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Special Relativity

  1. Nov 28, 2009 #1
    1. The problem statement, all variables and given/known data
    In a frame S, two identical particles with electric charge q move abreast along lines parallel to the x-axis, a distance r apart and with velocity v. Determine the force in S that each exerts on the other, by use of the force law for a uniformly moving charge.



    I would need a lorentz forc e law in 4 vector notation,

    what is it? Then where do I proceed?


    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Nov 28, 2009 #2

    diazona

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    Homework Helper

    My first thought would be to make a Lorentz transformation into the frame where both particles are at rest.
     
  4. Dec 7, 2009 #3
    We know its just the Coulomb force,

    we have the equation for field of a moving charge:

    [tex]
    e= \frac{Q \bf{r_o}}{\gamma^2 r_o^2 (1-u^2/c^2 sin^2(\theta))^{3/2}}
    [/tex]

    and we can determine the magnetic field in this case,
    [tex]
    cb = \frac{\bf{v} \times \bf{e}}{c}
    [/tex]

    I'm not sure at this point
     
    Last edited: Dec 7, 2009
  5. Dec 7, 2009 #4
    The above equation was obtained by this:

    [tex]
    \bf{e} = \frac{Q}{(cr-\bf{r}\bf{u})^3}\frac{c^2}{\gamma^2}(c\bf{r}-r\bf{u})
    [/tex]

    I'm not sure of I"m on the right track.
     
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