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Spherical capacitor
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Capacitance of concentric spheres.
C = 4πε₀ab/(b−a)Concentric spheres of radius a and b have C = 4πε₀ab/(b − a). With b → ∞ the isolated sphere has C = 4πε₀a.
Earth's capacitance ≈ 710 μF.
The inner sphere carries the charge.
In more detail
A spherical capacitor has two concentric spherical shells, with capacitance C = 4πε0 ab/(b − a), where a and b are the inner and outer radii.
Real-world uses
- Models of the capacitance of isolated spheres in electronics.
- Calculating capacitance of spherical electrodes in lab experiments.
- Engineers use concentric spherical capacitors as a model for capacitance of spherical electrodes.
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Frequently asked questions
What if the outer radius is very large?
The capacitance approaches 4πε0a, the value for an isolated sphere.
Why use concentric shells?
Because the field is radial and symmetric, which simplifies the calculation.
What happens when the outer sphere becomes very large?
The capacitance approaches four pi times the permittivity times the inner radius, which is the capacitance of an isolated sphere.
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Dielectrics · Polarisation · Dielectric breakdown · Cylindrical capacitor · Van de Graaff generator · Lightning and discharge