Formula Cylindrical Capacitor Capacitance Length Inner radius Outer radius Relative permittivity Permittivity of free space
$$C ~=~ 2\pi \, \varepsilon_0 \, \varepsilon_{\text r} \, l \, \frac{ 1 }{\ln{ \left( \frac{R_2}{R_1} \right) }}$$ $$C ~=~ 2\pi \, \varepsilon_0 \, \varepsilon_{\text r} \, l \, \frac{ 1 }{\ln{ \left( \frac{R_2}{R_1} \right) }}$$ $$l ~=~ \frac{C}{ 2\pi \, \varepsilon_0 \, \varepsilon_{\text r} } \, \ln{ \left( \frac{R_2}{R_1} \right) }$$ $$R_1 ~=~ R_2 \, \mathrm{e}^{ - \frac{2\pi \, \varepsilon_0 \, \varepsilon_{\text r} \, l}{ C } }$$ $$R_2 ~=~ R_1 \, \mathrm{e}^{ \frac{2\pi \, \varepsilon_0 \, \varepsilon_{\text r} \, l}{ C } }$$ $$\varepsilon_{\text r} ~=~ \frac{C}{ 2\pi \, \varepsilon_0 \, l} \, \ln{ \left( \frac{R_2}{R_1} \right) }$$ $$\varepsilon_0 ~=~ \frac{C}{ 2\pi \, \varepsilon_{\text r} \, l} \, \ln{ \left( \frac{R_2}{R_1} \right) }$$
Capacitance
\( C \) Unit \( \text{F} \) 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 \( \text{m} \) Length of the cylinder. The longer the cylinder, the greater its electric capacitance.
Inner radius
\( R_1 \) Unit \( \text{m} \) Radius of the inner electrode of the charged cylindrical capacitor.
Outer radius
\( R_2 \) Unit \( \text{m} \) 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.
Permittivity of free space
\( \varepsilon_0 \) Unit \( \frac{\text{As}}{\text{Vm}} \) Permittivity of free space is a physical constant and has the value: \( \varepsilon_0 = 8.854187817 ~\cdot~ 10^{-12} \, \frac{\text{As}}{\text{Vm}} \).