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 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 copper atom consists of a copper nucleus surrounded by $29$ electrons. The atomic weight of copper is $63.5 \mathrm{g} {\mathrm{mol}}^{-1}$. Let us now take pieces of copper each weighing $10 \mathrm{g}$. Let one electron from one piece be transferred to another for every $1000$ atoms in a piece.

(a) Find the magnitude of the charge appearing on each piece.

(b) What will be the Coulomb force between the two pieces after the transfer of electrons if they are $10 \mathrm{cm}$ apart? (Avogadro’s number is $6\times {10}^{23} \mathrm{m}\mathrm{o}{\mathrm{l}}^{-1}$).