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Speed of Electron in Orbit

  1. Jan 27, 2014 #1
    1. The problem statement, all variables and given/known data

    A 2.70-mm-diameter glass sphere has a charge of + 1.10 nC.

    What speed does an electron need to orbit the sphere 1.50mm above the surface?

    2. Relevant equations

    a = v^2/r -> force = m*v^2/r

    electrostatic force = K*Q1*Q2/distance^2

    therefore:

    m*v^2/r=K*Q1*Q2/distance^2

    3. The attempt at a solution

    (9.10938291 × 10-31 kg)(v^2)/((2.7*10^-3)/2) = 8.99*10^9*(1.60*10^-19)*(1.1*10^-9)/(1.50*10^3)^2

    I get 32282518 m/s which is the incorrect answer. However, I just noticed something. The radius I'm using is half of the sphere, should I be adding the separation distance to the radius as well?
     
  2. jcsd
  3. Jan 27, 2014 #2

    lightgrav

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    yes, the circle's radius is bigger than the glass radius.
     
  4. Jan 27, 2014 #3
    I got an answer of 4.69*10^7 m/s and it still says it's incorrect.
     
  5. Jan 27, 2014 #4

    lightgrav

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    I didn't get that speed. why don't you cancel one of the radius variables, and try the calculation again.
     
  6. Jan 27, 2014 #5
    Here are my values:

    Mass of electron = 9.10938*10^-31 kg
    v = ???
    radius = half of glass sphere plus separation distance = (2.7/2)*10^-3+1.5*10^-3
    K = 8.99*10^9
    Q1 = 1.6*10^-19 (charge of electron in coulombs)
    Q2 = 1.1*10^-9
    distance = 1.5*10^-3

    Now I'm realizing the distance should probably be (2.7/2)*10^-3+1.5*10^-3 also...
     
  7. Jan 27, 2014 #6
    With the change, I'm getting an answer of 2.469*10^7 m/s. Does this look familiar?
     
  8. Jan 27, 2014 #7

    lightgrav

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    I think it rounds up to 24.7 Mm/s ... the E-field has spread more at that distance, so is weaker at the electron.
     
  9. Sep 22, 2016 #8
    Well, this is obviously way too late, but for all of you physics nerds out there here it is.

    Uniformly Charged Sphere Equation:

    E=Q/(e0*4*r^2*pi)

    E=electric field
    Q=charge of sphere 1.1*10^-9 (in this case)
    e0=8.85*10^-12
    r=1.5*10^-3 (in this case)
    pi = pi ;)

    Take that E and plug it into the following Electric Force Equation:

    E=F/q

    E= what you solved for previously
    F=Force that you want to derive
    q=1.6*10^-19 (constant for charge of electron)

    Take that F and plug it into this standard Force Equation:

    F=ma

    F=what you solved for previously
    m=9.11*10^-31
    a=what you want to solve for


    Last, but not least plug the a you solved for into the following Uniform Circular Motion Equation:

    a=v^2/r

    a=what you just solved for
    v=what you want to solve for
    r=1.5*10^-3 (in this case)


    That's it ladies and gents. Physics = MAGIC
     
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