In fig. 21-25, particle 1 of charge & 1.0 mc and particle 2 of charge $3.0 mc are held at separation l ! 10.0 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?

Since the particle 1 and 2 are on the x-axis, the 3rd particle should also be on the x-axis in order the net force on it to be zero.

Let's denote the distance between particles 1 and 3 as x. Therefore the distance between particles 2 and 3 is (0.1 - x), since the distance between 1 and 2 is 0.1 m.

Coulomb's Law states the force between charges as

The question asks that , so

We will take the positive root:

away from the first particle.

Explanation:

Since Fig. 21-25 is not given in the question, the exact locations are not known. However, the location of the third particle is found to be 0.036 m away from the first particle and the third particle is located between the particles 1 and 2.

this would be about 43%