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Spherical capacitor

spherical capacitor finite element analysis

Problem Type:
Axisymmetric problem of electrostatics.

Geometry:
Spherical capacitor Find the capacitance of spherical capacitor and compare it with analytical solution Air R r +q -q

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.

spherical capacitor voltage distribution

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

*Wikipedia, Capacitance.

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