How this calculator works
A long straight wire creates a magnetic field that acts on the current in a parallel wire. Currents in the same direction attract, and opposite currents repel. The force law is naturally per unit length. Multiplying by a segment length estimates total force only when end effects are negligible, so the parallel sections should be long compared with their separation.
Formula
F/length = mu0 I1 I2/(2 pi d). This page assigns attraction a positive sign and repulsion a negative sign.
Worked example
Currents of 2 A and 3 A, separated by 0.1 m, attract with about 0.000012 N/m. With 1 A in each wire at 1 m separation, force density is about 0.0000002 N/m.
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Frequently asked questions
Which distance should I measure?
Use centre-to-centre separation. Thin-wire assumptions become less suitable when wire radius is comparable with separation.
Why is the output N/m?
For very long wires the interaction is uniform along the wire. The finite-segment total is only an approximation to that local force density.
Is vacuum permeability exactly 4 pi times 10^-7?
In the revised SI it is measured. This page uses the CODATA 2022 value shared by the physics calculators.