Equilibrium of an electric dipole

[kihr]

As per my understanding, the position of most stable equilibrium of a dipole placed in a uniform electric field is when it is aligned with the field, i.e. when E and p (dipole moment) are in the same direction. Also the position of most unstable equilibrium is at the position where the dipole experiences maximum torque, i.e. where the angle between E and p is 90 deg. This understanding is contrary to the definition that the positions of stable and unstable equilibrium are in terms of the angles between E and p corresponding to the maximum and minimum potential energy of the dipole. Could you please explain this to me, as my idea of stability is related to the torque on the dipole and not to its potential energy. Many thanks.

 

[Doc Al]

As per my understanding, the position of most stable equilibrium of a dipole placed in a uniform electric field is when it is aligned with the field, i.e. when E and p (dipole moment) are in the same direction.

OK.

Also the position of most unstable equilibrium is at the position where the dipole experiences maximum torque, i.e. where the angle between E and p is 90 deg.

That's not an equilibrium position at all--the torque is maximum, not zero.

This understanding is contrary to the definition that the positions of stable and unstable equilibrium are in terms of the angles between E and p corresponding to the maximum and minimum potential energy of the dipole. Could you please explain this to me, as my idea of stability is related to the torque on the dipole and not to its potential energy.

An equilibrium position is one where the torque is zero. A stable equilibrium position is one where small displacements produce a restoring torque. So an angle of 0 degrees between E and p is a stable equilibrium position, while an angle of 180 degrees is unstable. This corresponds to minimum and maximum potential energy.

 

[Naty1]

Post #2 is perfect.

 

[kihr]

When the angle between E and p is 90 deg., the torque is maximum. Since the torque is maximum at this angle, the dipole should be at a stage of UNSTABLE equilibrium, as stated in my query, since if released from this position it will go back to its stable position. When the angle between E and p is 180 deg., the torque on the dipole is zero. It is therefore still not clear to me as to why the position of unstable equilibrium is not the position where it experiences the maximum torque. Kindly elucidate. Thanks.

 

[Doc Al]

To be in equilibrium the torque must be zero--that's what equilibrium means. If the torque is not zero, then you do not have any kind of equilibrium, stable or unstable. The position of maximum torque is not an equilibrium position.

 

[kihr]

I have no issues whatsoever with regard to the position of stable equilibrium. My doubt is with respect to the position of the most UNstable equilibrium. Should this be for the angle between E and p as 90 deg. or 180 deg? My point is: Since 90 deg is the position of maximum torque, this should also be the position of the MOST Unstable equilibrium. This is contrary to what the books say, viz. the position of MOST UNstable equilibrium is at an angle of 180 deg. Trust I have been able to make my doubt clear. Thanks.

 

[Doc Al]

It sounds to me like you do not understand what an equilibrium position means. Please reread my previous posts.

 

[kihr]

I repeat: My doubt is regarding the position of the MOST UNSTABLE equilibrium. Why should this not be at the angle of 90 deg between E and p (where torque is max) instead of at 180 deg (where torque is zero)? Maybe you could help me by defining what unstable equilibrium signifies, and why it is related to the PE at the angle of 180 deg. instead of to the torque. I have no issues at all with the understanding of STABLE equilibrium. Trust I have made my point clear. Thanks once again.

 

[Born2bwire]

You need to reread Doc Al's posts, he answered your question there.

OK.

That's not an equilibrium position at all--the torque is maximum, not zero.

An equilibrium position is one where the torque is zero. A stable equilibrium position is one where small displacements produce a restoring torque. So an angle of 0 degrees between E and p is a stable equilibrium position, while an angle of 180 degrees is unstable. This corresponds to minimum and maximum potential energy.

 

[kihr]

Let me re-phrase my question by eliminating the word 'equilibrium' which is the source of all the confusion.
Which orientation of a dipole would make it the most unstable? Is it where the angle between E and p is 180 deg (zero torque) or 90 deg (max. torque)? Whatever the answer I would like to understand the logic behind it. I hope I am clear now about my doubt.

 

[nasu]

How do you measure the amount of instability?
There is no common way (as I know) to compare two states regrading their instability.
The torque (or force) may be larger in one state than in the other. Does this make it "more unstable"?
Does "unstable" even have degrees of comparison in the common language?
You need to define your concepts before you can discuss them...

In physics I think you could define some kind of "amount of stability" for metastable states (equilibrium states). It may take more or less energy to push the system out of the metastable state so you can say that one is more stable than the other.
But these are equilibrium states (and stable, at least locally). No connection with the dipole case.

 

[Doc Al]

Let me re-phrase my question by eliminating the word 'equilibrium' which is the source of all the confusion.
Which orientation of a dipole would make it the most unstable? Is it where the angle between E and p is 180 deg (zero torque) or 90 deg (max. torque)? Whatever the answer I would like to understand the logic behind it. I hope I am clear now about my doubt.

In this context, the terms "unstable" and "stable" are only used in describing equilibrium positions. When the dipole is oriented at 90 degree to the field, it's experiencing maximum torque. Instead of trying to use the term "unstable" in some nonstandard way, why not just stick with that description?

 

[kihr]

To sum up my understanding, we may only refer to the state of stable equilibrium, i.e. the position where the dipole is aligned with the electric field. Any other orientation would lead to a state of instability of the dipole. Therefore it would, perhaps, not be in order to specify that an angle of 180 deg between E and p (or any other angle for that matter) is uniquely an unstable position of the dipole, as any angle other than zero deg would put the dipole in this state. If you are in agreement with me, let me conclude by thanking you for having cleared this issue.

 

[Doc Al]

To sum up my understanding, we may only refer to the state of stable equilibrium, i.e. the position where the dipole is aligned with the electric field.

No. We only refer to the stability of an equilibrium state (where torque = 0); that equilibrium state may be stable or unstable.

Any other orientation would lead to a state of instability of the dipole. Therefore it would, perhaps, not be in order to specify that an angle of 180 deg between E and p (or any other angle for that matter) is uniquely an unstable position of the dipole, as any angle other than zero deg would put the dipole in this state.

Again, I would disagree with that statement. There are two positions where the dipole is in equilibrium; one is stable, the other unstable. In all other positions, there is a torque on the dipole.

 

[kihr]

Your last post has made the position crystal clear. Thanks again for having taken the pains to answer so many queries of mine!

 

[rajib123]

i want to know the equation for work done when an amount of angle has been made from the equilibrium position of an electric dipole...?