Hello everyone. My understanding of a dipole moment is it defines the strength o

Question

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.

Explanation / Answer

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.

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