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Magnetic Fields and Lorentz force flaw

  1. Feb 5, 2009 #1
    HI all:
    I have one confused question. a infinitely long wire carrying constant direct current is placed in the space. One particle with charge q and velocity v is moving in the magnetic field which is created by current-carrying wire. We know in the lab frame. particle will accelerate in this magnetic field and feel a lorentz force(F=(q/c)(vxB)). Now if we switch from lab reference frame to the rest frame of particle, in this rest frame, particle speed is zero. that means Lorentz force disappear. According F=q[E+1/c(vxB)]. A electrostatic field must appear.
    1) What is origin of this electric field? How does it generate?
    One mentions that positive charge and negative charge density in the wire are different value under different reference frame.
    For a line charge with length L, the electric field E=Q(1/r^2-L^2/2r^4). Because total charge are conserved. The first term is unaffected by choosing different reference frame. For the second term, they show length contraction in different reference frame. That is why they have different positive and negative charge density in the wire under different reference frame.
    In our lab frame, due to constant direct current in the wire, I assume positive charge density is larger than negative charge density.
    2) Why doesn't it generate electric field? that is to say, particle with charge q only feel magnetic force and no coulomb force?
    Does anyone give me detail explanation? thanks a lot
  2. jcsd
  3. Feb 5, 2009 #2


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  4. Feb 6, 2009 #3


    Staff: Mentor

    In short, it comes from length contraction. See http://physics.weber.edu/schroeder/mrr/MRRtalk.html for details.
  5. Mar 11, 2009 #4
    Feynman does a great job with this particular example. See Vol II, 13.6 of the Lectures.
    A similar problem: 2 (+) charges at rest repel each other, but viewed from a moving frame, they also feel a Lorentz B attraction...
    Follow-up: What's different for gravity??
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