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How long after the decay do ##e^{-}## and ##e^{+}## Collide

  1. Dec 9, 2015 #1
    1. The problem statement, all variables and given/known data
    A particular type of fundamental particle decays by transforming into an electron ##e^{-}## and a positron ##e^{+}##. Suppose the decaying particle is at rest in a uniform magnetic field of magnitude 3.53 mT and the ##e^{-}## and ##e^{+}## move away from the decay point in paths lying in a plane perpendicular to the magnetic field. How long after the decay do the ##e^{-}## and ##e^{+}## collide?

    2. Relevant equations

    3. The attempt at a solution

    The period which is all we need to solve this problem can be found to be ##T=\frac{2\pi m_{e}}{qB}## for this problem. Personally I think these particles would collide at ##t=T## but in the solutions manual it says they collide at ##t=T/2##. This doesn't entirely make sense to me since although both the particles are moving at a speed ##v## they won't have completed the entire rotation at ##T/2## although they will have travelled a total distance ##2\pi r##
     
  2. jcsd
  3. Dec 9, 2015 #2

    haruspex

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    Maybe I'm missing something, but won't they collide after each has gone half way around the circle?
     
  4. Dec 9, 2015 #3
    I understand the path they take now. I assumed that both electrons were traveling in the same direction at the start, in this case it will be T before they collide. But if the angle between the two speeds is 180 then it only takes T/2.
     
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