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Charge carrier drift velocity of wire

  1. Jan 16, 2017 #1
    1. The problem statement, all variables and given/known data
    1.JPG

    2. Relevant equations


    3. The attempt at a solution

    Current is I = nqvA so drift velocity V is: V = I/nqA

    Drift velocity for x is: Vx = I/nqA

    Drift velocity for y is: Vy = 2I/nqA

    So the ratio of Vx : Vy should be 2:1 since Vy is equal to 2 lots of Vx?? (but correct answer is B)
     
  2. jcsd
  3. Jan 16, 2017 #2

    gneill

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    Staff: Mentor

    You may want to rethink your logic there.

    Edit: My mistake. I presumed that their table presented the ratios as ##V_y:V_x##, but looking again at the text I see that it's the other way around. So the book's suggested answer is incorrect as you found.

    Edit2: I retract my retraction! See later postings.
     
    Last edited: Jan 16, 2017
  4. Jan 16, 2017 #3
    Nothing seems wrong with your calculation. Answer should be 2:1. But books sometimes give wrong answers.
     
  5. Jan 16, 2017 #4
    I've done this question a few times now and ended up with the same answer, but the question is from an official exam paper in the UK so I don't believe there's been a mistake.

    FYI, here's what the mark scheme says:

    1.JPG

    How can it still be B?
     
  6. Jan 16, 2017 #5

    gneill

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    Staff: Mentor

    I'm retracting my edit from before. Clearly the coffee isn't working this morning :smile:

    If the cross sectional area is halved the velocity doubles. So Vy is twice Vx as you originally pointed out:
    So ##V_y## is twice the size of ##V_x##. That makes the ratio ##V_x:V_y = 1:2## which is indeed answer B.
     
  7. Jan 16, 2017 #6
    Indeed. Vy/2=Vx , so Vx: Vy should be 1:2 because then Vy÷2=1.
     
  8. Jan 16, 2017 #7

    Vx = I/nqA

    and

    Vy = 2[I/nqA] = 2Vx

    so doesn't that mean that for every 1 part of Vx we have half a part of Vy? So that 2 parts of Vx gives 1 part of Vy so the ratio is still C, 2:1?? Argh!
     
  9. Jan 16, 2017 #8

    gneill

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    Staff: Mentor

    Pick a value for the magnitude of Vx, say 1. What value would you assign to Vy using your expressions?
     
  10. Jan 16, 2017 #9
    2Vx=Vy. So , if the value of Vx is 1, value of Vy should be 2 right?
     
  11. Jan 16, 2017 #10

    gneill

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    Staff: Mentor

    Right. So, Vx = 1, Vy = 2. What's Vx:Vy?
     
  12. Jan 16, 2017 #11
    Then Vx:Vy should be 1:2
     
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