I know I typed this question before... But the answers on there turn out not to be the method I'm looking for. So I'm going to post what I have so far and maybe someone can help me out with second part of this:

The question is:

Four particles form a square. The charges are and .

Just for your info, the particles are arranged as such:

1 2

3 4

(a)What is if the net electrostatic force on particles 1 and 4 is zero?

Here's my solution for part a:

(My notation for Force for particles is this, say I want to say the force of particle 2 on 1, I write )

This says that the net force on 1 is the sum of the forces on 1 from 4, 3, and 2.

Turns out I get the same thing for because the net force for Q is 0. So, now I get the net force on Q:

Since k and a are obviously not 0, then must be 0, so:

Is that right? If so, here's part b.

(b) Is there any value of q that makes the net electrostatic force on each of the four particles 0?