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Magnetic field caused by one Electron ?

  1. May 12, 2009 #1

    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 ?

  2. jcsd
  3. May 12, 2009 #2


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    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:


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


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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:


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


    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.

    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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