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Pair of moving charged particles

  1. Feb 7, 2012 #1
    A positron and an electron are simultaneously fired from paralle particle accelerators a distance d apart, with equal velocity v.

    One calculation says that each one will, being a moving charged particle, induce a magnetic field
    [tex]
    B=\frac{\mu_0 q v}{4\pi d^2}
    [/tex]
    and since the other is moving in that field, it experiences a force
    [tex]
    F=q v B = \frac{mu_0 q^2 v^2}{q\pi d^2}
    [/tex]
    As well as an effect from the electric field, but that's not a problem.

    The other calculation says that if I transform to the coordinate frame of the moving particles, they are not moving, and thus there is no force due to magnetic interactions (just the electrostatic one).

    I know that I can use a Lorentz transformation to convert the two fields without issue; I'm just not sure what happens with the interaction.

    ALSO: could someone refresh me on the latex tag?
     
    Last edited: Feb 7, 2012
  2. jcsd
  3. Feb 7, 2012 #2

    clem

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    Science Advisor

    Put tex in sqaure brackets before and /tex in sq. brackets after.
    Use quote to see the latex file below:
    [tex]B=\frac{\mu_0 q v}{4\pi d^2}[/tex]
     
  4. Feb 7, 2012 #3

    clem

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    Science Advisor

    [tex]{\bf F}=\frac{d{\bf p'}}{dt}
    =\frac{qq'[{\bf r}+{\bf v'\times(v\times r)}]}
    {\gamma_v^2[{\bf r}^2-({\bf v\times r)^2}]^{\frac{3}{2}}}.[/tex]
     
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