# What does the el.Dipole Moment increasing with charge separation mean?

## Main Question or Discussion Point

Hello everyone.

My understanding of a dipole moment is it defines the strength of various dipole interactions, eg the common example of torque in an electric field. My confusion stems from the fact that the magnitude of the dipole moment is proportional to the charge separation. In many areas of physics, we deal with quantities that are inversely proportional to distance. I can reason very intuitively that as I move further from something, our mutual interaction is reduced. The idea that in a dipole, the further you remove something, the stronger the interaction becomes is equally counter-intuitive to me.

For example, if I removed two charges to infinity from each other, their dipole moment is infinity, and they are the "strongest" dipole possible. In fact, why don't massive dipole moments exist between charged particles on earth and charge particles on some star light-years away. With such a large dipole moment, even the smallest electric field would result in an unimaginable torque on our charged particles. I know particle charges are distributed on a macroscopic scale very finely so as to be overall neutral, but there must be even to a minuscule order some small imbalance that would evidence these incredible torques.

I suppose I think of the dipole moment as some kind of force, or at least proportional to a force, and I am having trouble understanding how a force's effect can increase with distance.

Thank you for reading and any time or advice you are able to share.

## Answers and Replies

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The dipole moment of two charges separated by a distance indicates the strength of the dipole's electric field. It does not characterize the energy of one of the charges in the field of the other charge.

Rather, if you consider the potential energy of the two charges in an externally applied electric field you see that it scales with the distance between the charges. The torque depends on how the potential energy changes with angle, keeping the distance fixed.

In principle two arbitrary charges, say on earth and on the moon have a huge electric dipole moment. In practice, however, there are very few isolated charges that are not part of an atom or molecule.

For example, take two hydrogen atoms, one on earth and the other one on the moon. The earth electron and the moon proton make a huge dipole moment. But the earth proton and the moon electron also make a dipole moment that is just as huge but has the opposite sign. Now the interactions of the proton and electron within an atom are much stronger than with the other electron/proton across the earth-moon distance. Therefore the two dipole moments are coupled and you are dealing with the sum of the two dipole moments. This sum is very very very close to zero.

WannabeNewton
Science Advisor
The dipole potential still falls off as $\frac{1}{\text{distance}}$ so there is nothing counter-intuitive there. You are mixing the effect of the dipole separation with that of the distance from the entire dipole itself.

In principle two arbitrary charges, say on earth and on the moon have a huge electric dipole moment. In practice, however, there are very few isolated charges that are not part of an atom or molecule.
Thank you both for your replies! I have a few follow up questions that I hope make sense.

1. Given a dipole moment created by the separation of two charges, is there a distance of separation upon which the combination of two charges are no longer "bound" to each other; in other words the effects of a dipole do not exist anymore?

M Quack you mentioned that in principle two charges at a large distance would have a huge electric dipole. In practice, this may not occur often, but there are "very few isolated charges," due to which I presume it would be possible to observe such a dipole moment. To test that, could you theoretically construct a vacuum in an infinitesimal tube 3 meters long and observe the corresponding dipole moment between two isolated charges at opposite ends of the tube? If you extended this thin tube vacuum, along with the charge separation, to very long lengths, is there a point at which the separation of the charges would be so large that there would no longer be a dipole--any interaction between the charges would cease?

2.
It seems a little arbitrary that as I separate two charges, a greater torque is present as they rotate in an electric field. An explanation occurred to me that this larger torque is a result of the charges having to displace more space as they rotate. Is this an accurate position to take?

3.
First, please see the attached image for the formula for dipole potential that I am referencing. It is taken from:

http://en.wikipedia.org/wiki/Electric_dipole_moment (under the section potential and field of an electric dipole)

The key points being that the dipole potential is inversely proportional to the square of the distance from the dipole but proportional to the dipole moment. This is why WannabeNewton's post confused me, in that I took from it that the charge separation is not relevant to the potential field. Maybe my understanding of it is wrong.

So, perhaps I should have begun my first post (and probably this post too!) with the following hypothetical situation: If you view a two charge dipole side-on from very far away, like

<) → → ±

the dipole term of the potential decreases with the square of the distance. However, if I increase the separation between the charges, the dipole term of the potential increases. I could theoretically stand 100 meters from the dipole, yet separate the charges 10000 meters apart, and experience a potential from the dipole term as if I were one meter away (and the charges are separated by one meter). It is this logic, that an interaction between two particles, in this case opposite charges, increases with distance, that I am having trouble wrapping my head around. Is this just a fact of nature to accept, or can it be explained with even more fundamental physical interactions?

I know my questions probably seem out of context to someone who understands the bigger picture. I tried to make them specific to make it easier to answer. Again, I really appreciate any guidance here. I just couldn't find any other sources that talk about this. They simply define the electric dipole moment as p = d times r (analogously for the magnetic dipole moment), then move on right away to the applications of the dipole moment, and I'm still stuck scratching my head over what the dipole moment physically is!

Have a good day

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1. It all depends on the other charges. People have made dipoles with 2.5 kilometers (!) between the charges, but not using static charges. Instead they used oscillating charges to create an oscillating radio wave.

http://en.wikipedia.org/wiki/Herzogstand_Radio_Station

2. No. Think of the two charges as being stuck on the end of a stick. You rotate the dipole by rotating the stick about its center. The longer the stick the further the charges move. If the charges move agains an electric field, then the torque will be proportional to the distance traveled.

3. As you can see from the Taylor expansion, the dipole is an approximation for two separate charges when you are much further away (R) from the charges than the distance between them (d).

The case you describe is d>>R so the Taylor expansion diverges. The dipole approximation cannot be applied in this case.

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