Two charges `2muC and 1muC` are placed at a distance of 10cm. Where should a third charge be placed between them so that it does not experience any force.

Explanation

`Q_(1) = 2muC = 2 xx 10^(-6)C`
`Q_(2) = 1muC = 1 xx 10^(-6)C`
d= 10cm
Let the third charge Q be placed at a distance of X from `Q_(1)` then x= ?
The resultant force on 3rd charge is zero.
`vec(F)_(R )= vec(F)_(1 ) + vec(F)_(2) = 0 " " vec(F)_(1) + vec(F )_(2)= 0`
`(Q_(1))/(x^(2)) = (Q_(2))/((d-x)^(2)) rArr (2 xx 10^(-6))/(x^(2)) = (1 xx 10^(-6))/((10-x)^(2))`
By square rooting on both sides
`(1.414)/(x) = (1)/(10-x) rArr x= 5.9cm " from " 2muC`.