Question from Electrostatics -- Charged beads on a wire....

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Homework Help Overview

The discussion revolves around a problem in electrostatics involving charged beads on a frictionless non-conducting needle. Participants explore the implications of pulling the first bead and the conditions under which the chain of beads might break, considering the forces acting between them.

Discussion Character

  • Exploratory, Assumption checking, Conceptual clarification

Approaches and Questions Raised

  • Participants discuss the nature of the forces between the beads, referencing Coulomb's law and questioning how to apply it to the scenario. There are attempts to formulate equations related to tension and force, as well as considerations of whether a break will occur at all.

Discussion Status

The discussion is ongoing, with participants sharing insights about the forces involved and the mathematical representation of those forces. Some guidance has been offered regarding the formulation of equations, but there remains uncertainty about the specific application to the problem.

Contextual Notes

Participants note the lack of complete information in the original problem statement and express confusion about the implications of the setup, particularly regarding the behavior of the beads under tension.

Ankit Chowdhury
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Homework Statement



On a long friction-less non-conducting straight needle are threaded an infinitely large number of identical beads.The beads are made of insulating materials and have charges of equal magnitude and alternate plus and minus signs.Assume charge distribution on a bead unaffected by other charges in its vicinity. If the first bead is pulled out with a gradually increasing force, where will the chain break first?2. The attempt at a solution I have thought of making a variable function of Tension on the string and then differentiate it for the max value to get the position.but I have no idea about how I am going to make the equation.
 
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Ankit Chowdhury said:

Homework Statement



On a long friction-less non-conducting straight needle are threaded an infinitely large number of identical beads.The beads are made of insulating materials and have charges of equal magnitude and alternate plus and minus signs.Assume charge distribution on a bead unaffected by other charges in its vicinity. If the first bead is pulled out with a gradually increasing force, where will the chain break first?2. The attempt at a solution I have thought of making a variable function of Tension on the string and then differentiate it for the max value to get the position.but I have no idea about how I am going to make the equation.
What is the equation for the force between each pair of beads?
 
Not sure why there should be a "break" at all ...
 
I have already written the whole question and only this much of information was given .
 
Ankit Chowdhury said:
I have already written the whole question and only this much of information was given .
But from your textbooks and lectures, you know an equation for the force between two charged objects as a function of distance. What is that equation and how can you use it in this problem?
 
Wait let me upload the picture of the question.
 
IMG_20160706_003430.jpg
 
See question no. 26
 
You still have not answered my question about the equation... Please show some effort on this schoolwork problem of yours.
 
  • #10
That equation is called column's law where force is directly proportional to the multiplication of two charges and inversely proportional to the square of the distance between the two charges.But I am unable to figure out that how will I apply this here.
 
  • #11
Ankit Chowdhury said:
That equation is called column's law where force is directly proportional to the multiplication of two charges and inversely proportional to the square of the distance between the two charges.But I am unable to figure out that how will I apply this here.
Good! So can you write an equation for the force on the first bead from all of the other beads? It will be an infinite series. And then write the equation for the forces on the 2nd bead and so on. Then think about the forces on each bead as the first one is pulled a tiny bit away from the rest...
 
  • #12
OK thanks I will try it .
 
  • #13
But how will I say where will it break.
 
  • #14
Ankit Chowdhury said:
But how will I say where will it break.
As rude man said, maybe it will never "break", but by writing the infinite series for the forces on each bead, I do see a place where there is the biggest difference in forces to the left and right in the string of beads...
 
  • #15
berkeman said:
then write the equation for the forces on the 2nd bead and so on.
that's not quite it. In considering whether it will break between the nth and the n+1th, it's the force between the first n, as a unit, and the rest that matters.
 
  • #16
Ankit Chowdhury said:
column's law
Coulomb's?
 
  • #17
Yes that's a spelling mistake
 

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