Right now I'm taking an introductory E&M class that uses Purcell's book "Electricity and Magnetism." The chapter we're covering focuses on deriving the Lorentz force law for moving charges using SR arguments. This is confusing because we've never covered SR before, so I have a lot of difficulty going through the appropriate transformations and understanding what's going on. One problem that is troubling me a lot goes like this: 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? This is totally counterintuitive to me, and if someone could explain it for me I would really appreciate it.