D.3.6—Force between parallel wires

Use the force-per-length equation

For two long, straight, parallel wires, $r$ is their perpendicular separation and $\mu_0$ is the permeability of free space. The force acts along the line joining the wires.

Worked example — opposite currents

For $I_1=3.7\,\mathrm{A}$, $I_2=1.6\,\mathrm{A}$ and $r=12\,\mathrm{cm}=0.12\,\mathrm{m}$, $F/L=\mu_0I_1I_2/(2\pi r)=9.9\times10^{-6}\,\mathrm{N\,m^{-1}}$. Opposite current directions mean the wires repel; each force has the same magnitude and opposite direction.

Read attraction and repulsion

Parallel currents in the same direction attract; currents in opposite directions repel. Each wire experiences an equal-magnitude force in the opposite direction. The result follows because each wire lies in the magnetic field produced by the other.

Check the scaling

The force per unit length increases with either current and decreases inversely with separation. Keep $F/L$ units as $\mathrm{N\,m^{-1}}$, equivalently $\mathrm{kg\,s^{-2}}$.

Common trap

Do not reverse same-direction current behaviour, and do not confuse force on a finite length with force per unit length.