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Pair of parallel wires capacitance

two wire capacitance, two wire electric field

Problem Type:
Plane-parallel problem of electrostatics.

Geometry:
Pair of parallel wires capacitance Finding the mutual capacitance between two infinitely long parallel wires a1 a2 +q -q d Air

a1 = 4.72 mm, a2 = 1.13 mm, d = 100 mm.

Given:
Relative permittivity of vacuum ε = 1,
The charge q = 10-9 C
Model depth l = 1 m.

Task:
Find the mutual capacitance between two parallel wires and compare its value with analytical solution:
C = 2π·ε·ε0 l / ln( d²/a1·a2 ) [F]. *

Solution:
Wire's surfaces are marked as 'floating conductor', i.e. isolated conductors with unknown potential. At some point on each of wire's surface the charge is applied. The charge is then redistributed along the conductor surface automatically.

Results:

Potential distribution.

pair of parallel wires capacitance

The capacitance can be calculated as C = q / (U2-U1). The measured potential difference is U2-U1 = 135 V.
The capacitance is C = 10-9 / 135 = 7.41·10-12 F

 

QuickField

Theoretical result

C, pF
(model depth l = 1 m)
7.41

7.37

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  • *Power System Engineering, D.P.Kothari, I.J.Nargath.

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