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Main >> Applications >> Sample problems >> Non-concentric spheres capacitance
spherical capacitor simulation, spherical electrodes, electrostatic field between spheres
Problem Type:
Axisymmetric problem of electrostatics.
Geometry:
a = 100 mm, d = 500 mm.
Given:
Relative permittivity of air ε = 1,
The charge q = 10^{-9} C
Task:
Find the mutual capacitance between two spheres and compare its value with analytical solution:
C = 2π·ε·ε_{0} · a [F] *,
where D = d/ (2a).
Solution:
Sphere's surfaces are marked as 'floating conductor', i.e. isolated conductors with unknown potential. At some point on each of sphere's surface the charge is applied. The charge is then redistributed along the conductor surface automatically.
Results:
Electric field stress distribution around spheres.
The capacitance can be calculated as C = q / (U2 - U1) = 6.4e-12 / 1 = 6.4·10^{-12} F.
QuickField |
Theoretical result |
||
2D | 3D | ||
C, pF | 6.97 | 6.40 | 6.99 |