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Where is the net force zero?

  1. Sep 5, 2015 #1
    1. The problem statement, all variables and given/known data
    A charge of 2.21E-9 C is placed at the origin, and a charge of 3.78E-9 C is placed at x = 1.60 m. Find the position at which a third charge of 2.94E-9 C can be placed so that the net electrostatic force on it is zero.

    2. Relevant equations
    Coloumb's law

    3. The attempt at a solution

    All 3 charges are positive, so for the net force to be zero, I believe that the 3rd charge will go in the middle of the other 2 charges.

    +q1 |----1.60m - r -----| +q3 |------ r------| +q2

    Knowns:
    q1 = 2.21 x 10^-9 C
    q2 = 3.78 x 10^-9 C
    q3 = 2.94 x 10^-9 C
    r (between q1 and q2) = 1.60 m

    F1 = F2

    the k and q3 both cancel, leaving me with:

    q1 / (1.60m - r)^2 = q2 / r^2

    I cross multiplied, giving me:

    q1 / q2 = (1.60m - r)^2 / r^2

    This is where I think I'm having a problem. From this point, I found 2 different answers, and both turned out to be wrong: 0.91m and 1.05m (both from q1). Can anyone please help?
     
  2. jcsd
  3. Sep 5, 2015 #2

    HallsofIvy

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    Staff Emeritus
    Science Advisor

    You didn't completely "cross multiply" (and I dislike that term). You did multiply on both sides by the denominator on the left, (160- r)^2. Now multiply on both sides by the denominator on the right to get (q1/q2)r^2= (160- r)^2. Multiply out the square on the right and you a quadratic equation to solve for r.
     
  4. Sep 5, 2015 #3
    So if I multiply the square out on the right, there'll still be an r on the left side.
     
  5. Sep 5, 2015 #4
    My physics professor said to avoid using the quadratic equation in this situation. Where am I going wrong?
     
  6. Sep 6, 2015 #5
    Anyone?
     
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