# Electric field of two polar molecules

Why is it that for the case of two polar molecules the dipole moment does not depend on the electric field from the dipoles?

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turin
Homework Helper

Here is the question: Find the dependence of the van der Waals force on separation distance between two polar molecules.

Aren't Van der Waals force and dipole-dipole attraction two different things?

turin
Homework Helper
As I understand it (which is actually not very much), they are the same. More specifically, the Van der Waals force arises when the electron cloud of one atom/molecule induces a significant polarization on the nearby atoms/molecules and causes a chain reaction. I was not aware of the Van der Waals force between molecules that already have a dipole moment, but I suppose it is the same principle of attraction.

enkar,
regarding your original question, I don't know. I would be surprised to hear affirmation of this from an official source. I also think that the dipole moment and electric field should be related, so we are in the same boat with this question.

Well, it turns out that the dipole moment does not depend on the electric field. But I don't know why. That's what I'm trying to get here.

Gza
The dipole moment is used to describe how much of a torque an EXTERNAL electric field causes. It has nothing to do with the electric field of the charges that make the dipole moment.

But wouldn't a field be induced at the other molecule by the polarity of the first?

robphy
Homework Helper
Gold Member
Given two charges, +Q and -Q, separated by a displacement vector $\vec d$pointing from the negative charge to the positive charge, the dipole moment is defined by $\vec p = Q\vec d$. It is a quantity that describes the geometry of the arrangement of the two charges.

The molecules have equal charges. Would the fields effectively cancel each other resulting in no net effect?

turin
Homework Helper
I don't think so. From what I remember, the field of a charge distribution expands readily into a double infinite series of products of Legendre polynomials and spherical harmonics. For the dipole field, the zeroth order term vanishes, but the first order term is nontrivial. Unfortunately, I've trashed my EM notes (an an emotionally dominated decision), but I'm sure someone here has the expression (or is willing to sit and derive it). I still don't understand how the electric field from a dipole can be independent of the dipole moment. From the expansion, it directly depends on the charge and characteristic distance.

Gza
The molecules have equal charges. Would the fields effectively cancel each other resulting in no net effect?

To me at least, what happens between the charges that make up the dipole system is completely irrelevant in terms of what the dipole moment is for. You consider only the effects of external fields.

Doc Al
Mentor
polar molecules

enkar said:
Why is it that for the case of two polar molecules the dipole moment does not depend on the electric field from the dipoles?
The molecules have equal charges. Would the fields effectively cancel each other resulting in no net effect?
(2) about the electric field of a dipole? If so, realize that since there's a plus and minus charge close to each other, the field will drop off much more quickly than the field from a point charge. The field depends on: the dipole moment, the orientation with respect to the polar axis, and distance. For large distances, the field drops off as $1/r^3$.