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

[FalcorTheDog]

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!

 

[Curious3141]

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.

 

[FalcorTheDog]

This is just what I was looking for. Thanks for the help! Who knew such a seemingly simple problem could be so involved.