Finding Equilibrium Position for Three Charged Particles

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Homework Help Overview

The discussion revolves around finding the equilibrium position for a third charged particle in relation to two fixed charged particles in an xy plane, utilizing Coulomb's Law. The original poster presents a scenario involving specific charges and coordinates, seeking to determine the correct placement of the third charge to achieve a net electrostatic force of zero.

Discussion Character

  • Exploratory, Assumption checking, Problem interpretation

Approaches and Questions Raised

  • Participants discuss the setup of the force equations and the placement of the third charge, questioning the distances and the signs used in the equations. There is exploration of whether the third charge should be placed between the other two charges or outside them, as well as the implications of the magnitudes of the charges involved.

Discussion Status

The discussion is ongoing, with participants providing guidance on re-evaluating the force equations and the placement of the third charge. There is a recognition of the need to clarify assumptions about the distances and the relative positions of the charges, but no consensus has been reached on the final placement of the third charge.

Contextual Notes

Participants are navigating through potential misunderstandings regarding the distances between charges and the implications of charge magnitudes on the placement of the third charge. The original poster has expressed uncertainty about their calculations and the assumptions made in their approach.

jperk980
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[SOLVED] Coulomb's Law

The charges and coordinates of two charged particles held fixed in an xy plane are q1 = +3.5 µC, x1 = 3.0 cm, y1 = 0.50 cm, and q2 = -4.0 µC, x2 = -2.0 cm, y2 = 1.5 cm.
At what coordinates should a third charge q3 = +5.5 µC be placed such that the net electrostatic force on particle 3 due to particles 1 and 2 is zero?

I set both Forces together, F13= F23. When i simplified i i get the equation (q1/x^2)=(q2/(x-l)^2). I used the distance formula to find l and i came up with the answer .026.
When i solve for x i get .0126m or 1.26 cm. I understand i have to use sin and cosine to get the answers. I used the formula x= x2-x1cos -11.3 and the same for y using different numbers. X1 is the value i just solved for. by doing this i get an answer of -3.57 for x and -1.686 which are incorrect. I was able to find the angle by using the equation theta=Tan-1((y2-y1)/(x2-x1). i know that this value is correct because the system i used called webassign checks the answers immediately. Can someone please tell me what i did wrong.
 
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jperk980 said:
When i simplified i i get the equation (q1/x^2)=(q2/(x-l)^2). I used the distance formula to find l and i came up with the answer .026.
Are you sure that that is the distance between the charges? (Double check.)

Also, where must q3 be placed? Between the other charges? Or to one side?
 
Why x-l, as opposed to x+l?

What is the significance of the fact the magnitude of q2 > q1?
 
i believe that the charge should be to the left of q1 since q2 has a greater charge than q1 and and sorry the actual calculation was 5.099 cm which is equal to .05099 m
 
i assumed it was x-l but i learned that i am wrong by figuring out where the charge will be located
 
When you say "to the left of q1" do you mean between the charges?
 
i placed the charges in a cordinate plane and q2 was to the left of q1 considering it had a coordinate of -2 and to answer your question no it is outside the charges
 
jperk980 said:
... no it is outside the charges
Right. Which side?
 
it would have to be on the positive side since the charge on q2 is greater that the charge of q2
 
  • #10
jperk980 said:
it would have to be on the positive side...
Right. So redo your force equation accordingly.
 
  • #11
so as Astronuc said it would be x+l not x-l if that is the case the x value would be -2.4 cm or 73.9 cm
 
  • #12
Right. And only one of those answers makes sense.
 
  • #13
It would have to 73.9 because it is positive and i am looking for a positive value
 
  • #14
jperk980 said:
It would have to 73.9 because it is positive and i am looking for a positive value
Exactly. (Assuming your arithmetic is correct.) A negative answer would put the third charge between the other two--which is no good.
 
  • #15
Thank you Doc Al for your quick responses i was able to figure out the rest of the problem on my own using the angle. Once again thank you for your help!
 

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