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Four Charged Particles in a Square

  • #1

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?
hrw7_21-22.gif



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[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 5.25q2k/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.
 

Answers and Replies

  • #2
gneill
Mentor
20,743
2,733
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.
 
  • #3
Okay wow, thanks! Hehe, totally forgot how to find the resultant of two vectors I guess. :P Good call, I got it now!
 
  • #4
F2+F3=[tex]\sqrt{2}[/tex]kQq/a2
 

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