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Transient eddy currents in a two-wire line

QuickField simulation example

This is an example of the two-wire line simulation, performed with QuickField software.

Problem Type
Plane-parallel problem of transient magnetics.

Geometry
Transient eddy currents in a two-wire line Transmission line consists of two copper conductors with equal but opposite currents Copper Air O Ø 0.2 mm 20 mm

Transmission line consists of two copper conductors with equal but opposite currents. All dimensions are in millimeters.

Given
Magnetic permeability of air μ = 1;
Magnetic permeability of copper μ = 1;
Conductivity of copper g = 56 MS/m;
Voltage applied U = 0.001 V;

Task
Calculate the transient currents within the conductors.

Solution
The resistance of one conductor can be calculated as Rcond = l / (g · S),
where
    S = πr² - cross-section area of conductor,
    R - radius of conductor,
    L - length of the line.

The inductance of the transmission line can be calculated as L = μ0·l/π · (ln(D/r) + 0.25), where
   D - distance between conductors.

The transient current for equivalent electric circuit with lumped parameters (R and L in series) is described by the formula
I(t) = U/R · (1 - e-t/T), where T=L/R - characteristic time of the circuit.

Results
Conductor resistance (analytical value) is Rcond = 1 / (56·106 · (π·0.0001²)) = 0.5684 Ohm.
The resistance of both conductors in transmission line is R = 2·Rcond = 2·0.5684 = 1.1368 Ohm

Transmission line inductance (analytical value) is L = 4π·10-7·1/π · (ln(0.02/0.0001) + 0.25) = 2.219 μH
Eddy current density distribution in the wire.