Answer to Question #229133 in Physics for Mosses07

Question

Two charged particles 3.0 m apart exert on each other an attractive electric force of magnitude 8.0 × 10−3 N. If the charge on the two particles sums to 6.4 μC, what is the charge on each particle?

Answer 1

Assume that

$|q_1|+|q_2|=6.4\cdot10^{-6}\ (\mu C)$

$F=k\frac{q_1(6.4\cdot10^{-6}-q_1)}{r^2}\to q_1^2-6.4\cdot10^{-6}q_1+8\cdot10^{-12}=0$

So, we have

$q_1\approx-1.7\ (\mu C) \ \ or \ \ -4.7\ (\mu C)$ and

$q_2\approx4.7\ (\mu C) \ \ or \ \ 1.7\ (\mu C)$ respectively.