Transverse oscillation of the middle of three parallel currents (source code)

= Transverse oscillation of the middle of three parallel currents
{title2=$\Omega^2=\mu_0I^2/(\pi\mu_m d^2)$}

Two fixed outer wires at $x=\pm d$ attract a middle wire carrying the same <electric current> $I$. If the middle wire is displaced in the perpendicular direction $y$, the net magnetic <force> per unit length is $-\mu_0I^2y/[\pi(d^2+y^2)]$. For $|y|\ll d$, the wire's linear <mass density> $\mu_m$ gives the displayed <simple harmonic motion> <frequency>. Motion towards either outer wire in the original plane is unstable. Gravity must be absent from or balanced in the oscillation direction.