
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:
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 = 2πεε_{0} * 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 / ΔU^{2}.
Results:
Analytical solution (cylindrical capacitor without end effects):
C = 2*3.142*2*8.854e12 * 0.04 / ln(0.006/0.005) = 0.4451e11 / 0.1823 = 2.44e11 F.
Energy W 
Capacitance C 

2D axisymmetrical simulation 
1.24e12 J 
2.48e12 F 
3D extrusion simulation 
1.25e12 J 
2.50e12 F 
See the cylindrical_capacitor_2d.pbm, cylindrical_capacitor_3d.pbm problems in the Examples folder.