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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
    F=q2/cr2

    a=F/m

    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

    gneill

    User Avatar

    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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