Suppose the spheres A and B in Exercise 1.12 have identical sizes.

Distance between the spheres, A and B, r = 0.5 m

Initially, the charge on each sphere, $q=6.5 \times 10^{-7} \mathrm{C}$

When sphere $A$ is touched with an uncharged sphere $C, \frac{q}{2}$ amount of charge from $A$ will transfer to sphere $C$. Hence, charge on each of the spheres, $A$ and $C$, is $\frac{q}{2}$.

When sphere $C$ with charge $\frac{q}{2}$ is brought in contact with sphere $B$ with charge $q$, total charges on the system will divide into two equal halves given as,

$\frac{\frac{q}{2}+q}{2}=\frac{3 q}{4}$

Each sphere will share each half. Hence, charge on each of the spheres, $C$ and $B$, is $\frac{3 q}{4}$.

Force of repulsion between sphere A having charge $\frac{q}{2}$ and sphere B having charge $\frac{3 q}{4}=\frac{\frac{q}{2} \times \frac{3 q}{4}}{4 \pi \in_{0} r^{2}}=\frac{3 q^{2}}{8 \times 4 \pi \in_{0} r^{2}}$

$=9 \times 10^{9} \times \frac{3 \times\left(6.5 \times 10^{-7}\right)^{2}}{8 \times(0.5)^{2}}$

$=5.703 \times 10^{-3} \mathrm{~N}$

Therefore, the force of attraction between the two spheres is $5.703 \times 10^{-3} \mathrm{~N}$.