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Electric forces, net force = zero

  1. Oct 11, 2009 #1
    1. The problem statement, all variables and given/known data
    Three charges lie along the x -axis. The positive charge q1 = 10.0 microC is at x = 1.00 m, and the negative charge q2 = -2.00 microC is at the origin. Where must a positive charge q3 be placed on the x-axis so that the resultant force on it is zero?

    Answer: x = - 0.809 m

    2. Relevant equations
    Columb's Law
    F= k q1 q2
    - - - - - -
    r^2

    k = 8.9875 x 10^9

    3. The attempt at a solution

    Force of 1 acting on 3 = - k q1 q3 / (1 - x)^2
    Force of 2 acting on 3 = k q2 q3 / x^2

    k q2 q3 / x^2 - k q1 q3 / (1 - x)^2 = 0

    k's and q3's cancel out and I get

    q2(1 - x^2) = q1(x^2)
    -2(1 - 2x + x^2) = 10x^2
    -2 + 4x - 2x^2 = 10x^2
    12x^2 - 4x +2 = 0

    x = .167 m

    Needing a bit of help in setting this one up perhaps. No solutions guide is available. Can someone have a more conceptual explanation on how to solve this one?
     
  2. jcsd
  3. Oct 11, 2009 #2
    the problem seems to be a negative sign but I can't see where.
     
    Last edited: Oct 11, 2009
  4. Oct 12, 2009 #3

    rl.bhat

    User Avatar
    Homework Helper

    Since q1 and q2 are having opposite signs, There cannot be a zero field in between them. Bur you can have a zero field out side the two charges and the point is closer to the smaller charge. So rewrite your equation by taking (1 + x) rather than (1 - x).
     
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