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Homework Help: Electron speed

  1. May 11, 2008 #1
    1. The problem statement, all variables and given/known data

    The potential between the cathode and the screen of a computer is 12kV. What is the speed of an electron when it reaches the screen if it starts at rest at the cathode?

    3. The attempt at a solution

    First I found that the force that acts on the electron is 1.922E-15 N. I can then find the acceleration, but I need the distance between the cathode and the screen to find the speed.

    Can I use energy conservation? Probably. Gravitational forces can be ignored. (1/2)mv^2 = Epot But what is the the expression for potential energy? Not mgh. Can I simply replace m with charge, g with E and h with the potential?

    1/2)mv^2 = eEU

    ?
     
  2. jcsd
  3. May 11, 2008 #2
    Generally the electric and gravitational potentials will NOT take the same form - good try though. The answer is much simpler - it is contained in the problem statement (hint hint: what are the first 2 words?).
     
  4. May 11, 2008 #3
    The potential. Probably eV then? But why?
     
  5. May 12, 2008 #4
    The idea of replacing mgh with eEh is a bit careless but has some meaning if understood properly: Work done by constant forces is F*s, where F is -mg in the first case and eE in the second case. Since the change of energy equals -work, the analog expression of mgh is actually -eEh. However the electric field is not always uniform, so -Eh must generaly be replaced by Integral(-E*dh)=U
     
    Last edited: May 12, 2008
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