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Homework Help: Time for two charges to meet?

  1. Nov 2, 2007 #1
    1. The problem statement, all variables and given/known data

    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?

    2. Relevant equations

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

    3. 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!
  2. jcsd
  3. Nov 2, 2007 #2


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    Homework Helper

    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.
  4. Nov 2, 2007 #3
    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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