Two point electric charges of value `q` and `2q` are kept at a distance `d` apart from each other in air. A third charge `Q` is to be kept along the same line in such a way that the net force action on `q` and `2q` is zero. Calculate the position of charge `Q` in terms of `q` and `d`.

Answer

`(d)/(1+sqrt(2))`

Explanation

Q should be negative and it should be placed somewhere between q and 2q.

For net force on q to be zero:
`(kqQ)/(x^2)=(kq2q)/(d^2)` …(i)
For net force on 2q to be zero.
`(kQ2q)/((d-x^(2)))=(kq2q)/(d^2)`...(ii)
From eqs. (i) and (ii) , we get
`(1)/(x^(2))=(2)/((d-x)^(2)) or x=(d)/(1+sqrt(2))`.