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V required so ions passing through the region don't devitate

  1. Oct 22, 2016 #1
    1. The problem statement, all variables and given/known data
    Hydrogen ions moving at various speeds are directed at a region of combined electric and magnetic fields as shown in the diagram below. The electric field is between two parallel plates 10 mm apart with a potential difference V across them, while the magnetic field of flux density 0.1 T is at right angles to the electric field.

    5718ee396b15.jpg

    (a) Calculate the value of V required so that ions of speed 100 m s-1 pass through the region of the two fields without being deviated.

    (b) What is the kinetic energy per ion as they leave the combined fields?

    (1 u = 1.67 * 10-27 kg.)

    Answers: (a) 0.1 V, (b) 8.4 * 10-24 J.

    2. The attempt at a solution
    (a) Can't get it right. I use 0.5 m v2 = e V, where we don't know the mass m. I then tried to use F = B e v = 0.1 * 1.6 * 10-19 * 100 = 1.6 * 10-18 N and then F = m g so m = F / g = 1.6 * 10-18 / 10 = 1.6 * 10-19 kg -- not correct.

    I also used B e v = m v2 / r so m = B e r / v = 0.1 * 1.6 * 10-19 * 0.01 / 100 = 1.6 * 10-24 kg. Also not correct.

    I even thought that since we have hydrogen then its relative atomic mass is 1.008 and so 1.008 * 1.67 * 10-27 = 1.68 * 10-27 kg, also not correct.

    If we plug in 0.1 V (which we need to find) into the first formula we'll get m = 3.2 * 10-24 kg. But I've got no idea how to find it.
     
    Last edited: Oct 22, 2016
  2. jcsd
  3. Oct 22, 2016 #2

    gneill

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    You're plugging in numbers way too soon. Use symbols to start with.

    What condition must hold if the ions are not going to be deflected? Can you write an expression for that?

    Also, you may want to check that the given answer for part (b) is not a typo. Something on the order of 10-4 Joules for a single hydrogen ion would be mighty impressive indeed.
     
  4. Oct 22, 2016 #3
    Maybe you are talking about "An electron moving with velocity v at right angles to a magnetic field of flux density B experiences a force F, which is given by equation F = B e v."? And since the electron experiences this force, in order to move in the same direction it should have F to move + additional F to overcome the magnetic field force. Am I going in the right direction?

    Ah, sorry, it's -24, not -4!
     
  5. Oct 22, 2016 #4

    gneill

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    That's the idea. Only in this case the electron is replaced with a hydrogen ion. What's the charge on a hydrogen ion? And what force is it that's providing the "additional F"? What's an expression for that force?
    :smile:
     
  6. Oct 22, 2016 #5
    Chage on the ion is 1.

    Maybe it's F = 2 B e v?
     
  7. Oct 22, 2016 #6

    gneill

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    1 what?
    Are there two magnetic fields? What is the purpose of the parallel plates?
     
  8. Oct 22, 2016 #7
    Don't know. It only says something like this. Couldn't find a clear number. Some +1 or 1+ everywhere.

    Maybe I need to have: m = 2 B e r / v = 2 * 1.6 * 10-24 = 3.2 * 10-24 kg. Double it, since we have two plates.
     
  9. Oct 22, 2016 #8

    cnh1995

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    What do you think is the purpose of the plates? What forces are acting on the ion when it gets in between the plates?
     
  10. Oct 22, 2016 #9

    gneill

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    What is the charge on an electron? What is the charge on a proton?
     
  11. Oct 22, 2016 #10
    I'd say they remind me the Hall effect -- two plates that create a magnetic field that makes the particle deviate from its path. Don't know whether this applies here.
     
  12. Oct 22, 2016 #11

    gneill

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    Hint: The mass of the particle is irrelevant until you need to talk about kinetic energy. Only magnetic and electric forces are of interest right now.
     
  13. Oct 22, 2016 #12

    gneill

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    Plates do not create a magnetic field. What kind of field do they produce when they are supplied with a potential difference?
     
  14. Oct 22, 2016 #13

    cnh1995

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    You are close.
    Magnetic field will tend to deviate the ion. But if the ion is not supposed to deviate along its way, what will stop it from deviating?
     
  15. Oct 22, 2016 #14
    It's the elementary charge 1.6 * 10-19 C.

    It says on Wikipedia also 1.6 * 10-19 C...
     
  16. Oct 22, 2016 #15

    gneill

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    Right. What's the difference between the two?
     
  17. Oct 22, 2016 #16

    cnh1995

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    You'll soon notice that this value is also not necessary for calculation of V.
     
  18. Oct 22, 2016 #17
    An "electric field" as mentioned in the problem?

    A larger inner force? Like if we have a car which is going on an inclined road and has friction to be overcomed, we need more force.
     
  19. Oct 22, 2016 #18

    cnh1995

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    Yes.
    And who will provide this "inner force" in this problem? Also, should it be larger than the deviating force?
     
  20. Oct 22, 2016 #19
    Hydrogen ions? The plates only create an electric field that makes the ions deviate.

    Well, they are moving with FInitial, then they are experiencing a FE. Field force, so if we want them to continue in the same direction we need FInitial + F = FE. Field.
     
  21. Oct 22, 2016 #20

    cnh1995

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    The ion is not moving with an initial force. It has an initial velocity of 100m/s. To maintain that velocity throughout along its way, the ion must experience zero net force(Newton's 1rst law). How is this achieved when the ion is in between the plates?
     
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