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Transient eddy currents in a two-wire line
TEMagn2: Transient eddy currents in a two-wire line
This is an example of the two-wire line simulation, performed with QuickField software.
Plane problem of transient magnetics.
Transmission line consists of two copper conductors with equal but opposite currents. All dimensions are in millimeters.
Magnetic permeability of air μ = 1;
Magnetic permeability of copper μ = 1;
Conductivity of copper g = 56,000,000 S/m;
Voltage applied U = 0.001 V;
Calculate the transient currents within the conductors.
The resistance of one conductor can be calculated as Rcond = l / (g · S),
S = πr2 - cross-section area of conductor,
r - radius of conductor,
l - length of the line.
Rcond = 1 / (56·106 · (π·0.00012)) = 0.5684 Ohm
The resistance of both conductors is R = 2·Rcond = 2·0.5684 = 1.1368 Ohm
The inductance of the transmission line can be calculated as L = μ0·l/π · (ln(D/r) + 0.25), where
D - distance between conductors.
L = 4π·10-7·1/π · (ln(0.02/0.0001) + 0.25) = 2.219·10-6 Hn
The transient current for equivalent electric circuit with lumped parameter is
described by the formula
I(t) = U/R · (1 - e-t/T), where T=L/R - characteristic time of the circuit.
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