What is the time it takes for two charges to meet?

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SUMMARY

The time it takes for two point charges, +Q and -Q, to meet can be derived using the force equation F = (q1*q2)/(4*pi*Eo*r^2) and the relationship between force and acceleration, a = dv/dt. The instantaneous force acting on both charges results in an acceleration that can be calculated by dividing the force by the mass of an electron. To find the time until the charges meet, one must integrate the equations of motion, similar to solving the problem of two identical masses falling towards each other under gravity, potentially utilizing Kepler's third law of motion for a more straightforward approach.

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Homework Statement



I just came up with this seemingly simple problem today, but am having the hardest time solving it:

Two point charges of +Q and -Q lie a distance R from each other. How long will it take for them to meet?

Homework Equations



F = (q1*q2)/(4*pi*Eo*r^2) = ma
a = dv/dt


The Attempt at a Solution



So the instantaneous force on both particles will be: (Q^2)/(4*pi*Eo*r^2) towards one another.

The instantaneous acceleration will be this force divided by the mass of an electron.

From there you can find instantaneous velocity, but I don't know if that helps any.

I just can't figure out what it is I need to integrate. Thanks in advance!
 
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It's tedious, but an almost perfect analogy is with the problem of two identical masses free-falling into each other due to gravity. You can use Kepler's third law of motion to solve that one, or you can solve a second order o.d.e.

Read all about it here : https://www.physicsforums.com/showthread.php?t=119855 and you should be able to adapt that easily to this problem. Only the constants change.
 
This is just what I was looking for. Thanks for the help! Who knew such a seemingly simple problem could be so involved.
 

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