Coulomb's Law in Vector Form

Two identical conducting small spheres are placed with their centres $0.3 \mathrm{m}$ apart. One is given a charge of $12.0 \mathrm{nC}$ and the other a charge of $-18.0 \mathrm{nC}$.

(a) Find the electric force exerted by one sphere on the other?

(b) If the spheres are connected by a conducting wire, find the electric force between the two after they attain equilibrium.

A particle of mass $m$ carrying a charge $-q_1$ starts moving around a fixed charge $+q_2$ along a circular path of radius $r$. Find the time period of revolution $T$ of charge $-q_1$.

Two particles $A$ and $B$ having charges $8\times {10}^{-6 }\mathrm{C}$ and $-2\times {10}^{-6} \mathrm{C}$, respectively, are held fixed with a separation of $20 \mathrm{c}\mathrm{m}$. Where should a third charged particle be placed so that it does not experience net electric force?

Find the force on a charge $q_1\left(=20 \mathrm{\mu C}\right)$ due to the charge of $q_2\left(=-10 \mathrm{\mu C}\right)$ if the positions of the charges are given as $P\left(1\text{,} -1\text{,} 2\right)$ and $Q\left(-1\text{,} 1\text{,} 1\right)$ (see figure).