1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Accelerating Ions through semicircular plates

  1. Jan 27, 2009 #1
    1. The problem statement, all variables and given/known data
    Hey guys, this is from Purcell 3.19
    "Ions are accelerated through a potential difference [tex]V_0[/tex] and then enter the space between the semicylindrical electrodes A and B. Show that an ion will follow the semicircular path of radius [tex]r_0[/tex] if the potentials of the outer and inner electrodes are maintained, respectively, at [tex]2V_0*ln(b/r_0)[/tex] and [tex]2V_0*ln(a/r_0)[/tex]."

    2. Relevant equations

    3. The attempt at a solution
    Well i started with
    [tex]q*V_0 = KE = (mv^2)/2[/tex]
    [tex]V^2 = (2qV_0)/m[/tex]
    which combined with the rotational motion eq
    [tex]E = F/q = (mv^2)/(qr_0) = (2V_0)/r_0[/tex]
    but i can't think of any way to pin down what the field is between the two cylinders.
    just looking at the solution provided it seems like i should integrate the final equation for a variable r from b to r-nought and a to r-nought. I just don't know why. Any way to elucidate this for me?

    Attached Files:

    Last edited: Jan 28, 2009
  2. jcsd
  3. Jan 28, 2009 #2
    Attached a diagram (sorry for the paint) if it helps make it clearer
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook