Coaxial line leakage current

QuickField simulation example

Calculation of the DC current between coaxial electrodes.

Problem Type
Plane-parallel problem of DC conduction.

Geometry

Outer diameter D = 10 mm, inner diameter d = 4 mm.

Given
Electrical conductivity of media is σ = 1.4 nSm/m.
Cable length L = 10 km.

Task
Find the DC current flowing between electrodes, calculate resistance and compare with analytical solution

Solution
Analytical solution* gives the resistance value to be R = (1 / 2πLσ) * ln(D/d).

In QuickField we specify potential difference V and measure leakage current value I. Then resistance can be calculated as R = V / I.

Results
Analytical solution* R = (1 / (2*3.14159*10000*1.4e-9)) * ln(0.010/0.004) = 10416 Ω.
QuickField R = 1 V / 9.6e-5 A = 10416 Ω per 10 km of line length.
Coaxial line leakage current

*Steven W. Ellingson Electromagnetics, volume 1, Example 6.4. Conductance of a coaxial structure.

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