Two point charges `q_(1) and q_(2)` (like) are seperated by a distance r and fixed. Locate the point on the line joining those charges where resultant or net field is zero.

Explanation

Let P be the null point where `barE_("net") =0`
` rArr barE_(1)+barE_(2) =0` (due to those charges)
or `barE_(1) = -barE_(2) and E_(1)=E_(2)`
`rArr (1)/(4pi in_(0)) (q_(1))/(x^(2)) =(1)/( 4pi in_(0)) (q_(2))/((r-x)^(2)) or (q_(1))/(x^(2)) =(q_(2))/( (r-x)^(2))`
From this we get x.
If the charges are like, the neutral point will be between the charges, if the charges are unlike the neutral point will be outside the charge on the line joining them.

`:.` In this case `(q_(1))/(x^(2)) =(q_(2))/((r+x)^(2))`.