A Charge 2 C is placed at the origin and charge q is placed

A Charge +2 C is placed at the origin and charge –q is placed at the point (2; 0) m. Where can a third positive charge +q should be placed so that the force on it is zero?

Solution

if we place +q on the +x-axis the net force on +q never be zero

so it must be placed on -X-axis

then

Force on +q due to +2qC = Force on +q due to -q

let x be the distance from origin along -X-axis where force is zero

k*2q*q/x^2 = k*q*q/(2+x)^2

2/x^2 = 1/(2+x)^2

so at x = -6.82 cm or x = -1.17 cm

or
2/x^2 = 1/(x-2)^2

x = 6.82 cm or 1.17 cm