Four Charged Particles in a Square

[doogles8654]

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|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.

 

[gneill]

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.

 

[doogles8654]

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

 

[doogles8654]

F₂+F₃=$$\sqrt{2}$$kQq/a²