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Lorentz Transform of a radial & longitudinal dependent magnetic field

  1. Aug 5, 2014 #1
    Basically I am trying to lorentz transform the magnetic field along θ of a bunch particles which have a gaussian distribution to the radial electric field. However the magnetic field in θ is dependent on the longitiudinal distribution.
    Now initially i thought we would just use the standard LT,

    s'=/gamma (s-βct).
    Now someone suggested to me that infact the transform will be non trivial when a longitudinal dependent radial field is perpendicular to the boost axis.
    Can someone suggest some literature that would point me in the right direction?

    Just for reference the field follows as,

    B_{\theta}=Const \times r^(-1/2)e^{-r^{2}/2*sigma_{r}^{2}} e^{-s^{2}/2\sigma_{s}^{2}}

    Sorry i am not sure how to make it latex
    Last edited: Aug 5, 2014
  2. jcsd
  3. Aug 5, 2014 #2


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    Science Advisor

    You have to Lorentz transform the B vector also. This is described in advanced EM books.
  4. Aug 5, 2014 #3


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    Science Advisor
    Gold Member

    Put a double-dollar before and after
    $$B_{\theta}=Const \times r^(-1/2)e^{-r^{2}/2*sigma_{r}^{2}} e^{-s^{2}/2\sigma_{s}^{2}}$$
    Then correct the errors
    $$B_{\theta}=\mbox{Const} \times r^{-1/2}e^{-r^{2}/2 \sigma_{r}^{2}} e^{-s^{2}/2\sigma_{s}^{2}}$$
    ...if that's what you meant.
  5. Aug 5, 2014 #4


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    Staff: Mentor

    Maybe this will help:


    which presents the Lorentz transformation for E and B fields. To see the derivation, you have to work backwards through the preceding pages.
  6. Aug 6, 2014 #5
    Ok thanks.. I'll have a look through
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