Variable capacitor

Variable air capacitor consists of fixed stator plates and movable rotor. Capacitance between the stator plates depends on the position of the rotor.

Problem Type:
3D extrusion electrostatics.

Geometry:
Variable capacitor Variable air capacitor consists of fixed stator plates and movable rotor. Rotor V- V+ Stator Stator

Given:
Relative permittivity of air ε = 1,
Potential difference ΔU = 1000 V

Problem:
Find the mutual capacitance between two stators as a function of the rotor position.

Solution:

QuickField simulation gives stored electric energy value W. With known potential difference ΔU the capacitance then can be calculated as C = 2W / ΔU2.

Results:

Rotating angle α Energy W Capacitance C
0° 1.29e-6 J 2.58e-12 C
30° 2.25e-6 J 4.50e-12 C
60° 2.97e-6 J 5.94e-12 C
90° 3.22e-6 J 6.44e-12 C

See the variable_capacitor.pbm problem in the Examples folder.