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Cylindrical capacitor

cylindrical capacitor simulation, coaxial cylindrical electrodes, capacitor electric field

Capacitor consists of 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.

Problem Type
2D axisymmetric/3D extrusion electrostatics.

Geometry
Cylindrical capacitor Capacitor consists of two coaxial cylindrical collinear electrodes Grounded ΔU a b L

a = 5 mm, b = 6 mm, L = 40 mm.

Given
Relative permittivity of media ε = 2,
Voltage difference ΔU = 1 V.

Task
Find the capacitance of cylindrical capacitor.

Solution
Analytical solution gives the capacitance value of ideal cylindrical capacitor (without end effects) as
C = 2πεε0 * l / ln(a/b) [F]. *

QuickField simulation gives energy W and electric potential U distribution. The capacitance then can be calculated as C = 2W / ΔU².

Results
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.

Energy W Capacitance C
2D axisymmetrical simulation 1.24 pJ 2.48 pF
3D extrusion simulation 1.25 pJ 2.50 pF

cylindrical capacitor 2D simulation

cylindrical capacitor 3D simulation

*Wikipedia, Capacitance.

Eddy currents simulation with QuickField

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