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Radius of object in electric field

  1. Oct 15, 2014 #1
    1. The problem statement, all variables and given/known data

    Two parallel plates with opposite charges are 0.01 m apart and have a potential difference of 100 V. A charged spherical object has 20 excess electrons stays motionless between the plates. If the density of the object is 1000 kg/m^3, what is the radius of the spherical object?

    2. Relevant equations

    E=V/d
    Fq=qE
    Fg=mg
    density=m/Vs
    Vs = 4/3 pi r^3

    3. The attempt at a solution

    I equated the electric force and the gravitational force as they are equal.

    E = 100/0.01=10000 vollts/m

    Therefore, Fq = 20 x 1.602x10^-19 x 10000 = 3.204x10^-14

    Fg=m x 9.81 (I am assuming that I don't need to use the universal law of gravity because I don't know how high the apparatus is off the ground).

    Therefore, Fg=Fq => m x 9.81 = 3.204x10^-14 => m = 3.27 x 10^-15 kg

    density = m/Vs => Vs = m/density = 3.27 x 10^-18

    Vs = 4/3 pi r^3 => r = 0.92x10^-6 meters or 0.92 micro meters.

    However, this answer is wrong.

    Where have I gone wrong?

    Thank you for helping.
     
  2. jcsd
  3. Oct 15, 2014 #2

    ehild

    User Avatar
    Homework Helper
    Gold Member

    I do not see anything wrong in your derivation and result.

    ehild
     
  4. Oct 15, 2014 #3
    I thought so. Must be a mistake with the automated quiz.
     
  5. Oct 15, 2014 #4
    Have you tried 0.9 instead of 0.92? All your given values have only 1 significant digit.
     
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