
Plane capacitor with two discshaped plates. This problem may be simulated in both 2D axisymmetric and 3D extrusion formulation.
Problem Type:
2D axisymmetric/3D extrusion electrostatics.
Geometry:
a = 2.4 mm, d = 0.1 mm.
Given:
Relative permittivity of air ε = 1,
Relative permittivity of media ε = 2,
Potential difference ΔU = 1 V
Problem:
Find the capacitance of two disc capacitor.
Solution:
Analytical solution gives the capacitance value of two disc capacitor as
C = ε·ε_{0}·πa^{2} / d + ε·ε_{0}·a·(ln[16π·a/d]  1), [F]. *
QuickField simulation gives stored electric energy value W. With known potential difference ΔU the capacitance then can be calculated as C = 2W / ΔU^{2}.
Results:
Analytical solution: C = 2·8.854·10^{12}·3.142·0.0024^{2}/0.0001 + 2·8.854·10^{12}·0.0024·[ln(16·3.142·0.0024/0.0001)  1] = 3.205·10^{12} + 0.259·10^{12} = 3.464·10^{12} F.
Energy W 
Capacitance C 

2D axisymmetrical simulation 
1.67e12 J 
3.34e12 F 
3D extrusion simulation 
1.67e12 J 
3.34e12 F 
^{*} http://chemandy.com/calculators/circularcapacitorcalculator.htm
See the two_disc_capacitor_2d.pbm, two_disc_capacitor_3d.pbm problems in the Examples folder.