Equilibrium of Three Positively Charged Beads

Click For Summary

Homework Help Overview

The problem involves the equilibrium of three positively charged beads positioned along a horizontal insulating rod. Two beads with charges 3q and q are fixed at either end of the rod, while a third bead is free to slide and is to be positioned at equilibrium. The discussion centers on the conditions for equilibrium and the implications of the charge of the third bead.

Discussion Character

  • Exploratory, Assumption checking

Approaches and Questions Raised

  • Participants discuss the necessity of knowing the charge of the third bead and explore the idea of working symbolically with variables instead of specific values. There is a focus on the concept of equilibrium and how it can be achieved without knowing the exact charge.

Discussion Status

Participants are actively engaging with the problem, questioning the assumptions about the charge of the third bead and discussing the implications of working symbolically. There is a productive exploration of the conditions for equilibrium, with some guidance provided on the approach to take.

Contextual Notes

The problem specifies that the third bead is to be considered in equilibrium, raising questions about the stability of that equilibrium and the relevance of the charge values in determining the position of the third bead.

define_normal
Messages
5
Reaction score
0

Homework Statement


Two small beads having positive charges 3q and q are fixed at the opposite ends of a horizontal, insulating rod, extending from the origin to the point x = d. A third small bead (in the middle) is free to slide on the rod. At what position is the third bead in equilibrium? Can it be stable in equilibrium?


Homework Equations


Coulomb's Law
F = ke (q1q2)/r^2


The Attempt at a Solution


I'm not sure how to go about this problem because I don't know the charge of the third bead.
 
Physics news on Phys.org
define_normal said:
... I don't know the charge of the third bead.
You don't know any of the values, do you? Work symbollically. That is, just use q's and r's and such, instead of "actual numbers".
 
turin said:
You don't know any of the values, do you? Work symbollically. That is, just use q's and r's and such, instead of "actual numbers".

Hmm. So in order for me to do that, I don't need to know the charge of the third particle?
 
define_normal said:
Hmm. So in order for me to do that, I don't need to know the charge of the third particle?
That's right. You would need to know the charge if you wanted to calculate a non-vanishing force. But, the problem stipulates equilibrium, so it doesn't matter. You are looking for the location where - something, regardless of the amount of charge that is placed there - will calculate to be zero. Even then, you have to calculate this location symbolically (i.e. in terms of d).
 

Similar threads

  • · Replies 32 ·
2
Replies
32
Views
4K
  • · Replies 2 ·
Replies
2
Views
10K
Replies
3
Views
2K
  • · Replies 5 ·
Replies
5
Views
8K
  • · Replies 3 ·
Replies
3
Views
2K
  • · Replies 2 ·
Replies
2
Views
3K
Replies
7
Views
2K
  • · Replies 1 ·
Replies
1
Views
4K
  • · Replies 8 ·
Replies
8
Views
3K
  • · Replies 2 ·
Replies
2
Views
7K