Spherical capacitor - QuickField simulation example
Engineering question
How to calculate the capacitance of a spherical capacitor and verify analytically?
Answer
Treat the spherical electrodes as floating conductors, calculate capacitance from charge over potential difference, and compare the result with the analytical formula.
Typical applications
spherical capacitor electrodes, concentric sphere electrodes, electrostatic sphere systems
Download
- Download simulation files (files may be viewed using any QuickField Edition).
Simulation problem
Problem TypeAxisymmetric problem of electrostatics.
Geometry
R = 100 mm, R=50 mm.
Given
Relative permittivity of air ε = 1,
The charge q = 10-9 C
Task
Find the capacitance of spherical capacitor and compare it with analytical solution:
C = 4π·ε·ε0 · r·R / (R - r), [F]. *
Solution
Capacitor plate's surface is marked as 'floating conductor', i.e. isolated conductors with unknown potential. At some point on spheres' surface the charge is applied. The charge is then redistributed along the conductor surface automatically.
Results
Potential distribution inside of the spherical capacitor.
The capacitance can be calculated as C = q / (U2-U1).
The measured potential difference is U2-U1 = 89.87 V.
The capacitance is C = 10-9/ 89.87 = 11.13·10-12 F
| QuickField | Theoretical result | |
|---|---|---|
| C, pF | 11.13 | 11.11 |
Reference: Wikipedia, Capacitance.
Video
- Spherical capacitor 2D axisymmetric. Watch on YouTube
Spherical capacitor 3D. Watch on YouTube.
- View simulation report in PDF