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Current density and drift velocity

  1. Oct 9, 2012 #1
    1. The problem statement, all variables and given/known data
    1. A copper wire 2 mm in diameter carries a 4 A current. Determine the current density in the wire, drift velocity of the electrons and the mean time between collisions. Assume that each copper atom contributes one free electron. Hint: you may need some additional parameters of copper to solve this problem.


    2. Relevant equations
    A) For current density: J = I/A
    We know: A = ∏r2 m2

    B) Drift velocity: I = nqVdA . thus Vd = I / (nqA)
    We know: n = density/mass atom, or (8.95g/cm3 X 106 cm3/m3) / 1.05565 X 10-22g/atom = 8.478 X 1028 atoms/m3
    q = 1.602 X 10-19 C

    C) σ = (nqτ2)/me, thus τ = σme / nq2
    and σ = 1/p, p being resistivity, and resistivity for copper is 1.7 X 10-8 ohm*m

    3. The attempt at a solution
    A) ∏*0.0022m2 = 1.2265 X 10-5 m2
    4 / 1.2265 X 10-5 = 318,309.89 A

    B) Simply plug in the numbers: Vd = 4A / (8.478 X 1028/m3 * 1.602 X 10-19 C * 1.2265 X 10-5 m2 = 2.4012 X 10 -5 m/s

    C) For C, I have no clue in which direction to go, I've browsed through my book but can't find any relevant formula

    Any help for letter C would be appreciated, and also if you can check if what I did in A and B makes sense? Thank you!

    Edit: I found something in the book, would the formula on C make sense?
     
    Last edited: Oct 9, 2012
  2. jcsd
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