Ampere force law, magnetic force between two wires

This verification example compares the force of attraction between two thin parallel current-currying wires given by Ampere's law and calculated in QuickField using three formulations: magnetostatics, time harmonics and transient magnetics.

Geometry:

Given: I = 1 A - current of each wire; f = 50 Hz - frequency in time harmonics and transient magnetics problems; r = 1 m - distance between the wires.

Task:
Calculate interaction force (per meter of length) between two wires and compare with the value given by the Ampere's force law.

Solution:
Currents are set as linear ones. This way the model completely corresponds to Ampere's formulation.
In the time harmonics problem peak amplitude value of current is set √2·I.
In the transient magnetics current is set via formula I(t) = √2·I · sin(2·180·50·t).

According to the Ampere's law^{*} the force of the interaction between two parallel wires is determined as: F = 2·(μ_{0}/4π) · I·I / r [N/m]