Oscillations of Dipole in Electric Field: Stability & SHM

In summary, the conversation discusses the execution of angular SHM by a dipole in both stable and unstable equilibrium positions in a uniform electric field. It is mentioned that for larger starting angles, the solution is not well approximated by SHM. The potential function for a dipole in a non-uniform electric field is also briefly mentioned. However, it is noted that the specific details and results would depend on the specific situation.
  • #1
gracy
2,486
83
In a uniform electric field if a dipole is slightly displaced from it's stable equilibrium position it executes angular SHM.
What if a dipole is slightly displaced from it's unstable equilibrium position ,will it execute angular SHM?
 
Physics news on Phys.org
  • #2
gracy said:
What if a dipole is slightly displaced from it's unstable equilibrium position ,will it execute angular SHM?
Do you mean like in a situation where the dipole is hold at an arbitrary angle from the field and then released?
The SHM resulting from a small initial displacement from the equilibrium position is actually an approximation. For significantly bigger starting angle, the solution of the equation of motion is no longer well approximated by SHM. For this kind of problem, the solution involves certain type of elliptic integral.
 
  • #3
blue_leaf77 said:
Do you mean like in a situation where the dipole is hold at an arbitrary angle from the field?
I mean if the dipole initially makes 180 degrees with electric field and then it is displaced from there will it execute SHM?
 
  • #4
gracy said:
I mean if the dipole initially makes 180 degrees with electric field and then it is displaced from there will it execute SHM?
That example is also included in the situation I described above.
 
  • #5
blue_leaf77 said:
That example is also included in the situation I described above.
gracy said:
I mean if the dipole initially makes 180 degrees with electric field and then it is displaced from there will it execute SHM?
You mean it won't execute SHM?
 
  • #6
It will not.
 
  • Like
Likes gracy
  • #7
In a uniform electric field if a dipole is displaced for a large angle from it's stable equilibrium position will it execute angular SHM?I think no.
 
  • #8
The only logical difference between "slightly displaced from it's unstable equilibrium position" and "displaced for a large angle from it's stable equilibrium position" is that the second statement being just a special case of the first. If you want to know which case is an approximate SHM which is not, you should go to the equation of motion and see whether any approximation can be assumed. On the whole, a pendulum-type motion under uniform force field is strictly speaking not SHM.
 
  • #9
In a non uniform electric field if a dipole is displaced it won't execute angular SHM(no matter what it's starting angle is and whether it is displaced for a larger or smaller angle )
In this case motion of dipole is combination of translatory and rotatory motion .
Right?
 
  • #10
gracy said:
In this case motion of dipole is combination of translatory and rotatory motion .
Right?
What does your trained intuition tell you? Try to trust yourself if you know your reasoning can be supported by the known physics formula.
 
  • #11
blue_leaf77 said:
What does your trained intuition tell you? Try to trust yourself if you know your reasoning can be supported by the known physics formula.
If the displacement from stable equilibrium is small enough you can model the motion as a SHO. This is valid for any system, not restricted to dipole in a specific type of field.
 
  • #12
nasu said:
If the displacement from stable equilibrium is small enough you can model the motion as a SHO. This is valid for any system, not restricted to dipole in a specific type of field.
Right. For many potential functions, particularly in the case of one dimensional motion, a small displacement from a stable equilibrium position results in SHM, Simple Harmonic Motion.
 
  • Like
Likes gracy
  • #13
SammyS said:
a small displacement from a stable equilibrium position results in SHM, Simple Harmonic Motion.
Even in non uniform electric field?
 
  • #14
gracy said:
Even in non uniform electric field?
What is the potential function in this case?
 
  • #15
SammyS said:
What is the potential function in this case?
I just know dipole in non uniform electric field experiences a net force given by
##F##=##Δ(P.E)##

where p is the dipole moment and E is the electric field.I don't know abut potential.
 
  • #16
gracy said:
I just know dipole in non uniform electric field experiences a net force given by
##F##=##Δ(P.E)##

where p is the dipole moment and E is the electric field.I don't know about potential.
(In Post #12, I was commenting on Post #11.)

That should be ##\displaystyle \vec F = -\vec \nabla (\vec p \cdot \vec E) \ ## .

Do you understand what all of those symbols mean ?For the case of a non-uniform field, whatever happens will depend on the details, details which are not specified here.
 
Last edited:
  • #17
Please answer my post #13 .
 
  • #18
gracy said:
Please answer my post #13 .
I did.

Last sentence in Post #16.
 
  • Like
Likes davenn
  • #19
Thread closed for Moderation...
 

1. What is a dipole in an electric field?

A dipole in an electric field refers to a system where two opposite charges of equal magnitude are separated by a distance. This creates a dipole moment, which is the measure of the strength and direction of the dipole.

2. What is the stability of a dipole in an electric field?

The stability of a dipole in an electric field depends on the orientation of the dipole moment with respect to the electric field. If the dipole moment is aligned with the electric field, it is in a stable equilibrium. However, if the dipole moment is perpendicular to the electric field, it is in an unstable equilibrium.

3. What is simple harmonic motion (SHM) in relation to oscillations of a dipole in an electric field?

Simple harmonic motion is a type of oscillatory motion where the restoring force is directly proportional to the displacement from the equilibrium position. In the case of a dipole in an electric field, the restoring force is provided by the electric field, causing the dipole to oscillate back and forth in a regular pattern.

4. How does the strength of the electric field affect the SHM of a dipole?

The strength of the electric field affects the SHM of a dipole by determining the frequency of the oscillations. A stronger electric field will result in higher frequency oscillations, while a weaker electric field will result in lower frequency oscillations.

5. Can the oscillations of a dipole in an electric field be damped?

Yes, the oscillations of a dipole in an electric field can be damped by external forces such as friction or resistance. This will result in a decrease in the amplitude of the oscillations over time, eventually causing the dipole to come to a rest at its stable equilibrium position.

Similar threads

  • Other Physics Topics
Replies
12
Views
2K
  • Introductory Physics Homework Help
Replies
14
Views
642
  • Classical Physics
Replies
5
Views
1K
  • Introductory Physics Homework Help
Replies
11
Views
1K
Replies
1
Views
1K
Replies
1
Views
755
Replies
4
Views
368
  • Introductory Physics Homework Help
Replies
1
Views
360
Replies
4
Views
724
Replies
2
Views
1K
Back
Top