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:

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