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Trapping atoms

  1. Mar 23, 2009 #1
    1. The problem statement, all variables and given/known data
    We addrewss a one dimensional system. An atom moves along the x-axis with a kinetic energy K = 0.5*m*v**2. In the range -x0<x<x0 the atom enters the trap, and is affected by a magnetic fiels. The interaction with the magnetic field gives rise to a potential U(x) which we model:

    for abs(x)>= x0, U(x) = U0
    for abs (x) < x0, U(x) = U0*abs(x)/x0

    a) Find the force F(x) on the atom from the magnetic field. Is this force conservative?

    Let us also assume that the atom is charged and also subject to a constant electronic force, F0 acting in the positive x-direction

    b) If the atom has kinetic energy K = 0 at x = 0, how laarge must F0 be in order for the atom to escape? And if the kinetic energy is K = U0/2 at x = 0, how large must F0 then be in order for the atom to escape.
    2. Relevant equations



    3. The attempt at a solution

    a)
    F = -dU/dx

    F = 0 for abs(x) >= x0
    F = U0/x0 for -x0<x<0
    F = -U0/x0 0for 0<x<x0

    The force is conservative for it is only dependent on the position

    b) Here I need some help.
    Is the idea that the force must give the atom larger total energy than u0?
     
    Last edited: Mar 23, 2009
  2. jcsd
  3. Mar 23, 2009 #2

    Redbelly98

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    Not sure if that would be the case or not.

    The way I think about it is, how is the potential modified due to the presence of the constant electrostatic force?
     
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