Question

Find the excess (equal in number) of electrons that must be placed on each of two small spheres spaced 3 cm apart with a force of repulsion between the spheres to be ${10}^{-19}N$

Answer 1

Force between the two electrons,
$F=\frac{1}{4\pi {ϵ}_0}\times \frac{\left(ne\right)\left(ne\right)}{d^2}$
or $n^2=\frac{F\times 4\pi {ϵ}_0\times d^2}{e^2}$
$n^2=\frac{{10}^{-19}\times \frac{1}{9\times {10}^9}\times (3\times {10}^{-2}{)}^2}{(1.6\times {10}^{-19}{)}^2}$
$=(625{)}^2$
or $n=625$
$\therefore$ The number of electrons placed on each of the sphere $=625.$