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Charged Spheres +quadratic equation

  1. May 21, 2009 #1
    1. The problem statement, all variables and given/known data

    Two small, positively charged spheres have a combined charge of 14.0 × 10-5 C. If each sphere is repelled from the other by an electrostatic force of 0.9 N when the spheres are 1.7 m apart, what is the charge (in Coulombs) on the sphere with the smaller charge?

    2. Relevant equations

    (-b +/- sqt (b^2 - 4ac))/2a
    F = kq1q2/d^2
    q2 = 14 x 10^-5 - q1 --> substitute for q2 in above equation

    3. The attempt at a solution

    I solved the quadratic equation to get 2.22 x 10^-6 and 1.38 x 10^-4 .. neither answer is correct. Help?
     
  2. jcsd
  3. May 21, 2009 #2

    tiny-tim

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    Hi Shatzkinator! :wink:

    Show us your full calculations, and then we can see what went wrong, and we'll know how to help! :smile:
     
  4. May 21, 2009 #3
    0.9 = (8.99 x 10^9)q1 (14 x 10^-5 - q1)/ 1.7^2
    2.6 = 1.26 x 10^6 q1 - 8.99 x10^9 q1^2
    -8.99 x10^9 q1^2 + 1.26 x 10^6 q1 - 2.6 = 0

    quadratic..

    -1.26 x 10^6 + sqt ((1.26 x 10^6)^2 - 4(- 8.99^9)(-2.6)) / 2(-8.99^9) = 2.22 x 10^6

    the subtraction root from same equation = 1.38 x10^-4
     
  5. May 21, 2009 #4

    tiny-tim

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    Hi Shatzkinator! :smile:

    (try using the X2 tag just above the Reply box :wink:)
    hmm … looks ok, but there must be a mistake somewhere …

    the two solutions have to add up to 14 x 10-5 C
     
  6. May 21, 2009 #5
    i checked over calculations and everything... really stumped

    thkz for the 103 tip
     
  7. May 21, 2009 #6

    tiny-tim

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    I make the smaller charge nearer 1.8 x 10-6

    it's very much smaller than the other one …

    maybe you're rounding off too much?
     
  8. May 21, 2009 #7
    1.8 x 10-6 is incorrect as well :(

    my answer is 2.22 x 10^-6 not 6
    both are incorrect anyways
     
  9. May 21, 2009 #8

    gabbagabbahey

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    I get [itex]2.10\times10^{-6}\text{C}[/itex]. Try not rounding any of your numbers off until the very end of your calculations.
     
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