QuickField : electrostatics examples

Cylindrical condensator

A cylindrical air capacitor is formed by two coaxial armatures. The central armature is set to the potential V and the central armature to the potential 0.
With R₁=10 cm, R₂=20 cm and h = 50 cm. Side effects are neglected .

  What is the capacitance value ?
  What is the maximum potential to avoid a spark ?

  Disruptive field : 1 MV/m^-1, C = 2πε₀h/ln(R₂/R₁) , E_max=V₀/[R₁ln(R₂/R₁)]

  Answer : 48 pf, 69 kV

   Student (about 175 nodes)   (6 Ko)
   Pro (about 5500 noeuds)   (150 Ko)

cylindrical capacitance

Dihedral capacitor

A dihedral capacitor with Oz edge is formed by two semi-planes making an angle α. The electrical charge is carried by a rectangle whose two sides are parallel to 0z, of length L and abscissa a and b. L = 40 cm, a = 10 cm, b = 50 cm

  Check that the potential is a linear function along arc of circles.
  What is the capacitance value ?

  The field lines are arc circles, C = (ε₀L/α)/ln(b/a) , E = (U₊ - U_-)/xα

  Answer : 4.3 pf ( using "Capacitance wizard" ). Theory : 3.62 pf (The difference explains itself by the low number of nodes and the small volume in which is set the system)

   Student (about 152 nodes)   (6 Ko)

Dihedral condensator

Condensator with plane and cylindrical electrodes

A metal cylinder of radius R = 5 cm is placed at an equal distance from two planes separated by a distance 2a = 60 cm.

  What is the linear capacitance value ?

  Several symmetries will be built for the "Student" model,
  C = 4πε₀/ln[(a + √(a² - R²))/(a - √(a² - R²))]
  (don't forget to multiply by 2 or 4 according to the number of symmetries)

  Answer : 26.2 pf/m ("Student"), 26.6 pf/m ("Pro").

   Student (about 165 noeuds)   (6 Ko)

   Pro (about 800 noeuds)   (23 Ko)

Condensateur plan