Coulomb's Law And Superposition

Coulomb's law tells us that the force between two point charges is $F=\frac{1}{4\pi {\epsilon }_0}\frac{q_1{q}_2}{r^2}$, where the constant $\frac{1}{4\pi {\epsilon }_0}=9\times 10^9\mathrm{N}{\mathrm{m}}^2/{\mathrm{C}}^2$. Here both charges are $q=2\times 10^{-6}$ C and the separation is $r=0.30$ m. Substituting the values gives $F=9\times 10^9\times \frac{(2\times 10^{-6})(2\times 10^{-6})}{(0.30{)}^2}$. The numerator of the charge product is $4\times 10^{-12}$, and dividing by $r^2=0.09$ yields $\frac{4\times 10^{-12}}{0.09}=4.44\times 10^{-11}$. Multiplying by $9\times 10^9$ gives $F\approx 0.4$ N. The answer 0.2 N is wrong because it comes from mistakenly using $r$ instead of $r^2$ in only half the calculation. The value 4.0 N is wrong because it drops a factor of 10 by treating $r$ as 0.3 without squaring correctly. The value 0.04 N is wrong because it uses $r$ in centimetres incorrectly, shifting the magnitude by two orders. As stated in NCERT Class 12, Chapter 1 (Electric Charges and Fields), like charges repel along the line joining them. A magnitude check confirms micro-coulomb charges at tens of centimetres give sub-newton forces, so 0.4 N is physically reasonable.