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Main >> Applications >> Sample problems

Coaxial cylinders capacitance

QuickField simulation example

Find the mutual capacitance between two coaxial infinitely long cylinders.

Engineering question
How to find mutual capacitance of coaxial cylindrical conductors?

Engineering answer
Set up a plane-parallel QuickField Electrostatics problem for coaxial cylindrical conductors and evaluate mutual capacitance from computed field results.

Typical applications
coaxial transmission lines, cylindrical capacitors, shielded cable structures

Problem Type
Plane-parallel problem of electrostatics.

Geometry
Coaxial cylinders capacitance Capacitor consists of two coaxial cylindrical coaxial electrodes -q +q a b

a = 5 mm, b = 10 mm.

Given
Relative permittivity of air ε = 1,

Task
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 = 12.4585 V.
The capacitance is C = 10-9 / 12.4585 = 8.027·10-11 F = 80.27 pF per 1 meter of model length. Reference value* is 80.26 pF/m
Coaxial cylinders capacitance

Reference: *Wikipedia, Capacitance.