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:**

**Given:**

Relative permittivity of air ε = 1,

Potential difference Δ*U* = 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 Δ*U* the capacitance then can be calculated as *C* = 2*W* / Δ*U*^{2}.

**Results:**

Rotating angle α |
Energy |
Capacitance |

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.