Question

Two identical conducting small spheres are placed with their centres $0.3m$ apart. One is given a charge of $12.0nC$ and the other a charge of $-18.0nC$. If the spheres are connected by a conducting wire, The electric force between the two after they attain equilibrium is $n\times {10}^{-7}N$. Find $n$.

Answer 1

When they are connected by a conducting wire, finally charge on each will be half of total charge on both. Let q be the final charge on each, then $q=\frac{12-18}{2}=-3nC$
Using Coulomb's law, $F=\frac{1}{4\pi {ϵ}_0}\frac{q^2}{r^2}=(9\times {10}^9)\times \frac{(3\times {10}^{-9}{)}^2}{(0.3{)}^2}=9\times {10}^{-7}N$ (positive sign for repulsive force)
So, $n=9$.