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Slab Beam of electrons through Neutralising Ions

  1. Dec 19, 2014 #1
    1. The problem statement, all variables and given/known data
    A slab beam of electrons of thickness a, width w >> a, charge density
    (-ρb ), (Take ρb to be positive.) and velocity vbez passes through a channel of
    neutralizing ions with charge density f*ρb where f is some number between zero and one
    (all parameters given above apply in the "lab" frame).
    1. Calculate the electric and magnetic fields produced by this combination of charges and currents in the region y << w / 2 .
    2. Find f such that there is no net force on any electron in the beam.
    2. Relevant equations
    F
    = q(E + v x B)



    3. The attempt at a solution
    I have an idea as how to begin. But I am not very sure about it.

    At any instant of time the new current flowing is given by (ρb - f *ρb)*w*a*vb. If this is the current, then the magnetic field is given by Biot Savarts law (μo/4π)*I/2R ? I just dont get this .

    Can anybody guide me on how to start ?
     
  2. jcsd
  3. Dec 21, 2014 #2

    mfb

    User Avatar
    2016 Award

    Staff: Mentor

    I'm not sure what "channel of neutralizing ions" means, but I don't think those ions move in our lab frame.
    How did you apply Biot-Savart to your disk of electrons?
     
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