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

Explanation

Let we have two charger `q_1 and q_2` separated by distance d.
F = Force between the two charges
`F =1/(4pi in_0)(q_1q_2)/(d^2)`
Now let the distance between the two charges be d., so that the force between them
becomes `F/3`
Then `F. =(1)/(4pi in_0) (q_1q_2)/((d.)^2)" "...(1)`
`F. = F/3` (given )
`implies F/3=1/(4piin_0)(q_1q_2)/((d.)^2)`
Using eq. (1)
`1/(3).(1)/(4piin_0)(q_1q_2)/(d^2)=1/(4piin_0)(q_1q_2)/((d.)^2)`
`implies (d.)^2 = 3d^2`
`d. = sqrt3d`