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

[tellmesomething]

Homework Statement

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

Relevant Equations

Not relevant

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?

 

[PhysicsEnjoyer31415]

Is the ring also charged ?

 

[PhysicsEnjoyer31415]

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

 

[tellmesomething]

Is the ring also charged ?

Yes

 

[haruspex]

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.

 

[PhysicsEnjoyer31415]

Yes

Same charge or opposite charge

 

[tellmesomething]

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...

 

[tellmesomething]

Same charge or opposite charge

Same charge

 

[Orodruin]

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.

 

[PhysicsEnjoyer31415]

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

 

[Lnewqban]

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?

 

[tellmesomething]

Does a rubber band get stretched when you force it to slide down a cone?

View attachment 345575

Yes..