College Physics
posted by Stephanie13 .
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?

The point where electric field is zero may be either to the left from q1 or to the right from q2; ycoordinate 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