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# Coaxial cylinders capacitance

QuickField simulation example

Find the mutual capacitance between two coaxial infinitely long cylinders.

Problem Type
Plane-parallel problem of electrostatics.

Geometry

a = 5 mm, b = 10 mm.

Given
Relative permittivity of air ε = 1,

Find the mutual capacitance between two coaxial infinitely long cylinders and compare it with analytical solution*: C = 2πεε0 / ln(a/b) [F/m].

Solution
Each of the conductor's surface is marked as 'floating conductor', i.e. isolated conductors with unknown potential. At some point on each of conductor's surface the charge is applied q = 1 nC. The charge is then redistributed along the conductor surface automatically.
The capacitance can be calculated as C = q / ΔU

Results
The measured potential difference is ΔU = 12.459 V.
The capacitance is C = 10-9 / 12.459 = 8.027·10-11 F = 80.27 pF per 1 meter of model length. Reference value* is 80.26 pF/m Reference: *Wikipedia, Capacitance. 