Electric Dipoles: Properties and Potential Solutions

In summary: Jackson's E&M book may interest you.In summary, the dipoles in a gas do not behave like free particles. They have translational, rotational and vibrational degrees of freedom, each of which is 1/2 kT per molecule in this simple approximation. The potential energy of interaction between a dipole and a point charge (if you draw out the two charges seperated) that is far away is \nabla_a (\frac{1}{r}) .
  • #1
Schrodu
21
0
Suppose we have a gas of randomly oriented (and in random motion) electric dipoles. Obviously the dipoles do not behave as free particles. How do we describe it's properties? Can we define potential etc. ?
I am looking for a solution without the large volume approximation. Is it possible to get an expression for the mean kinetic energy etc. of a particle given its total energy?
 
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  • #2
will get some answers here shreyas.
though i strictly believe this isseroius mixture of eveidence and thermodynamic arguements
 
  • #4
you are talking about a truly many-body problem, where you must (usually) include the induced dipole-induced dipole interactions. if they don't matter, then why bother?

there are ways of doing this numerically, but they are difficult. you can start with an analytic expression by considering a dipole, mu=dq, interacting with a point charge, you'll then get

[tex]
\nabla_\alpha \nabla_\beta \frac{1}{r}
[/tex]

as the induced field contribution, which needs to be solved for numerically for anything but the simplest of systems. that's why most molecular simulation techniques ignore induced dipoles.
 
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  • #5
quetzalcoatl9 said:
there are ways of doing this numerically, but they are difficult. you can start with an analytic expression by considering a dipole, mu=dq, interacting with a point charge, you'll then get

[tex]
\nabla_\alpha \nabla_\beta \frac{1}{r}
[/tex]

.
Could you clarify that a bit? I am not used to the standard notations. In my original attempt, I calculated the potential energy of two interacting dipoles in terms of their spacing and orientation. I want to average this out in some way (integrating over the angle obviosly gives net potential energy 0)

Thanks for the help.
 
  • #6
If you're looking for a simple solution, the only viable one is to treat it like a semi-ideal gas. The dipoles have translational, rotational and vibrational degrees of freedom, each of which is 1/2 kT per molecule in this simple approximation.
 
  • #7
Schrodu said:
Could you clarify that a bit? I am not used to the standard notations. In my original attempt, I calculated the potential energy of two interacting dipoles in terms of their spacing and orientation. I want to average this out in some way (integrating over the angle obviosly gives net potential energy 0)

Thanks for the help.

the potential energy of interaction between a dipole and a point charge (if you draw out the two charges seperated) that is far away is [tex]\nabla_a (\frac{1}{r})[/tex]

since [tex]E = -\nabla V[/tex] then the dipoles contribution to the induced field is the expression i gave.

do a scholar google search for "molecular polarization" if you are more interested. there are review articles out there that summarize the field. also, Jackson's E&M book may interest you.
 
  • #8
I found in this paper(page no. 4)

dipole field [tex]E=\frac{\mu}{4\pi \epsilon_0 r^3}[/tex] ...
... [tex]\frac{mv_w^2(r)}{2}=kT-(\frac{\mu_r^2}{4\pi \epsilon_0})(\frac{1}{d^3}-\frac{1}{r^3})[/tex]
Shouldn't there be a term to take care of direction, [tex]U=\frac{\mu_r^2\cos\alpha}{4\pi \epsilon_0}[/tex]?, [tex]\alpha[/tex] is angle between field and the axis
 
  • #9
You can also consider a mean field approximation -- that will allow you to calculate the potential energy due to the orientation of the dipoles. In fact, with that approximation, I guess you'd get a hybrid free-gas / Curie ferromagnet effect, with a phase change due to the orientation. As far as dipole-dipole forces beyond merely torque, perhaps use the Van de Waals approximation?
 

1. What is an electric dipole?

An electric dipole is a pair of equal and opposite charges that are separated by a distance. This separation creates a dipole moment, which is a measure of the strength and direction of the dipole.

2. What are some properties of electric dipoles?

Electric dipoles have a dipole moment, which is a vector quantity. They also have an electric field that depends on the distance between the charges and their magnitudes. Additionally, electric dipoles can experience a torque when placed in an external electric field.

3. How are electric dipoles used in everyday life?

Electric dipoles are used in many electronic devices, such as capacitors and antennas. They are also an important concept in understanding the behavior of molecules, as many molecules have a permanent dipole moment.

4. Can electric dipoles have a net charge?

No, electric dipoles have equal and opposite charges and therefore have a net charge of zero.

5. How can electric dipoles be oriented in an external electric field?

Electric dipoles tend to align themselves with the direction of the external electric field. If the field is uniform, the dipole will align itself parallel to the field. If the field is not uniform, the dipole will experience a torque and may rotate to align with the field.

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