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An Ion passing through an electric and magnetic field

  1. Mar 15, 2009 #1
    1. The problem statement, all variables and given/known data
    A singly charged proton ion of 7 Li has a mass of 1.16E-26 kg. Starting from rest it is accelerated in the positive x-direction through a potential difference of 165 kV.
    The ion then enters a uniform magnetic field that has magnitude 0.325 T and is directed in the negative z-direction.

    (a) What is the speed of the ion when it enters the magnetic field?
    (b) What is the radius of the ion's circular path in the magnetic field?
    (c) In which plane will the particle's circular path in the magnetic field lie: x-z, x-y, or y-z?
    (d) What is the speed of the ion after it has turned through 90 degrees in the magnetic field?
    (e) What is the direction of the ion after it has turned through 90 degrees in the magnetic field?

    2. Relevant equations

    eq 1: Fb = q*vxB (charge times velocity cross product B)
    eq 2: Fc = (mv^2)/r

    3. The attempt at a solution

    For part A, I am completely lost as to how to start this problem.
    I found the charge on the ion to be 1.26E-18 C. (7 * 1.609E-19)

    Because you don't know how long the ion is in the electric field (I'm assuming that it is in an electric field?), how can you figure out the velocity? You can figure out the force, but without knowing for how long (in s) or how far (in m) the ion is in / travels in the electric field, how can you find the velocity?

    For part B, once I find the force in part a, i can sub this into the equation F = (mv^2)/r

    Part C, the circular orbit will be perpendicular to the magnetic field if I am not mistaken, meaning that the circular path will lie in the x-y plane.

    Part D, I am not sure how to calculate this? Would you calculate the force divided by 4 us eq 2, and then calculate the velocity using equation 1?

    Part E, The direction would be negative Y if I am not mistaken.

    In advance, I would like to greatly thank anyone for their time / help.
     
  2. jcsd
  3. Mar 16, 2009 #2

    ehild

    User Avatar
    Homework Helper
    Gold Member

    a. Read the text carefully. The Li ion is singly charged. (Its mass number is 7.)

    Remember the definition of electric potential. It is connected to the work done on unit charge. When a particle carrying q charge moves from point A to B and the potential difference is U volts between these points the work done by the electric field is W=q*U. This work will increase the kinetic energy of the particle.

    b. OK.
    c. Right.
    d. The force is always perpendicular to the velocity. Does it change the speed????
    e. No. What is the direction of the force? Draw the orbit of the ion.

    ehild
     
  4. Mar 16, 2009 #3
    Ah thanks a lot, figured it out :)
     
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