Opposite charges attract

Electricity and Magnetism Level 4

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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