Question

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?

Answer 1

k = [8.99 \times 10^{9} N \times m ^{2}/C ^{2}\]

Answer 2

\[Q_1 + Q_2 = Q_{tot}\]
\[F_{el} = {{k Q_1Q_2} \over {d^2}}\]
\[Q_1 = {d^2 F_{el} \over k Q_2}\]
\[{d^2 F_{el} \over {k Q_2}} + Q_2 = Q_{tot}\]
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...