Charged Spheres +quadratic equation

[Shatzkinator]

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?

 

[tiny-tim]

Hi Shatzkinator!

Show us your full calculations, and then we can see what went wrong, and we'll know how to help!

 

[Shatzkinator]

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

 

[tiny-tim]

Hi Shatzkinator!

(try using the X² tag just above the Reply box )

… -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

 

[Shatzkinator]

i checked over calculations and everything... really stumped

thkz for the 10³ tip

 

[tiny-tim]

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?

 

[Shatzkinator]

1.8 x 10^-6 is incorrect as well :(

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

 

[gabbagabbahey]

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