# Opposite charges attract

Two point charges $$+q=1~\mu\mbox{C}$$ and $$-q=-1~\mu\mbox{C}$$ with mass $$m=1~\mbox{g}$$ are fixed at the positions $$\pm \vec{r}_{0}$$ with $$|r_{0}|=1~\mbox{m}$$. The charges are released from rest at $$t=0$$. Find the time $$\tau$$ in seconds at which they collide.

Hint: Can you do it without integrating by using Kepler's laws?

Details and assumptions

$k=\frac{1}{4\pi \epsilon_{0}}= 9\times 10^{9}~\mbox{m/F}$

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