Question

Two small spheres separated by a distance of 0.3 m have similar charges. How many exceeding electrons must be in each sphere if the magnitude of the repulsive force between them is of 5.5x10-21N?

Answer 1

The Coulomb law states

$$F=k\frac{q_1q_2}{r^2}=k\frac{q^2}{r^2}.$$

The charge of one sphere

$$q=\sqrt{Fr^2/k}$$ $$=\sqrt{5.5\times 10^{-21}\times 0.3^2/9\times 10^9}=2.3\times 10^{-16}\:\rm C.$$

The amount of exceeding electrons

$$N=\frac{q}{e}=\frac{2.3\times 10^{-16}}{1.6\times 10^{-19}}=1466.$$