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Homework Help: Debye Shielding Problem

  1. Aug 25, 2011 #1
    1. The problem statement, all variables and given/known data

    Consider a positive point charge +q, immersed in plasma. Show that the net charge in the Debye shielding cloud exactly cancels the test charge. Assume the ions are fixed and that e*phi <<< kTe.

    2. Relevant equations

    f(u) = A exp [-(1/2*m*u^2 + q*phi)/k_b*T_e]
    u is the x component of velocity

    3. The attempt at a solution

    Really lost on this one. I think I could make a hand waivey argument with Gauss's Law but I don't see where to go on this one.
  2. jcsd
  3. Aug 25, 2011 #2
    You should use the Boltzmann distribution:
    n(\mathbf{x}) = n_{0} \, \exp\left(-\frac{U(\mathbf{x})}{k_{B} T_{e}}\right)
    to give the distribution of electrons. Here, [itex]n(\mathbf{x})[/itex] is the number density of electrons around a point given by the position vector [itex]\mathbf{x}[/itex], [itex]n_{0}[/itex] is their equilibrium density, [itex]U(\mathbf{x})[/itex] is the potential energy of the electrons (the equilibrium density is reached at the part of space where [itex]U = 0[/itex] according to the above formula).

    Think about what is the potential of charged particles in a polarized medium where electric fields might exist. After you answer this question, we can proceed further.
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