Quote by afulldevnull
1. The problem statement, all variables and given/known data
Two particles lie on the x axis. The first particle is at the origin with a charge of +1.6uC and the other has a charge of 3.1uC and is +10.5cm away. 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 is the coordinates of the third particle?
2. Relevant equations
Coloumbs Law: F = k (q1 q2) \ r^2
3. The attempt at a solution
Since the charges of the particles are opposite, and because particle 1 has a smaller magnitude, then the third particle must go to the left of particle 1 and must have a negative charge. This is because for the net to be 0, then the strong force at a distance must repel as strongly as the small force nearby attracts. If the net force is to be 0, then the forces must have the same magnitude. So: k(1.6q)/d^2 = k(3.1q) / (10.5+d)^2.
I get the 26 cm, but that can't be right. Any thoughts?

You said that d was on the left of the origin  so is negative.
The solution of the quadratic equation yields approx 26 and also around 4.
Perhaps it is the "4" you are after.
Also, the charge of q3 can be either positive or negative.