How do you calculate Spherical Capacitor?

Use the formula C = 4πε0 × a × b / (b − a). A spherical capacitor consists of two concentric conducting spheres separated by a gap. Enter the values you know in the calculator above and it solves for the remaining variable.

What is the formula for Spherical Capacitor?

The Spherical Capacitor formula is C = 4πε0 × a × b / (b − a), where C—Capacitance (F); a—Inner sphere radius (m); b—Outer sphere radius (m); ε0—Permittivity of free space (× εr if filled).

Spherical Capacitor

C = 4πε0 · a · b / (b − a)

Calculator

Capacitance

Inner Radius

Outer Radius

Result

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Formula

C = 4πε0 × a × b / (b − a)

Description

A spherical capacitor consists of two concentric conducting spheres separated by a gap. Its capacitance depends on the inner and outer radii and the permittivity between them. As the outer sphere recedes to infinity it reduces to the self-capacitance of an isolated sphere (4πε0·a). The geometry is the textbook model for screened spherical electrodes and Van de Graaff terminals.

Variables

C — Capacitance (F)
a — Inner sphere radius (m)
b — Outer sphere radius (m)
ε0 — Permittivity of free space (× εr if filled)

Practical Notes

For a dielectric-filled gap multiply by εr. With b → ∞ the formula gives an isolated sphere’s capacitance C = 4πε0·a (about 0.11 pF per cm of radius).

Related Concepts

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