anonymous
  • anonymous
Two small nonconducting spheres have a total charge of 90.0 micro Coulombs. (a) When placed 1.16 m apart, the force each exerts on the other is 12.0 N and is repulsive. What is the charge on each? (b) What if the force were attractive? r = 1.16m F = 12.0 N k = (F x r^2)/(Q1 x k) = Q2, (F x r^2)/(Q2 x k) = Q1 I know that I'm supposed to find Q1 and Q2, but I can only find one in terms of the other. I have Q2 = (1.796 x 10^(-9) C^2)/Q1, but that's as far as I can get. Any pointers?
Physics
katieb
  • katieb
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anonymous
  • anonymous
k = [8.99 \times 10^{9} N \times m ^{2}/C ^{2}\]
anonymous
  • anonymous
\[Q_1 + Q_2 = Q_{tot}\] \[F_{el} = {{k Q_1Q_2} \over {d^2}}\] \[Q_1 = {d^2 F_{el} \over k Q_2}\] \[{d^2 F_{el} \over {k Q_2}} + Q_2 = Q_{tot}\] Multiplying by Q2, \[Q_2 ^2 + ({d^2 F_{el} \over k})Q_2 - Q_{tot} = 0\] \[\Delta = ({d^2.F_{el} \over k})^2 + 4Q_{tot}\] \[Q_2 = {{({d^2F_{el} \over k}) \pm \sqrt{\Delta}} \over 2}\] There's gonna be a lot of work when really substituting the values...

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