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Finding the drift speed of a conduction electrons

  1. Nov 30, 2016 #1
    1. The problem statement, all variables and given/known data
    The figure shows wire section 1 of diameter 4R and wire section 2 of diameter 2R, connected by a tapered section. The wire is copper and carries a current. Assume that the current is uniformly distributed across any cross-sectional area through the wire's width. The electric potential change V along the length L = 1.95 m shown in section 2 is 13.5 µV. The number of charge carriers per unit volume is 8.49x10^28 m-3. What is the drift speed of the conduction electrons in section 1?

    hrw7_26-28.gif

    2. Relevant equations
    v = j/nq
    j=E/p = v/pL

    3. The attempt at a solution
    I got J2 using the provided v2 and p ( of copper = 1.72e-8) and the L2
    J2 = (13.5e-6)/(1.72e-8)(1.95) = 402.5 A/m^2
    Then I used the relation between the two sections > J1A1 = J2A2 >>> J1(0.25Pi 4^2 ) = J2(0.25Pi 2^2) >>> j1 = 100.625 A/m^2
    The drift speed of sec 1 would be >>> V1 = J1 / nq = 100.625/(8.49e28)(1.6e-19) = 7.41e-9 m/s ( which was a wrong answer ) what is my mistake ?
     
    Last edited: Nov 30, 2016
  2. jcsd
  3. Nov 30, 2016 #2

    TSny

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    I don't see any errors. Be sure that you are using the values for n and ρ from your textbook rather than from the internet. The values could vary a little depending on the source of information.
     
  4. Nov 30, 2016 #3
    I double checked my p and n , they are correct ( from the book (copper = 1.72e-8 ) , n from the question itself = 8.49x10^28 ) , but it's still telling me that my answer is wrong :(
     
  5. Nov 30, 2016 #4

    TSny

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    I still can't find any error in your calculation. Maybe we're overlooking something that someone else will catch.
     
  6. Nov 30, 2016 #5
    Any one ? :)
     
  7. Nov 30, 2016 #6
    I am not real familiar with this kind of problem, but the math looked right. I did find an example on Wiki (under "Drift Velocity"), and because of the negative charge of an electron, the result came out to be negative. That's the only possibility I can come up with.
     
  8. Nov 30, 2016 #7

    TSny

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    That's a thought. But speed is the magnitude of velocity, so I would think the answer should be positive. Anyway, thanks for the input, Tom.
     
  9. Nov 30, 2016 #8
    Yep, good point.
     
  10. Nov 30, 2016 #9

    ehild

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    Maybe, they meant mV instead of μV. It was a wire almost 2 m long!
     
  11. Nov 30, 2016 #10

    TSny

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    Yes, could be. I had noticed the current density and drift speed were coming out very small. For j = 400 A/m2 and a wire of cross-sectional area 0.5 mm2, the current is only 0.20 mA.
     
  12. Nov 30, 2016 #11
    I get your point , but this is how the question is :D
    I think that I won't be able to solve it ....
     
  13. Nov 30, 2016 #12

    ehild

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    Yes, the set-up and data for such a practically usual problem should be "real" , with a common voltage source and voltage measurable with a common voltmeter, multimeter. The smallest range of a common multimeter is 100-200 mV.
    @Omar FTM Your solution is correct. It is quite possible that it was a misprint in the text of the problem.
     
  14. Nov 30, 2016 #13
    Tried answering using V as mV instead of micro V , still wrong :(
     
  15. Nov 30, 2016 #14

    ehild

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    It is also possible that the problem writers made some mistake. It happens quite often.
     
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