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Liwk
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Homework Statement
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
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?
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