Three point charge are lying along the x-axis. IF two charges `q_(1)=-2C` and `q_(2)=-3C` are placed at `x_(1)=2`m and `x_(2)=-1m`, repectively and the third positive charge is so located between the first two charges that the resultant force on it is zero, find the position of the third charge.

Explanation

In fig two charges `q_(1)` and `q_(2)` are placed at the points A and B along the x-axis. Suppose the third charge q is placed in between `q_(1)` and `q_(2)` at C at a distance x m from the origin O so that the resultant force on its is zero.

`:.1/(4 pi epsilon_(0)) . (q q_(1))/((2-x)^(2))= 1/ (4pi epsilon _(0)) . (q q_(2))/((1+x)^(2))`
or `(-2)/((2-x)^(2))=(-3)/((1+x)^(2))` or `2(1+x)^(2)=3(2-x)^(2)`
or `sqrt(2)(1+x)=sqrt(3)(2-x)` or `(sqrt(2)+sqrt(3))x=2sqrt(3)-sqrt(2)`
`:.x=(2sqrt(3)-sqrt(2))/(sqrt(2)+sqrt(3))=((2sqrt(3)-sqrt(2))(sqrt(3)-sqrt(2)))/(3-2)=8+-3sqrt(6)~~0.65`
Therefore, the third charge is to be placed at a distance of `+0.65`m from the origin O.