Four Charged Particles in a Square

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?

F=k|q1||q2|/r2
a2+b2=c2

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/a2 so their resultant is 2kQq/a2.

The distance between particle 1 and 4 i called c. a2+b2=c2. In this case a and b are both a(according to the diagram) so: a2+a2=c2. Thus c=a$$\sqrt{2}$$.

I used this to get the force of 4 on 1: kQ|-5.25Q|/a$$\sqrt{2}$$2, which when simplified becomes 5.25q2k/2a2.

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.

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gneill
Mentor
Check your resultant for forces 2 and 3. They form vector components and so should be added accordingly to find the magnitude of the resultant.

Okay wow, thanks! Hehe, totally forgot how to find the resultant of two vectors I guess. :P Good call, I got it now!

F2+F3=$$\sqrt{2}$$kQq/a2