Cylindrical capacitor

Capacitor consists from two coaxial cylindrical collinear electrodes. It may be simulated as 2D axisymmetric or 3D extrusion problem.

Problem Type:
2D axisymmetric/3D extrusion electrostatics.

Geometry:

collinear cylinders model

a = 5 mm, b = 6 mm, l = 40 mm.

Given:

Relative permittivity of air ε = 1,

Relative permittivity of media ε = 2,
Voltage difference ΔU = 1 V.

Problem:
Find the capacitance of cylindrical capacitor.

Solution:

Analytical solution gives the capacitance value of ideal cylindrical capacitor (without end effects) as
C = 2πεε0 * l / ln(a/b) [F]. *

QuickField simulation gives stored electric energy value W. With known potential difference ΔU the capacitance can be calculated as C = 2W / ΔU2.

Results:

Analytical solution (cylindrical capacitor without end effects):
C = 2*3.142*2*8.854e-12 * 0.04 / ln(0.006/0.005) = 0.4451e-11 / 0.1823 = 2.44e-11 F.

Energy W

Capacitance C

2D axisymmetrical simulation

1.24e-12 J

2.48e-12 F

3D extrusion simulation

1.25e-12 J

2.50e-12 F

*Wikipedia, Capacitance.

See the cylindrical_capacitor_2d.pbm, cylindrical_capacitor_3d.pbm problems in the Examples folder.