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Charged Spheres +quadratic equation

  • #1

Homework Statement



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?

Homework Equations



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

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?
 

Answers and Replies

  • #2
tiny-tim
Science Advisor
Homework Helper
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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:
 
  • #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
 
  • #4
tiny-tim
Science Advisor
Homework Helper
25,832
249
Hi Shatzkinator! :smile:

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

the two solutions have to add up to 14 x 10-5 C
 
  • #5
i checked over calculations and everything... really stumped

thkz for the 103 tip
 
  • #6
tiny-tim
Science Advisor
Homework Helper
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249
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?
 
  • #7
1.8 x 10-6 is incorrect as well :(

my answer is 2.22 x 10^-6 not 6
both are incorrect anyways
 
  • #8
gabbagabbahey
Homework Helper
Gold Member
5,002
6
1.8 x 10-6 is incorrect as well :(

my answer is 2.22 x 10^-6 not 6
both are incorrect anyways
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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