Formula: Plate Capacitor Attraction Force Voltage Distance Area Relative permittivity
$$F ~=~ \frac{\varepsilon_0 \, \varepsilon_{\text r} \, A}{2d^2}\, U^2$$
$$F ~=~ \frac{\varepsilon_0 \, \varepsilon_{\text r} \, A}{2d^2}\, U^2$$
$$U ~=~ d \, \sqrt{ \frac{2F}{\varepsilon_0 \, \varepsilon_{\text r} \, A} }$$
$$d ~=~ U \sqrt{ \frac{\varepsilon_0 \, \varepsilon_{\text r} \, A}{2F} } $$
$$A ~=~ \frac{2d^2 \, F}{ \varepsilon_0 \, \varepsilon_{\text r} \, U^2 }$$
$$\varepsilon_{\text r} ~=~ \frac{2d^2 \, F}{\varepsilon_0 \, A \, U^2}$$
Attraction Force
$$ F $$ Unit $$ \mathrm{N} $$
Force with which the two plates (electrodes) attract each other.
Voltage
$$ U $$ Unit $$ \mathrm{V} = \frac{ \mathrm J }{ \mathrm C } = \frac{ \mathrm{kg} \, \mathrm{m}^2 }{ \mathrm{A} \, \mathrm{s}^3 } $$
Voltage applied between the two capacitor plates. If you double the voltage, the attraction force between the plates quadruples.
Distance
$$ d $$ Unit $$ \mathrm{m} $$
Distance between the two plates of the capacitor.
Area
$$ A $$ Unit $$ \mathrm{m}^2 $$
Area of one side of the capacitor plate.
Relative permittivity
$$ \varepsilon_{\text r} $$ Unit $$ - $$
Relative permittivity is a dimensionless number describing the dielectric (e.g. air, water, glass) between the two capacitor plates. In vacuum, the relative permittivity has the value \( \varepsilon_{\text r} = 1 \).
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:
$$ \varepsilon_0 ~\approx~ 8.854 \, 187 \, 8128 ~\cdot~ 10^{-12} \, \frac{\mathrm{As}}{\mathrm{Vm}} $$