= 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 $d\mathbf F=I_2d\boldsymbol\ell\times\mathbf B_1$. Hence for equal currents,
$$
\boxed{\frac{|\mathbf F|}{\ell}=\frac{\mu_0I^2}{2\pi d},\qquad\text{attractive for parallel currents}.}
$$
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.
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