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

In summary, to understand the direction of tension in a charged closed ring, one must consider the effects of electric forces acting on the charges within the ring. When the ring is charged, like charges repel each other, creating a tension that pulls the charges apart. The tension direction can be determined by analyzing the forces acting on individual charges and applying the right-hand rule to visualize the resultant force vector. Additionally, the ring's geometry and the distribution of charge play crucial roles in determining the overall tension direction within the system.
  • #1
tellmesomething
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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 ?
 
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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
 
  • #4
PhysicsEnjoyer31415 said:
Is the ring also charged ?
Yes
 
  • #5
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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  • #6
tellmesomething said:
Yes
Same charge or opposite charge
 
  • #7
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...
 
  • #8
PhysicsEnjoyer31415 said:
Same charge or opposite charge
Same charge
 
  • #9
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..
 

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

1. What is the basic principle behind the tension in a charged closed ring?

The tension in a charged closed ring arises from the electric forces acting on the charged particles within the ring. When charges are distributed uniformly along the ring, they create an electric field that exerts forces on each charge, leading to a net tension that keeps the ring in equilibrium.

2. How do I determine the direction of tension in the ring?

To determine the direction of tension in a charged closed ring, consider the forces acting on a small segment of the ring. Each charge experiences repulsive or attractive forces from other charges, and the resultant vector of these forces indicates the direction of tension. Generally, tension acts radially inward toward the center of the ring.

3. Does the tension change if the charge distribution is not uniform?

Yes, if the charge distribution is not uniform, the tension will vary around the ring. Areas with higher charge density will experience greater repulsive forces, leading to increased tension in those segments, while areas with lower charge density will experience less tension.

4. How does the radius of the ring affect the tension?

The radius of the ring influences the tension because it affects the distance between charges. A larger radius generally leads to a decrease in the electric field strength at any given point on the ring, which can reduce the overall tension. Conversely, a smaller radius can increase the electric field strength and, therefore, the tension.

5. Can external electric fields influence the tension in the charged ring?

Yes, external electric fields can significantly influence the tension in a charged ring. An external field can exert additional forces on the charges in the ring, altering the balance of forces and potentially changing the direction and magnitude of the tension. This can lead to a net force that either enhances or counteracts the internal tensions within the ring.

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