Static Charged Particles on a Wire

In the \(xy\)-plane, there is a semi-infinite wire in the shape of the curve \(y = x\).

Particle 1, with mass and charge \(\big(m_1 = 0 \text{ kg}, q_1 = +10^{-4} \text{ C}\big)\), is fixed at the origin.
Particle 2, with mass and charge \(\big(m_2 = 1 \text{ kg}, q_2 = +10^{-4} \text{ C}\big)\), can slide freely along the wire.

There is a uniform downward gravitational acceleration \(g = \SI[per-mode=symbol]{10}{\meter\per\second\squared}\).
The Coulomb constant is \(k_e = \SI[per-mode=symbol]{9e9}{\newton\meter\squared\per\coulomb\squared}\).

If Particle 2 is in static equilibrium, what is the \(x\)-coordinate of its position (in meters, to 2 decimal places)?


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