TEMagn2: Transient eddy currents in a two-wire line

Problem Type:
A plane problem of transient magnetics.

Geometry:

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 = 56 000 000 S/m;
Voltage applied U = 0.001 V;

Problem:
Calculate the transient currents within the conductors.

Solution:
The resistance of one conductor can be calculated as R_cond = l / (g · S), where
   S = πr² - cross-section area of conductor,
   r - radius of conductor,
   l - length of the line.
R_cond = 1 / (56·10⁶ · (π·0.0001²)) = 0.5684 Ohm.

The resistance of both conductors is R = 2·R_cond = 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 H

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.

Results:

See the TEMagn2.pbm problem in the Examples folder.