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

Explanation

Let we have two charges `q_(1) and q_(2)`. separated by distance d
Force of between two charges F
`F=1/(4pi varepsilon)(q_(1)q_(2))/d^(2)" "...(i)`
Now let the distance between the two charges be d., so that the force between them become `F/3`
Then`" "F.=1/(4 pi varepsilon_(0))(q_(1)q_(2))/(d.)^(2)" "...(ii)`
put`" "F.=F/3"in"(ii)`
`F/3=1/(4 pi varepsilon_(0))(q_(1)q_(2))/((d.)^(2))`
Using equation (1)
`1/(3).cancel((1)/(4 pi varepsilon_(0)))(q_(1)q_(2))/d^(2)=cancel(1/(4 pi varepsilon))(q_(1)q_(2))/(d.)^(2)`
`1/(3d^(2))=1/(d.)^(2)`
`(d._^(2)=3d^(2)`
`d.=sqrt(3)d`