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Cylindrical capacitor Cylindrical capacitor
Capacitor consists from two coaxial cylindrical collinear electrodes. It may be simulated as 2D axisymmetric or 3D extrusion problem. Both approaches give same result and good correlation with analytical solution.
2D axisymmetric/3D extrusion electrostatics.
a = 5 mm, b = 6 mm.
Model depth l = 40 mm.
Relative permittivity of air ε = 1,
Relative permittivity of media ε = 2,
Voltage difference ΔU = 1 V.
Find the capacitance of cylindrical capacitor. Solution:
Analytical solution gives the capacitance value of ideal cylindrical capacitor (without end effects) as
C = 2πεε 0 * l / ln( a/ b) [F]. *
QuickField simulation gives energy
W and electric potential U distribution. The capacitance then can be calculated as C = 2 W / Δ U 2.
Analytical solution (cylindrical capacitor without end effects):
C = 2*3.142*2*8.854e-12 * 0.04 / ln(0.006/0.005) = 0.4451e-11 / 0.1823 = 2.44e-11 F.
2D axisymmetrical simulation
3D extrusion simulation
* Wikipedia, Capacitance.
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