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Acceleration of an electron through a uniform electric field

  1. Nov 11, 2007 #1
    Question:
    An electron is accelerated through a uniform electric field of magnitude 2.5x10^2 N/C with an initial speed of 1.2x10^6 m/s parallel to the electric field.

    -----------<---------------
    ------------<--------------
    e- ----------------------->
    ------------<--------------
    -----------<---------------

    a) Calculate the work done on the electron by the field when the electron has travelled 2.5cm in the field.
    b) Calculate the speed of the electron after it has travelled 2.5 cm in the field.

    My attempt:
    For a), I used W=[tex]\epsilon[/tex]q[tex]\Delta[/tex]d
    and I got 1.0x10^-18 J.

    For b), I tried
    W=[tex]\Delta[/tex][tex]E_{K}[/tex]
    =0.5m[tex]v_{2}^{2}[/tex]-0.5m[tex]v_{1}^{2}[/tex]
    After rearranging the equation to solve for [tex]v_{2}[/tex],
    [tex]v_{2}[/tex]=[tex]\sqrt{2W/m}[/tex]+[tex]v_{1}[/tex]
    =2.7x10^6m/s
    for m, I plugged in the mass of an e-.

    However, the answer is supposed to be 1.9x10^6 m/s.
    Can someone please tell me what I'm doing wrong?
     
  2. jcsd
  3. Nov 11, 2007 #2

    Doc Al

    User Avatar

    Staff: Mentor

    This is OK.
    But this is not OK.

    Try this:

    [tex]1/2 m v_f^2 = 1/2 m v_i^2 + W[/tex]
    [tex]v_f^2 = (2/m)(1/2 m v_i^2 + W)[/tex]

    ...and so on.
     
  4. Nov 11, 2007 #3
    Thank you =)
     
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