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Mutual capacitance of collinear cylinders

Find the mutual capacitance between two collinear infinitely long cylinders.

Problem Type:
Plane problem of electrostatics.

Geometry:
Cylindrical capacitor Capacitor consists of two coaxial cylindrical collinear electrodes -q +q a b l = 1000 mm

a = 5 mm, b = 10 mm.

Given:
Relative permittivity of air ε = 1,
The charge q = 1 nC.

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

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. The charge is then redistributed along the conductor surface automatically.

Results:
Potential distribution between collinear cylinders.

collinear cylinders voltage distribution

The capacitance can be calculated as C = q / (U2 - U1). The measured potential difference is U2-U1 = 12.459 V.
The capacitance is C = 10-9 / 12.459 = 8.027·10-11 F.

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Theoretical result

C, pF
(model depth l = 1 m)

80.27

80.26

*Wikipedia, Capacitance.

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