Closest Approach

There are two identical particles (mass = \(1 \text{ kg}\), charge = \(+10^{-4} \text{ C}\)) positioned on the \(x\)-axis. Both charges are free to move.

Particle 1 is initially at \((x = -1 \text{ m})\) with a speed of \(10 \text{ m/s}\) in the \(+x\) direction.

Particle 2 is initially at rest at \((x = 0 \text{ m})\).

In meters, to 3 decimal places, what is the minimum distance that ever separates the two particles?

Note: The Coulomb constant is \(9 \times 10^{9} \text{ N m}^{2} / \text{ C}^{2}\)

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