Formula Cylindrical Capacitor Capacitance Length Inner radius Outer radius Relative permittivity Vacuum Permittivity
$$C ~=~ 2\pi \, \varepsilon_0 \, \varepsilon_{\text r} \, l \, \frac{ 1 }{\ln{ \left( \frac{R_2}{R_1} \right) }}$$ $$C ~=~ 2\pi \, \varepsilon_0 \, \varepsilon_{\text r} \, l \, \frac{ 1 }{\ln{ \left( \frac{R_2}{R_1} \right) }}$$ $$l ~=~ \frac{C}{ 2\pi \, \varepsilon_0 \, \varepsilon_{\text r} } \, \ln{ \left( \frac{R_2}{R_1} \right) }$$ $$R_1 ~=~ R_2 \, \mathrm{e}^{ - \frac{2\pi \, \varepsilon_0 \, \varepsilon_{\text r} \, l}{ C } }$$ $$R_2 ~=~ R_1 \, \mathrm{e}^{ \frac{2\pi \, \varepsilon_0 \, \varepsilon_{\text r} \, l}{ C } }$$ $$\varepsilon_{\text r} ~=~ \frac{C}{ 2\pi \, \varepsilon_0 \, l} \, \ln{ \left( \frac{R_2}{R_1} \right) }$$ $$\varepsilon_0 ~=~ \frac{C}{ 2\pi \, \varepsilon_{\text r} \, l} \, \ln{ \left( \frac{R_2}{R_1} \right) }$$
Capacitance
$$ C $$ Unit $$ \mathrm{F} = \frac{ \mathrm{C} }{ \mathrm{V} } $$ Capacitance is a measure of how much charge can be separated on the electrodes of the cylindrical capacitor, in other words - how good the cylinder can store electric charge.
Length
$$ l $$ Unit $$ \mathrm{m} $$ Length of the cylinder. The longer the cylinder, the greater its electric capacitance.
Inner radius
$$ R_1 $$ Unit $$ \mathrm{m} $$ Radius of the inner electrode of the charged cylindrical capacitor.
Outer radius
$$ R_2 $$ Unit $$ \mathrm{m} $$ Radius of the outer electrode of the charged cylindrical capacitor.
Relative permittivity
$$ \varepsilon_{\text r} $$ Unit $$ - $$ Relative permittivity depends on the dielectric medium between the outer and inner cylinder and indicates the permeability of the electric field. In vacuum it has the value: \( \varepsilon_r ~=~ 1 \). By using a different medium (e.g. air or water) between the electrodes of the cylinder capacitor, the capacitance of the cylinder can be increased.
Vacuum Permittivity
$$ \varepsilon_0 $$ Unit $$ \frac{\mathrm{As}}{\mathrm{Vm}} $$ Permittivity of free space is a physical constant and has the value: \( \varepsilon_0 = 8.854187817 ~\cdot~ 10^{-12} \, \frac{\text{As}}{\text{Vm}} \).