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Violation of Newton 2?

  1. Jan 20, 2010 #1
    An infinite sheet of positive charge lies in the xz-plane of IRF K. A negatively charged particle, q (on the positive y-axis), accelerates downward toward the sheet. The force on the negative particle is at all times (Fx) = (Fz) = 0; (Fy) = (q)(Ey) where (Ey) > 0 is the sheet’s field.
    IRF K’ moves in the positive x-direction of K at speed v. The force transformation from K to K’ is (Fx)’ = (Fx) – (v/c^2)(Fy)(uy) = -(v)(uy)(q)(Ey)/c^2 < 0 ((uy) < 0 is the particle’s y-component of velocity at a given instant). Evidently there is a negative (Fx)’, even though (Fx) = 0.
    According to the acceleration transform, (ax)’ = (ax)(1-v^2/c^2)^3/2/(1-(v)(ux)/c^2) = 0. Thus (Fx)’ < 0 whereas (ax)’ = 0. How can this be?
  2. jcsd
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