Two particles are fixed to an x axis

Question

Two particles are fixed to an x axis: particle 1 of charge q₁ = 2.18 × 10^-8 C at x = 17.0 cm and particle 2 of charge q₂ = -4.41q₁ at x = 78.0 cm. At what coordinate on the x axis is the electric field produced by the particles equal to zero?

Answer 1

Let E=kq/r² hence q₁/x² +q₂/ (61 +x)² =0 where x is the point where the field is 0. So this gives q₁(61+x)²+q₂x² =0 so (61+x) = √4.41 x and this gives (61+x) =±2.1x. For positive sign x= 55.45cm and for the negative sign x =-19.67cm.