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Electrostatic equilibrium between 3 styrofoam balls

  1. Feb 5, 2012 #1
    1. The problem statement, all variables and given/known data
    Three identical small Styrofoam balls (m = 1.95 g) are suspended from a fixed point by three nonconducting threads, each with a length of 52.1 cm and with negligible mass. At equilibrium the three balls form an equilateral triangle with sides of 28.3 cm. What is the common charge q carried by each ball?

    2. Relevant equations
    F = (k q1 q2) / r^2
    F = mg
    k = 9 * 10^9

    3. The attempt at a solution
    First I need to find the angle the string makes with the vertical, I start from one of the vertices and imagine a right triangle that connects with the midpoint of the equilateral triangle connecting the 3 balls. Given that I know from the corner of this right triangle will be 30 degrees, and that the adjacent side will be (28.3/2) cm, I calculate the hypotenuse to be 16.339 cm then I use this value to find the angle I want.

    θ = sin^-1 ( 16.339 / 52.1 )
    = 18.2768 degrees with vertical

    Now I can find F tension in the same plane as the electrostatic forces.

    Ft = mg tan 18.2768
    = 6.3179 * 10 ^(-3)

    This is equal in magnitude to the resultant vector of the two opposing electrostatic charges. I take the components of each electrostatic force with 30 degree angles to the resultant.

    resultant = kq^2 cos 30 /r^2 + kq^2 cos 30 / r^2

    6.3179 * 10^(-3) = kq^2 ( cos 30 + cos 30 ) / r^2
    q = 3.3168 * 10^(-7)

    CAPA says this is wrong, and I have no idea where I'm going wrong.

    EDIT: I solved it, it seems I was making a mistake somewhere with the vector part.
    Last edited: Feb 6, 2012
  2. jcsd
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