Two disc capacitor - QuickField simulation example
Capacitance of a two-disc air capacitor for the specified plate radius and separation, with results from axisymmetric and three-dimensional geometry compared.
How to calculate the capacitance of a two-disc capacitor?
Answer Typical applications Geometry 2D axisymmetric/3D extrusion.
a = 2.4 mm, d = 0.1 mm.
Given
Task
Solution
QuickField simulation gives energy W and electric potential U distribution. The capacitance then can be calculated as C = 2W / ΔU².
Results * http://chemandy.com/calculators/circular-capacitor-calculator.htm
Engineering question
Calculate the stored electrostatic energy and obtain capacitance from C = 2W/U^2, then compare the 2D or 3D result with the analytical formula.
disc capacitors, circular plate capacitors, parallel disc electrodes
Download
Simulation problem
Problem Type electrostatics.
Relative permittivity of air ε = 1,
Relative permittivity of media ε = 2,
Potential difference ΔU = 1 V
Find the capacitance of two disc capacitor.
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]. *
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 C
3.34e-12 F
3D extrusion simulation
1.67e-12 J
3.34e-12 F
Video
2D electrostatics simulation
3D electrostatics simulationRelated examples