Zero E Field help please!?

Question

A positive point charge Q1 = 2.21E-5 C is fixed at the origin of coordinates, and a negative charge Q2 = -6.71E-6 C is fixed to the x axis at x = +1.98 m. Find the location of the place along the x axis where the electric field due to these two charges is zero.

Answer 1

It's beyond q2, at 4.40997 m.

R = x2-x1 = 1.98 m

S = sign(q1q2) =-1

d1 = r/(1+S*sqrt(|q2/q1|)) = 4.40996808597259 m

d2 = R-d1 =-2.4299680859726 m

E field null point (point of null net force on a 3rd charge) is at

d1 (= +4.40996808597259 m) from x1, at  4.40996808597259 m, and

-d2 (= +2.4299680859726 m) from x2, at  4.40996808597259 m

Derivation: (d2/d1)^2 = -q2/q1 ==> d2/d1 = -sqrt(|q2/q1|) ==>

R/d1 = 1-sqrt(|q2/q1|) ==> d1 = R/(1-sqrt(|q2/q1|))]