Two point charges ( +Q) and (-2Q) are fixed on the x-axis at positions a and 2a from origin, respectively. At what positions on the axis, the resultant electric field is zero?

Suppose electric field is zero at a point P which lies at a distanced from the charge+ Q. At PkQd2=k(2Q)(a+d)2 ⇒1d2=2(a+d)2⇒d=a(2−1)Since d > a, i.e., point P must lies on negative x-axis as shown at a distance x from origin. Hencex=d−a=a(2−1)−a=2aActually P lies on negative x-axis, so x=−2a