Question

Two point charges are 5 m apart and their
combined charge is 100 uC. If one repels
the other with a force of 0.9 N. Calculate
their values.

Answer 1

$$q_1 + q_2 = 100\cdot 10^{-6} C = 10^{-4} C$$

On the other hand

$$F = \frac{kq_1 q_2}{r^2}$$

with k = 9 10⁹ N m²/C². The charges repel, so their values have the same sign. Hence

$$\bigg\{\begin{matrix} q_1 + q_2 & = & 10^{-4} C \\ q_1 q_2 & = & Fr^2/k = 25 \cdot 10^{-10} C^2 \end{matrix}$$

$$(10^{-4} C - q_1) q_1 = 2.5 \cdot 10^{-9} C$$ $$q_1^2 -10^{-4} C \cdot q_1 + 2.5\cdot 10^{-9} C^2 = 0$$ $$q_1 = \frac{1}{2} \bigg( 10^{-4} \pm \sqrt{10^{-8} - 4\cdot 2.5 \cdot 10^{-9}}\bigg) C = 5 \cdot 10^{-5} C$$ $$q_2 = 5\cdot 10^{-5} C$$