A particle of charge +2q is placed at the origin and particle of charge -q is placed on the x-axis at x = 2a. Where on the x-axis can a third positive charge be placed so that the net electric force on it is zero? a is the unit of distance.

Explanation:

We know that the electric force equation is:

Now, we have three particles, the first one at x=0, the second one at x=2a and the third in some place between these two particle.

1. Let's find the electric force between the first particle and the third particle.

r(31) is the distance between 3 and 1

2. Now,  let's find the electric force between the third particle and the second particle.

r(32) is the distance between 3 and 2.

Now, or

The net force must be zero so:

We just need to solve it for r(31)

Therefore the distance from the origin will be:

I hope it helps you!