Opposite charges attract

Two point charges +q=1 μC+q=1~\mu\mbox{C} and q=1 μC-q=-1~\mu\mbox{C} with mass m=1 gm=1~\mbox{g} are fixed at the positions ±r0\pm \vec{r}_{0} with r0=1 m|r_{0}|=1~\mbox{m}. The charges are released from rest at t=0t=0. Find the time τ\tau in seconds at which they collide.

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

Details and assumptions

k=14πϵ0=9×109 m/Fk=\frac{1}{4\pi \epsilon_{0}}= 9\times 10^{9}~\mbox{m/F}

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