of the entire material is still conserved.

Linear Dielectrics¹ are materials that obey the equation $P = epsilon_0 chi_e E$ for $E$ s that are not too strong. $chi_e$ is called the "electric susceptibility", and it can be thought of as describing how far the charges are free to shift when the electric field pushes on them. Linear Dielectrics simplify a lot of math and therefore can be quite useful, but that's outside the scope of this brief discussion. For a more detailed account of dielectrics and polarization, please see The Physics Hypertextbook.

In Linear Dielectrics, the equation we discussed earlier eventually gives us the equation $epsilon = epsilon_r epsilon_0$ , where $epsilon$ describes an electric field's strength in a given material. Higher $epsilon$ means a weaker field, and vice versa. We can understand this in the context of polarization as $epsilon$ representing how much the charges in the dielectric shift to counteract the electric field. We can rearrange the above equation to .

$epsilon_0$ is the "permittivity of vacuum", and can be thought of as describing the strength of an electric field when there isn't a dielectric around to become polarized and oppose the field. $epsilon_r$ is the ratio between the permittivity of a material and the permittivity of vacuum, so it's a ratio that describes how much weaker an electric field is in a given material relative to vacuum (hence Relative Permittivity). For example, if $epsilon_r$ for a given material is 2, then an electric field in that material will be half as strong as it would be in vacuum.

^ Griffiths, David J. "Electric Fields in Matter." Introduction to Electrodynamics. 4th ed. N.p.: Prentice Hall, 2013. 185-86. Print.