Physics

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Spherical Capacitor Calculator.

Calculate capacitance of a concentric spherical capacitor.

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01

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Capacitance: 0 F

Capacitance

0.000000F

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Use Cases

Designing spherical capacitors

Engineers and students can use this calculator to determine the capacitance of a spherical capacitor for a given geometry and dielectric material, aiding in circuit design or academic projects.

Example: Find the capacitance of a sphere with inner radius 0.01 m, outer radius 0.02 m, and relative permittivity 2.1.

Educational demonstrations

Physics teachers and learners can quickly compute capacitance values to verify theoretical concepts and explore how changing radii or dielectric affects capacitance.

Example: Compare capacitance when the outer radius is doubled.

Frequently Asked Questions

What is a spherical capacitor?
A spherical capacitor consists of two concentric conducting spheres separated by a dielectric. The inner sphere carries a charge, and the outer sphere carries an equal and opposite charge. The capacitance depends on the radii and the dielectric material between them.
How is the capacitance calculated?
The capacitance is calculated using the formula C = 4πε₀εᵣ / (1/a - 1/b), where a is the inner radius, b is the outer radius, ε₀ is the vacuum permittivity, and εᵣ is the relative permittivity of the dielectric.
What units should I use for the radii?
The calculator expects the inner and outer radii in meters (m). Ensure both radii are positive and the outer radius is greater than the inner radius for a valid capacitor.

Tips & Common Mistakes

Tips

  • Ensure the outer radius is larger than the inner radius; otherwise, the capacitance calculation is invalid.
  • Use consistent units (meters) for both radii to get accurate results in farads.
  • For vacuum or air, set relative permittivity to 1. For other materials, look up the dielectric constant.
  • Remember that capacitance increases as the gap between spheres decreases or as the dielectric constant increases.

Common Mistakes to Avoid

  • Entering radii in different units (e.g., centimeters) without converting to meters, leading to incorrect capacitance.
  • Setting the outer radius equal to or less than the inner radius, which is physically impossible for a capacitor.
  • Using the relative permittivity of the conductor instead of the dielectric material between the spheres.

Last updated: August 13, 2026