Formula Spherical Capacitor Capacitance Inner radius Outer radius Relative permittivity
$$C ~=~ \frac{4\pi \, \varepsilon_{\text r} \, \varepsilon_0}{\frac{1}{R_1} ~-~ \frac{1}{R_2}}$$ $$C ~=~ \frac{4\pi \, \varepsilon_{\text r} \, \varepsilon_0}{\frac{1}{R_1} ~-~ \frac{1}{R_2}}$$ $$R_1 ~=~ \frac{R_2}{ \frac{4\pi \, \varepsilon_{\text r} \, \varepsilon_0 \, R_2}{C} + 1 }$$ $$R_2 ~=~ - \frac{R_1}{ \frac{4\pi \, \varepsilon_{\text r} \, \varepsilon_0 \, R_1}{C} - 1 }$$ $$\varepsilon_{\text r} ~=~ \frac{ C }{ 4\pi \, \varepsilon_0 } \, \left( \frac{1}{R_1} ~-~ \frac{1}{R_2} \right)$$ $$\varepsilon_0 ~=~ \frac{ C }{ 4\pi \, \varepsilon_{\text r} } \, \left( \frac{1}{R_1} ~-~ \frac{1}{R_2} \right)$$
Capacitance
\( C \) Unit \( \text{F} \) Electric capacitance determines how much charge the spherical capacitor can store separately when a certain voltage is applied between the two electrodes of the capacitor.
Inner radius
\( R_1 \) Unit \( \text{m} \) Radius of the inner charged sphere of the spherical capacitor.
Outer radius
\( R_2 \) Unit \( \text{m} \) Radius of the outer charged sphere of the spherical capacitor.
Relative permittivity
\( \varepsilon_{\text r} \) Unit \( - \) Relative permittivity depends on the medium and indicates the permeability of the electric field. In vacuum it has the value: \( \varepsilon_r ~=~ 1 \). The capacitance of the spherical capacitor can be increased by using a different medium (e.g. air, water, glass) between the inner and outer sphere.
Permittivity of free space
\( \varepsilon_0 \) Unit \( \frac{\text{As}}{\text{Vm}} \) Permittivity of free space is a natural constant and has the value: \( \varepsilon_0 = 8.854 \cdot 10^{-12} \, \frac{\text{As}}{\text{Vm}} \).