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Homework Help: Motion of charged particles

  1. Sep 13, 2012 #1
    1. The problem statement, all variables and given/known data
    This is a problem I was thinking about which I haven't come across in my course.

    Two particles with mass, m, and a positive charge, q, are separated by a distance r0. One particle is unable to move while the other is released and is repelled. Find an equation for the motion of the particle.

    2. Relevant equations


    3. The attempt at a solution

    The problem I have in working out the acceleration at any time here is that r is a time dependent variable.
    Although this seems like a pretty important thing to know how to calculate I end up going around in circles with the maths.
  2. jcsd
  3. Sep 13, 2012 #2
    This is not a simple problem. Even if we assume that the accelerating particle does not radiate energy (which in reality it would do), we still end up with a differential equation. You can get this equation from conservation of total energy. The resultant equation can be integrated, but it will be a complicated expression, where the distance depends on time implicitly.
  4. Sep 13, 2012 #3


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    Staff: Mentor

    You can easily find the velocity at some position r via the change in potential energy that occurs in moving from position ro to new position r. That'll give you some expression:

    ##v = \sqrt{f(r)}##

    where f(r) is a function of r (it's for you so work out!).

    Then make v = dr/dt, shuffle to group the appropriate variables and integrate both sides. That'll leave you with an expression of the form t = g(r), for g some function of r (again, for you to work out).

    As for finding r in terms of t, that is, r(t), well you might find that solving t = g(r) for r is not trivial. Good luck!
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