Question

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`?
A. `2sqrt(3)d`
B. `3d`
C. `9d`
D. `sqrt(3)d`

Answer 1

Correct Answer - d
Let `q_(1)` and `q_(2)` be the two point charges. Then, force between the charges, when kept at a distance `d` apart,
`F=(1)/(4piepsilon_(0))*(q_(1)q_(2))/(d^(2))`
Suppose that force between the two charges becomes `F//3`, when the charges are kept at a distance `x` apart. Then
`(1)/(4pi epsilon)*(q_(1)q_(2))/(x^(2))=F/3`
or `1/(4piepsilon_(0))*(q_(1)q_(2))/(x^(2))=1/3(1/(4piepsilon_(0))*(q_(1)q_(2))/(d^(2)))`
Or `x= sqrt(3)d`