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Magnetic field caused by one Electron ?

  1. May 12, 2009 #1
    Hi

    I have read Bio-Savar , Amper law (also maxwell) about Magnetic fields

    but all of them had I
    bio-savar :
    B = [tex]\frac{[tex]\mu[/tex]0}{4[tex]\pi[/tex]
    }[/tex] [tex]\frac{ids Sin\theta}{r2}[/tex]

    Amper :
    [tex]\int[/tex] B.ds = Iin [tex]\mu[/tex]0

    but what about a Electron moving in a line path ? how big will be its magnetic field ? it musnt be permenent though



    and what about a Electron spining around itself ? this time it must be permenant but how big what are the vectors ?

    Thanks
     
  2. jcsd
  3. May 12, 2009 #2

    Born2bwire

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    Science Advisor
    Gold Member

    You can still use the Biot-Savart law for a point charge. You just replace the current with the appropriate equivalence. I think the wikipedia article has the equation:

    http://en.wikipedia.org/wiki/Biot-Savart_law

    That's for constant non-relativistic velocity though. I can't remember the equation for an arbitrary path/velocity.
     
  4. May 12, 2009 #3

    jtbell

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    Staff: Mentor

    For a uniformly moving charge, you can calculate the E and B fields by starting with the E field for a stationary charge, and performing a Lorentz transformation:

    http://farside.ph.utexas.edu/teaching/em/lectures/node125.html

    The electron has a fixed intrinsic magnetic dipole moment, but the "spin" that it arises from is quantum-mechanical in nature.

    http://hyperphysics.phy-astr.gsu.edu/Hbase/spin.html

    I'm not sure how much sense it makes to insert this dipole moment into the equations for the field of a magnetic dipole, because of its small size.

    http://scienceworld.wolfram.com/physics/MagneticDipole.html
     
    Last edited: May 12, 2009
  5. May 12, 2009 #4
    I'm pretty sure the moving electron gives you exactly the type of field you get from the infinitesimal current element of Boit-Savart. You can set up a loop anywhere along the axis of symmetry and there will be a rate of increase of electric flux through this loop. The magnetic field integrated around the loop (constant field x 2pi*r) is equal to the increase of electric flux.
     
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