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·(μ0/4π) · I·I / r [N/m]