1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: 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?
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted