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

 

[rwisz]

I would suggest double checking your calculations and equations to ensure accuracy. It is important to also consider the direction of the forces and use vector addition to accurately calculate the resultant force on particle 1. Additionally, it may be helpful to label the diagram with the distances between the particles to make it easier to visualize and calculate the forces.