Force of attraction between two point electric charges placed at a distance d in a medium is F. What distance apart should these be kept in the same medium, so that force between them becomes F/3?

Let ${\mathrm{q}}_1 \mathrm{and} {\mathrm{q}}_2$ be the two point charges. Then force between the charges when kept at a distance d apart,

$\mathrm{F}=\frac{1}{4{\mathrm{\pi \epsilon }}_{\mathrm{o}}}.\frac{{\mathrm{q}}_1{\mathrm{q}}_2}{{\mathrm{d}}^2}$

Suppose that force between the two charges becomes  F/3 when the charges are kept at a distance x apart, then

$\begin{array}{l}\frac{1}{4{\mathrm{\pi \epsilon }}_{\mathrm{o}}}.\frac{{\mathrm{q}}_1{\mathrm{q}}_2}{{\mathrm{x}}^2}=\frac{\mathrm{F}}{3}\\ \mathrm{Or}\frac{1}{4{\mathrm{\pi \epsilon }}_{\mathrm{o}}}.\frac{{\mathrm{q}}_1{\mathrm{q}}_2}{{\mathrm{x}}^2}=\frac{1}{3}\left(\frac{1}{4{\mathrm{\pi \epsilon }}_{\mathrm{o}}}.\frac{{\mathrm{q}}_1{\mathrm{q}}_2}{{\mathrm{x}}^2}\right)\\ \mathrm{Or}\mathrm{x}=\sqrt{3}\mathrm{d}\end{array}$