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.

^* http://chemandy.com/calculators/circular-capacitor-calculator.htm

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