An incorrect universe

Electricity and Magnetism Level 5

In one imaginary universe two charges \(q_1\) and \(q_2\), both of mass 1 g, obey the following inverse cube law instead of Coulomb's law

\[\large{ \vec{F} = k_e\frac{q_1q_2 }{|r_{21}|^3} } \hat{r_{21}} \]

In this universe, the two charges \(q_1 = 1\mu C\) and \(q_2=-1\mu C\) are placed at \(-1\) m and \(1\) m on the x-axis, respectively. The charges are released from rest at \(t=0\). Find the time \(\tau\) in seconds at which they collide.

Assumptions and Details

  • \(K_e = 9\times10^9 \frac{m^2}{F} \)

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