# B Oscillations of dipole

1. Feb 6, 2016

### gracy

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?

2. Feb 6, 2016

### blue_leaf77

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. Feb 6, 2016

### gracy

I mean if the dipole initially makes 180 degrees with electric field and then it is displaced from there will it execute SHM?

4. Feb 6, 2016

### blue_leaf77

That example is also included in the situation I described above.

5. Feb 6, 2016

### gracy

You mean it won't execute SHM?

6. Feb 6, 2016

It will not.

7. Feb 6, 2016

### gracy

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. Feb 6, 2016

### blue_leaf77

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. Feb 6, 2016

### gracy

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. Feb 6, 2016

### blue_leaf77

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. Feb 6, 2016

### nasu

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. Feb 6, 2016

### SammyS

Staff Emeritus
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.

13. Feb 6, 2016

### gracy

Even in non uniform electric field?

14. Feb 6, 2016

### SammyS

Staff Emeritus
What is the potential function in this case?

15. Feb 6, 2016

### gracy

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. Feb 6, 2016

### SammyS

Staff Emeritus
(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: Feb 6, 2016
17. Feb 7, 2016

### gracy

18. Feb 7, 2016

### SammyS

Staff Emeritus
I did.

Last sentence in Post #16.

19. Feb 7, 2016