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Charged particle moving relativistically through E field

  1. Nov 20, 2008 #1
    1. The problem statement, all variables and given/known data
    Hi.
    This is the problem I'm trying to solve:

    Consider the trajectory of a charged particle moving with a speed 0.8c in the x direction when it enters a large region in which there is a uniform electric field in the y direction. Show that the x velocity of the particle must actually decrease. What about the x component of momentum?


    2. The attempt at a solution and Relevant Equations
    This one is for discussion mainly. Thus, these are my conclusions:

    When the charged particle enters on the Electric Field, F=qE is perpendicular to the Px-component of the momentum (as it is in y-direction). Thus, there's no force acting on the Px-component of the motion. So, we can use Momentum Conservation Principle.

    This is,


    Pxi= Pxf

    m0Vxi/(1-(Vxi2/c2))1/2 = m0Vxf/(1-(Vxf2+Vy2)/(c2))1/2

    Solving for Vxf,

    Vxf2 = Vxi2(1-(Vy/c)2)​

    Thus if Vy increases, then Vxf decreases.

    Am I correct?
     
    Last edited: Nov 20, 2008
  2. jcsd
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