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Homework Help: Motion of a hydrogens ions

  1. Dec 16, 2008 #1
    1. The problem statement, all variables and given/known data
    Some hydrogens and deuterium ions are accelerated by a potential difference V. These ions entered then in a region with a magnetic field B orthogonal to their velocity. In the position H and K (along the axis parallel to the velocity) there are two sensors and the distance between them is d. Find the the V you need to make the hydrogen ions go towards H and deuterium towards K


    2. Relevant data
    d=0.8cm
    B=0.4T
    q(e)=1.6*10(-19)
    m(H)=1.67*10^-27
    m(D)=3.34*10^-21Kg


    3. The attempt at a solution
    Velocity of the ions after the acceleration by a potential difference V:
    qV(1)=1/2mv^2+qV(2) ==> v=sqrt[(2qV)/(m)] where m is m(D) or m(H)

    motion of the ions in the magnetic field: circular motion with radius:
    r(D)=v(D)m(D)/qB
    r(H)=v(H)m(H)/qB

    The distance between the two sensors is d, so r(D)-r(H)=d ==> 4qV=dqB ==> V=0,00008V

    Is this right?
     
  2. jcsd
  3. Dec 16, 2008 #2

    Redbelly98

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    Without seeing a figure of the magnetic field region, we can't say.

    By any chance are the ion trajectories 90 degrees, or 1/4, of a full circle?
     
  4. Dec 16, 2008 #3
    It's 1/2 circle
     

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  5. Dec 16, 2008 #4

    Redbelly98

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    Okay, that makes more sense now.

    The distance between H and K is not the difference in radii of the two circles. Can you look at the figure again and see how that distance does relate to the circles?
     
  6. Dec 16, 2008 #5
    Is it the difference between the diameters?
     
  7. Dec 16, 2008 #6

    Redbelly98

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  8. Dec 18, 2008 #7
    Now it works... thanks!
     
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