# Charged particle moving relativistically through E field

1. Nov 20, 2008

### Liwk

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