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Position of third charged particle

  1. Oct 29, 2015 #1
    1. The problem statement, all variables and given/known data
    Two particles are separated by a distance d, Particle A has charge +Q and Particle B has charge +3Q. At what distance from particle A along the line connecting particles A and B would you place a third charged particle such that no net electrostatic force acts on it ?

    2. Relevant equations
    F = kq1q2 / r^2

    3. The attempt at a solution
    Since there is no net electrostatic force on the third particle, the force from Particle A to C, and force from Particle B to C must be equal.

    So I set up the equation
    k(Q) / x^2 = k(3Q) / (d-x)^2

    and solved for x using the quadratic formula.

    I got

    x = .366d

    However, the answer is d/9, which is x = .111d

    Can anyone help me ? Thank you
     
  2. jcsd
  3. Oct 29, 2015 #2

    Mister T

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    I get the same answer as you. The value can't be a rational fraction of the separation distance.

    Note that they don't define d in the statement of the problem, yet they state their answer in terms of d. That's a clue right there that there's something amiss. Perhaps a typo!
     
  4. Oct 29, 2015 #3

    haruspex

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    I also agree with .366, but d is given.

    The author seems to have made two errors:
    Taken distance as inversely proportional to square of force, instead of the other way around;
    Taken the ratio of the two distances instead of the ratio of the shorter distance to the total distance.
    Very sloppy.
     
  5. Oct 29, 2015 #4

    Mister T

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    Oh, yeah, so it is. How'd I miss that?
     
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