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Main > Application > Sample problems

Non-concentric spheres capacitance

Problem Type:
Axisymmetric problem of electrostatics.

Geometry:

non-concentric_spheres_capacitance

a = 100 mm, d = 500 mm.

Given:
Relative permittivity of vacuum 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·ε0 · 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:

Potential distribution around spheres.

sphere in front of wall capacitance

The capacitance can be calculated as C = q / (U2 - U1). The measured potential difference is U2 - U1 = 143.4 V.
The capacitance is C = 10-9 / 143.4 = 6.97·10-12 F.

QuickField

Theoretical result

C, pF

6.97

6.99

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*Wikipedia, Capacitance.