How to understand the direction of tension in a charged closed ring?

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Homework Help Overview

The discussion revolves around understanding the direction of tension in a charged closed ring, particularly in relation to electrostatic forces exerted by a charge at the center of the ring. Participants explore the nature of tension in the context of charged and conducting rings.

Discussion Character

  • Conceptual clarification, Assumption checking, Exploratory

Approaches and Questions Raised

  • Participants discuss the relationship between electrostatic forces and tension, questioning why tension is considered tangential rather than radial. Some explore the implications of the ring being charged or conducting, while others suggest analogies to physical systems like pressurized containers.

Discussion Status

The discussion is active, with participants raising questions about the nature of the forces involved and seeking rigorous proofs for their reasoning. There is a mix of interpretations regarding the tension's direction and the effects of charge distribution.

Contextual Notes

Some participants note the need for clarity on whether the ring is charged or conducting, which influences the discussion on induced charges and tension. The complexity of the problem is acknowledged, with references to free body diagrams and analogies to other physical scenarios.

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Homework Statement
How to understand the direction of tension in a charged closed ring?
Relevant Equations
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This is the direction of the electrostatic force on each element due to the charge kept in the center of the ring.

According to me tension in each element of the charged ring should be balancing each of these forces...so its pointing radially inwards

But I know I am wrong because the solution says the tension is tangent to the ring ...

I dont get why?
 
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Is the ring also charged ?
 
If it is not charged but if it is a conducting ring , the central charge will induce both positive and negative charges on the ring in such a way that all the tension created due to the repulsion of positive charges outwards and attraction of negative charges inwards will stretch the ring , as this will happen the logic is that it induces charges to neutralize too*dont forget it is induced* which will ofc be tangential due to repulsion as well
 
PhysicsEnjoyer31415 said:
Is the ring also charged ?
Yes
 
tellmesomething said:
This is the direction of the electrostatic force on each element due to the charge kept in the center of the ring.

According to me tension in each element of the charged ring should be balancing each of these forces...so its pointing radially inwards

But I know I am wrong because the solution says the tension is tangent to the ring ...
If you consider a short element of a very thin ring, tension is the force each such element exerts on its neighbours. The two ends of the element are not quite parallel, so the net force on the element from those tensions is radially inwards. Thus, although the tension is everywhere tangential, it results in an inward force on any short element.
 
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tellmesomething said:
Yes
Same charge or opposite charge
 
haruspex said:
If you consider a short element of a very thin ring, tension is the force each such element exerts on its neighbours. The two ends of the element are not quite parallel, so the net force on the element from those tensions is radially inwards. Thus, although the tension is everywhere tangential, it results in an inward force on any short element.
Is there a way to prove both of these rigorously? If so can you give me some ideas...
 
PhysicsEnjoyer31415 said:
Same charge or opposite charge
Same charge
 
tellmesomething said:
Is there a way to prove both of these rigorously? If so can you give me some ideas...
Just make a free body diagram of a small part of the ring (or even better - half the ring!)

The ideas here are completely analogous to those presented by a pressurized cylindrical container.
 
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Ok so the electric field of a point charge is uniform in all directions , so imagine this , the field is applying a equivalent force on all points of the charged ring, now imagine all those charges on the charged ring to be like little people(who hate each other) so they push the person standing beside them , tension prevents the force from breaking the ring and hence acts tangentially too
 
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  • #11
tellmesomething said:
Is there a way to prove both of these rigorously? If so can you give me some ideas...
Does a rubber band get stretched when you force it to slide down a cone?

2Fdfd94d3f-f194-43fe-a7c1-5d529f81de66%2FphpUDHLED.png
 
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  • #12
Lnewqban said:
Does a rubber band get stretched when you force it to slide down a cone?

View attachment 345575
Yes..
 

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