A new approach to field modelling

Language:
Language Global English Deutsch Espanol Francais Italiano Danmark Ceske Chinese no-Pyccku


RSS Twitter Facebook Linkedin YouTube

>> >> >>

Non-concentric spheres capacitance

Problem Type:
Axisymmetric problem of electrostatics.

Geometry:

non-concentric spheres electric field

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 non-concentric spheres capacitance analytical solution [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

*Wikipedia, Capacitance.

Download PDF icon View simulation report in PDF.

Download Download simulation files (files may be viewed using any QuickField Edition).

There are no restrictions applied to the QuickField Student Edition postprocessors.
You can view field maps, make plots, calculate integrals and print pictures in the same way that the Professional Edition users do.