Answer to Question #300714 in Physics for Suki

Question

Two identical tiny metal balls have charges Q1 and Q2. The repulsive force one exerts on the other when they are 25 cm apart is 7.33 x 10^-4 N. After the balls are touched together and then separated again to 25 cm, the repulsive force is found to be 9.67 x 10^-4 N. What are the charges of Q1 and Q2

Answer 1

Given:

$d=0.25\:\rm m$

$F_1=7.33*10^{-4}\:\rm N$

$F_2=9.67*10^{-4}\:\rm N$

The Coulomb's law says

$$F_1=k\frac{Q_1Q_2}{d^2}$$

$$F_2=k\frac{((Q_1+Q_2)/2)^2}{d^2}$$

Hence

$$Q_1Q_2=5.09*10^{-15}$$

$$Q_1+Q_2=1.64*10^{-7}$$

Roots:

$$Q_1=4.15*10^{-8}\:\rm C,\quad Q_2=1.22*10^{-7}\:\rm C$$