## Spherical Capacitor (Capacitance, Radius)

`$$ C ~=~ \frac{4\pi \, \varepsilon_{\text r} \, \varepsilon_0}{\frac{1}{R_1} ~-~ \frac{1}{R_2}} $$`

$$C ~=~ 2\pi \, \varepsilon_0 \, \varepsilon_{\text r} \, l \, \frac{ 1 }{\ln{ \left( \frac{R_2}{R_1} \right) }}$$ $$C ~=~ 2\pi \, \varepsilon_0 \, \varepsilon_{\text r} \, l \, \frac{ 1 }{\ln{ \left( \frac{R_2}{R_1} \right) }}$$ $$l ~=~ \frac{C}{ 2\pi \, \varepsilon_0 \, \varepsilon_{\text r} } \, \ln{ \left( \frac{R_2}{R_1} \right) }$$ $$R_1 ~=~ R_2 \, \mathrm{e}^{ - \frac{2\pi \, \varepsilon_0 \, \varepsilon_{\text r} \, l}{ C } }$$ $$R_2 ~=~ R_1 \, \mathrm{e}^{ \frac{2\pi \, \varepsilon_0 \, \varepsilon_{\text r} \, l}{ C } }$$ $$\varepsilon_{\text r} ~=~ \frac{C}{ 2\pi \, \varepsilon_0 \, l} \, \ln{ \left( \frac{R_2}{R_1} \right) }$$ $$\varepsilon_0 ~=~ \frac{C}{ 2\pi \, \varepsilon_{\text r} \, l} \, \ln{ \left( \frac{R_2}{R_1} \right) }$$

Capacitance 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 of the cylinder. The longer the cylinder, the greater its electric capacitance.

Radius of the *inner* electrode of the charged cylindrical capacitor.

Radius of the *outer* electrode of the charged cylindrical capacitor.

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 is a physical constant and has the value: \( \varepsilon_0 = 8.854187817 ~\cdot~ 10^{-12} \, \frac{\text{As}}{\text{Vm}} \).

**Copyright**: © 2020**License**: CC BY 4.0**Summary**: Formula you can use to calculate the capacitance of a cylindrical capacitor, given the cylinder radii and length of the cylindrical capacitor.- This formula was added by Alexander Fufaev on
12/13/2020 - 22:03 . - This formula was updated by Alexander Fufaev on
04/30/2022 - 10:11 .

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