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An electron is shot directly away from a uniformly charged plastic sheet Find σ.

  1. Oct 9, 2009 #1
    1. The problem statement, all variables and given/known data

    In figure (a) below, an electron is shot directly away from a uniformly charged plastic sheet, at speed vs = 2.13 × 10^5 m/s. The sheet is nonconducting, flat, and very large. Figure (b) below gives the electron's vertical velocity component v versus time t until the return to the launch point. What is the sheet's surface charge density?

    There is also a graph that shows Velocity at various times. It is 0 at 7 ps.

    2. Relevant equations

    V = Vo + at

    a = QE/m (Q = 1.609 x 10^-19, m = 9.109 x 10^-31)

    E = σ/ε₀ (ε₀ = 8.85 x 10^-12) -> σ = Eε₀

    3. The attempt at a solution

    So I found acceleration with the first formula, then found E with the second, and found σ with the third. My answer was correct to the second decimal point, but when I did my friends' problems, the answer required me to subtract .4 from both of them to get the correct answer. I'm not sure if I did something wrong or if the homework website was wrong. If its any help, my solution was about 1.5. One of my friends problem had initial velocity of 2.03 x 10^5, all other numbers used were the same (give the same graph), and I calculated 1.4, but the correct answer was a little under 1.

    Thanks for any help.
     
    Last edited: Oct 9, 2009
  2. jcsd
  3. Oct 10, 2009 #2

    Andrew Mason

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    Re: An electron is shot directly away from a uniformly charged plastic sheet...Find σ

    Why not show us what you have done. Also, what units are you working in? An answer of 1.5 means nothing without units.

    Get acceleration from [itex]\Delta v = a\Delta t[/itex] which it looks like you have done. What did you use for [itex]\Delta t[/itex]? The answer I get is:

    a = 5.8e16 m/sec^-2

    The force on the electron is F=ma where m is the mass of the electron. Since this is the coulomb force, qE, you have it correct that:

    E = ma/q where q is the electron's charge.

    I get: E = 9.11e-31 x 5.8e16/1.60e-19 = 3.3e5 N/coulomb

    So [itex]\sigma = E\epsilon_0[/itex] = 3.3e5 x 8.85e-12 = 2.92e-6 coulomb/m^2

    AM
     
  4. Oct 10, 2009 #3
    Re: An electron is shot directly away from a uniformly charged plastic sheet...Find σ

    For change in time I used 7 picoseconds. Velocity changes from 2.13e5 to 0 in 7 ps. And I forget to edit it last night, but it wants the answers in microColoumbs/m^2.

    So i got 2.13e5/ 7e-12 = a, which resulted in a = 3.04e16.

    then I found E, so E = (9.109e-31) * (3.04e16) / (1.609e-19) . E = 172102.9.

    Then σ = Eε₀. so σ = (172102.9) * ( 8.85 e-12) = 1.523e-6 C/m^2, converted to microColoumbs/m^2 is 1.523. Which was correct. 1.5313 is the answer given for my problem on the website.

    For my friends I did, a = 2.03e5 / 7e-12 = 2.9e16

    then E = (9.109e-31) * (2.9e16) / (1.609e-19). E = 164177.1287

    then σ = (164177.1287) * (8.85 e -12) = 1.453e-6 C/m^2 = 1.453 microColoumbs/m^2. But according to the website the correct answer for his is 0.92875.

    So I'm not sure what is causing the discrepancy between the problems of my 2 friends, since my problem worked out fine.

    Thanks again.
     
  5. Oct 11, 2009 #4

    ideasrule

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    Re: An electron is shot directly away from a uniformly charged plastic sheet...Find σ

    That can't possibly be correct. 2.03 is just 5% lower than 2.13, so you'd expect the final answer to be 5% lower than 1.5. 0.929 is way off.
     
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