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I Electro-magnetic force in special relativity

  1. Jan 25, 2017 #1
    Hi! I came out with a problem last night I wasn't able to solve:

    Let's assume we have a condensator with a uniform electric field E confined in its inside, lying on the z axes. Let's also assume we have a piece of a ferromagnetic object aligned with the condensator at time t = 0, on the y-axes. We now perform a boost along the x-axes for both the object: we will find the electric field shifted by a gamma factor and a new magnetic field along the y-axes. So, in the moving frame, the ferromagnetic object would now feel a force toward the condensator.
    I cannot understand how this is possible being the Lorentz transformation a switch among inetrial frames.
  2. jcsd
  3. Jan 25, 2017 #2


    Staff: Mentor

    Don't forget to transform the ferromagnetic object too!
  4. Jan 26, 2017 #3
    Do I have to transform every magnetic domain? Aren't they negligible?
  5. Jan 26, 2017 #4


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    The force on an object depends on the internal charges and currents. Not only on the EM field. Charge and current densities also need to be properly transformed.
  6. Jan 26, 2017 #5


    Staff: Mentor

    Clearly they are not negligible in this problem.

    The electric field and the magnetic field are components of the electromagnetic field tensor, so what is purely an electric field in one frame becomes both an electric and a magnetic field in another frame. Similarly the magnetization and polarization are components of the magnetization-polarization tensor, so what is purely magnetization in one frame becomes both magnetization and polarization in another frame.
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