 Magnetic force between neutral wires

A long straight wire carrying current $I_1$ produces field magnitude $B_1={\mu }_0|I_1|/(2\pi d)$ at a parallel wire a distance $d$ away. The magnetic force on a current-carrying wire is $d\mathbf{F}=I_{2}d\mathbf{\ell }\times {\mathbf{B}}_1$. Hence for equal currents,The two forces have equal magnitude and opposite directions. Net electrical neutrality removes a lab-frame external electrostatic force between ideal uniform wires, but does not remove their magnetic interaction.