Two disc capacitor
QuickField simulation example
Plane capacitor with two disc-shaped plates. This problem may be simulated in both 2D axisymmetric and 3D extrusion formulation.
Problem Type electrostatics.
Geometry 2D axisymmetric/3D extrusion.
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
Task
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 energy W and electric potential U distribution. 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 C | 3.34e-12 F |
| 3D extrusion simulation | 1.67e-12 J | 3.34e-12 F |
* http://chemandy.com/calculators/circular-capacitor-calculator.htm
2D electrostatics simulation
3D electrostatics simulation
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