Spherical Capacitor Calculator

What Is a Spherical Capacitor?

A spherical capacitor consists of two concentric conducting spheres separated by a dielectric. Charge on the inner sphere and opposite charge on the outer shell create an electric field in the gap. Capacitance depends on both radii and the relative permittivity of the fill material.

Spherical Capacitor Formula

\(a\) is the inner radius, \(b\) is the outer radius, \(\varepsilon_0 \approx 8.854 \times 10^{-12}\,\text{F/m}\) is the vacuum permittivity, and \(\varepsilon_r\) is the relative permittivity (dielectric constant). The outer radius must be greater than the inner radius.

Example: \(a = 1\,\text{cm}\), \(b = 2\,\text{cm}\), \(\varepsilon_r = 1\) gives \(C \approx 2.22\,\text{pF}\).

Applications

Spherical capacitors model concentric electrodes in sensors, high-voltage bushings, and electrostatic theory problems. Adding a dielectric with \(\varepsilon_r > 1\) increases capacitance proportionally.

Related tools: Capacitor Design Calculator and Capacitor Size Calculator.