Question

particle 1 of charge q1 = 1.04 ìC and particle 2 of charge q2 = -2.99 ìC, are held at separation L = 10.8 cm on an x axis. If particle 3 of unknown charge q3 is to be located such that the net electrostatic force on it from particles 1 and 2 is zero, what must be the (a)x and (b)y coordinates of particle 3?

Answer 1

The point where electric field is zero may be either to the left from q1 or to the right from q2; y-coordinate of the ‘zero point’ is zero.
Let ‘x’ be the distance to the “zero point” located to the left from q1. Then
E1=k•q1/x², (the field deiected to the left)
E2=k•q2/(10.8+x)² ,(to the right)
E1=E2
k•q1/x²= k•q2/(10.8+x)²
1.04/ x² = 2.99/(10.8+x)².
Solve for “x”
I obtained x1=18.35 cm and x2=-15.64 cm . Check my calculations