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## Homework Statement

In the figure below, four particles form a square. The charges are q1 = +Q, q2 = q3 = q, and q4 = -5.25Q. What is q/Q if the net electrostatic force on particle 1 is zero?

## Homework Equations

F=k|q

_{1}||q

_{2}|/r

^{2}

a

^{2}+b

^{2}=c

^{2}

## The Attempt at a Solution

I first drew a free body diagram of particle one with the forces of particles 2 and 3. Their resultant force needs to balance exactly the force of particle 4 in order for the net force on particle 1 to be zero.

Forces 2 and 3 both equal kQq/a

^{2}so their resultant is

**2**kQq/a

^{2}.

The distance between particle 1 and 4 i called c. a

^{2}+b

^{2}=c

^{2}. In this case a and b are both a(according to the diagram) so: a

^{2}+a

^{2}=c

^{2}. Thus c=a[tex]\sqrt{2}[/tex].

I used this to get the force of 4 on 1: kQ|-5.25Q|/a[tex]\sqrt{2}[/tex]

^{2}, which when simplified becomes 5.25q

^{2}k/2a

^{2}.

In setting this equal to the resultant of forces 2 and 3, I end up with 5.25/4=1.31=q/Q. This is not coming up as the right answer.