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Electron movement in conductors

  1. Apr 7, 2016 #1
    This is not a normal problem help topic. The difficulty I've encountered is in understanding an alternative solution.

    1. The problem statement, all variables and given/known data

    In a real conductor, electrons (with mass m), conducted by external electric fields, constantly collide with defects and impurities within the conductor. The average effect of those collisions is similar to a viscosity force ƒ= -mv/τ (ƒ and v have vector hats), where τ is a constant parameter, named collision time.
    1. Write the second law of dynamics that helps finding the speed of an electron. Ignore the interactions between electrons.
    2. Consider that E(t) = E0 sinωt (E and E0 have vector hats), find the expression for the speed of an electron. Note: it's convenient to use the complex form E(t) = E0 eiωt. You can use e = cosθ +i sinθ.

    ....(there are other tasks, but they are rather easy)
    2. Relevant equations
    ma +mv/τ = qE0 sinωt (a, v, E do not have vector hats)

    ma= -mv/τ - qE0 eiωt (a, v, E are vectors)

    3. The attempt at a solution
    I can solve the first differential equation (that is the equation I have derived) the classical way (find homogeneous and particular solutions). Tough, in the key, they write the equation in the second form and then they get the next equation:

    iωmv= -mv/τ - qE0 (v, E are vectors)

    What is the explanation for their equation. I just can't get it.
     
  2. jcsd
  3. Apr 8, 2016 #2
    If you solve your above equation for velocity, then you get a function that doesn't change with time. How can you have an acceleration if your velocity is constant with respect to time?
     
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