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Lorentz Force Law

  1. Jun 13, 2016 #1
    1. The problem statement, all variables and given/known data
    A relativistic proton is traveling next to a stream of negatively charged particles that are traveling at the same velocity as the proton. I'm to find the force on the proton by transforming the field from the negative stream to a stationary lab frame.

    2. Relevant equations
    f= q (E+(vxB))

    3. The attempt at a solution
    My question is, when I want to apply the Lorentz force law to find the force on the particle what form of the Lorentz force law do I use? Is it just the equation I have typed up top with the transformed fields plugged in? Or is there a relativistic equation I need to use that I don't know about?

    Thanks for any help.
     
  2. jcsd
  3. Jun 14, 2016 #2
    Welcome to PF!
    There are two ways:
    1. Find the force with the original fields in the moving frame (v=0 thus F = qE ...) [easy], and then transform the force with the relativistic force transformation pattern (formula) [I don't know if you are familiar with it (?)].
    2. Since you seem to be familiar with the fields transformations, that's the easiest way. Transform the fields to the stationary lab frame and calculate the Lorentz force with your formula.

    You get the same result. I have actually done it (long time ago).
     
  4. Jun 14, 2016 #3
    Thank you so much! I'm going to give it a go.
     
  5. Jun 14, 2016 #4
    There is also a 3rd way: calculate all fields and force directly in the lab frame from the beginning.
    [Edit: for that though, you need the formulas for E and B fields of moving charges (or extract those by transforming the fields - cf. 2. [equivallent]). The Lorentz force law of course still holds.]
    Note: Everything is consistent, and your post has an even deeper consequence and meaning for E&M and Special Relativity (that's why I liked it and responded). I will explain later, if you think it's a good idea. But first you have to play around and see what you get.
     
    Last edited: Jun 14, 2016
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