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# Non-concentric spheres capacitance

Problem Type: electrostatics.

Geometry:

a = 100 mm, d = 500 mm.

Given:
Relative permittivity of air ε = 1,
The charge q = 10-9 C

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.
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. 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
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