Answer to Question #189635 in Electricity and Magnetism for carolina

Question

Two charged spheres placed 43 cm apart exert a force of 1.40 × 10^-14 N on each other. If one of the spheres has a charge of 1.68 × 10^-17 C, what is the charge of the other sphere?

Answer 1

The force between two point charges obeys the Coulomb's law:

$$F = k\dfrac{|q_1||q_2|}{r^2}$$

where $q_1 = 1.68\times10^{-17}C,\space q_2$ are the charges of the first and second spheres respectively, $r = 43cm = 0.43m$ is the distance between the spheres, and $k = 9\times 10^9 N\cdot m^2/C^2$ is the Coulomb's constant. Expressing the second charge and substituting $F = 1.4\times 10^{-14}N$ , obtain:

$$q_2 = \dfrac{Fr^2}{kq_1}\\ q_2 = \dfrac{1.4\times 10^{-14}\cdot 0.43^2}{9\times 10^9\cdot 1.68\times 10^{-17}} \approx 1.7\times 10^{-10}C$$

Answer. $1.7\times 10^{-10}C$.