This equation can calculate relative permittivity. it assumes that the permittivity (`epsilon`) is measured in Farads per meter. For some common dielectric constants, please see.
`epsilon_r` is inversely proportional to how much stronger the electric field is in a given material compared to vacuum.
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 Dielectrics 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 .
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.