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Physics Question Concerning Coulomb's Law

  1. Jun 24, 2015 #1
    1.An electric charge q1 (-e) is located at the origin. A second electric charge q2 (-4e) is located at a distance d from the origin on the x-axis. A third charge q3 (+e) is located a distance x, which is less than d, on the x-axis between q1 and q2. In terms of d, what is the distance x where the net electric force is zero?

    2. I just need a pretty thorough explanation. Not a broken stream of steps.


    F = F1 - F2
    F = 0
    then
    F1 = F2
    kq1q3 / x^2 = kq2q3 / (d-x)^2
    q1 / x^2 = q2 / (d-x)^2
    (d-x)^2 - (q2/q1)x^2 = 0
    .....

    I've made it as far as this and then asked for help on another site. Someone responded with the following:

    F = F1 - F2 [forces are opposite]
    F = 0
    then
    F1 = F2
    kq1q3 / x^2 = kq2q3 / (d-x)^2
    q1 / x^2 = q2 / (d-x)^2
    (d-x)^2 - (q2/q1)x^2 = 0
    (1-q2/q1)x^2 -2dx + d^2 = 0
    -3x^2 -2dx + d^2 = 0
    x = [2d +- (4d^2 - 12d^2)^1/2] / (-6)
    x = d/3

    I have no clue what he/she did after line 9 (-3x^2 -2dx+d^2 = 0).
     
  2. jcsd
  3. Jun 24, 2015 #2

    haruspex

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    She just applied the standard formula for solving a quadratic.
     
  4. Jun 24, 2015 #3
    I figured it out. Thanks.
     
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