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Homework Help: Potential generated by an ionized plasma between two plates

  1. Dec 4, 2013 #1
    1. The problem statement, all variables and given/known data

    An ionized plasma flows with a velocity v in the z direction, though a rectangular pipe with x, y, z dimensions of w, h, l respectively. The walls at [itex] x=\pm w/2 [/itex] are insulating while the walls at [itex]y=\pm h/2[/itex] are conducting. Lastly there is a magnetic field B in the x direction.

    Find the potential between the conducting walls.

    2. Relevant equations

    Maxwell's equations

    3. The attempt at a solution

    I'm not used to problems with plasmas, but I take it the velocity somewhat similar to current here. I'm not sure what I need to find the potential though, perhaps the electric field between the plates, but then I'm not sure where to find that. I think my main problem is I'm just not sure where to start. Any help would be appreciated.
  2. jcsd
  3. Dec 4, 2013 #2
    Plasma consists of charged particles. Consider one of them, with charge q. It is said to flow with velocity v in the z direction. That means the net force on the particle is zero. But there are a magnetic field and an electric field, both exerting forces on it.
  4. Dec 4, 2013 #3
    Yea that really simplifies things from how I was approaching it. So [itex]F_{mag} = F_{electric}[/itex]
    [tex]EQ=Q(v \times B) [/tex]
    [tex]E=-vB [/tex]
    so then
    [tex]V = hBv[/tex]
  5. Dec 4, 2013 #4
    Not exactly. Rather, it is ##F_e + F_m = 0##. So check the signs in what follows.
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