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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:

a = 5 mm, b = 10 mm.
Model depth l = 1 m.

Given:

Relative permittivity of vacuum ε = 1,
The charge q = 10^-9 C.

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 surfaces 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.

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.

	QuickField	Theoretical result
C, pF (model depth l = 1 m)	80.27	80.26

Download simulation files.

*Wikipedia, Capacitance.