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Relativistic invaraiance of a simple electrodynamic quantity

  1. Jan 11, 2008 #1
    1. The problem statement, all variables and given/known data
    Under what conditions is the quantity [tex]E^2+B^2[/tex] relativistically invariant?


    2. Relevant equations
    [tex]E\cdot B[/tex] and [tex]E^2-c^2B^2[/tex] are invariant.

    (Also Lorentz transformation laws for E and B which I won't type here.)

    3. The attempt at a solution

    I think you can just subtract multiples [tex]E^2-c^2B^2[/tex] from the given quantity to show that [tex]E^2[/tex] and [tex]B^2[/tex] must also be separately invariant if the given quantity is invariant, which I think happens only if E and B are both zero. But I have been told this is wrong by someone.
     
  2. jcsd
  3. Jan 11, 2008 #2
    (Technical point: You may set c=1 in the above expressions.)
     
  4. Jan 13, 2008 #3

    pam

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    I don't think there are any such conditions, except if each is zero.
     
  5. Jan 13, 2008 #4

    olgranpappy

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    E^2 + B^2 is not invariant in general since it is the energy-density of the field and thus transforms as the 00 component of a rank 2 tensor... but... how about rotations?
     
  6. Jan 14, 2008 #5

    pam

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    It is invariant under rotations.
     
  7. Jan 14, 2008 #6

    olgranpappy

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