The magnitude of the electrostatic force between two point charges is given by Coulomb's Law: $F = k \frac{|q_1 q_2|}{r^2}$.

Given: $F = 0.2 \, \text{N}$ $q_1 = 0.4 \, \mu\text{C} = 0.4 \times 10^{-6} \, \text{C}$ $|q_2| = |-0.8 \, \mu\text{C}| = 0.8 \times 10^{-6} \, \text{C}$ $k = 9 \times 10^9 \, \text{N m}^2\text{C}^{-2}$

Rearranging the formula to solve for distance $r$: $r^2 = \frac{k |q_1 q_2|}{F} = \frac{(9 \times 10^9)(0.4 \times 10^{-6})(0.8 \times 10^{-6})}{0.2}$ $r^2 = \frac{2.88 \times 10^{-3}}{0.2} = 14.4 \times 10^{-3} = 144 \times 10^{-4} \, \text{m}^2$ Taking the square root: $r = \sqrt{144 \times 10^{-4}} = 12 \times 10^{-2} \, \text{m} = 12 \, \text{cm}$.