# Two disc capacitor

Plane capacitor with two disc-shaped 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·ε0·πa2 / d + ε·ε0·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 / ΔU2.

Results:
Analytical solution: C = 2·8.854·10-12·3.142·0.00242/0.0001 + 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 1.67e-12 J 3.34e-12 F 3D extrusion simulation 1.67e-12 J 3.34e-12 F

See the two_disc_capacitor_2d.pbm, two_disc_capacitor_3d.pbm problems in the Examples folder.