
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 = πr^{2}  crosssection area of conductor,
r  radius of conductor,
l  length of the line.
R_{cond} = 1 / (56·10^{6} · (π·0.0001^{2})) = 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 = μ_{0}·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 

Results:
See the TEMagn2.pbm problem in the Examples folder.