Formula: Electric Field in Matter Electric field (E field) Polarization Vacuum Permittivity
$$\class{purple}{E_{\text m}} ~=~ \class{purple}{E} ~-~ \frac{ \class{red}{P} }{ \varepsilon_0 }$$
$$\class{purple}{E_{\text m}} ~=~ \class{purple}{E} ~-~ \frac{ \class{red}{P} }{ \varepsilon_0 }$$
$$\class{purple}{E} ~=~ \class{purple}{E_{\text m}} ~+~ \frac{ \class{red}{P} }{ \varepsilon_0 } $$
$$\class{red}{P} ~=~ \varepsilon_0 \, \left( \class{purple}{E} ~-~ \class{purple}{E_{\text m}} \right)$$
Electric field in matter
$$ \class{purple}{E_{\text m}} $$ Unit $$ \frac{\mathrm V}{\mathrm m} $$
The average electric field within the dielectric (non-conductive but polarizable) material.
Electric field (E field)
$$ \class{purple}{\boldsymbol E} $$ Unit $$ \frac{\mathrm{V}}{\mathrm{m}} = \frac{\mathrm{N}}{\mathrm{C}} = \frac{\mathrm{kg} \, \mathrm{m}}{\mathrm{A} \, \mathrm{s}^3} $$
External electric field in which the dielectric material is situated.
Polarization
$$ \class{red}{\boldsymbol P} $$ Unit $$ \frac{ \mathrm C }{ \mathrm{m}^2 } $$
Polarization describes the density of electric dipoles in a material (number per volume) and induces a polarization field \( \class{purple}{E_{\text{p}}} \), which can be aligned either opposite or in the same direction as the external electric field, thereby amplifying or weakening the external electric field.
Vacuum Permittivity
$$ \varepsilon_0 $$ Unit $$ \frac{\mathrm{As}}{\mathrm{Vm}} $$
The vacuum permittivity is a physical constant that appears in equations involving electromagnetic fields. It has the following experimentally determined value:
$$ \varepsilon_0 ~\approx~ 8.854 \, 187 \, 8128 ~\cdot~ 10^{-12} \, \frac{\mathrm{As}}{\mathrm{Vm}} $$