Question

define dipole moment ?

Answer 1

There are a number of ways to do that. The most formal and precise is rather mathematical: you expand the electric field produced by an arrangement of charges in a set of radially-symmetric functions (functions that depend only on distance r from the origin) multiplied by spherical harmonics (functions that depend only on angular coordinates). The coefficient of the first nontrivial spherical harmonic (the first function that isn't a constant) is the dipole momet of the collection. Ugly, no?

From a physical standpoint: if a collection of charges is overall neutral (so you have equal positive and negative charges) *but* there is some asymmetry to the collection, so that, if you stand far away, you see an electric field attractive to positive charge on one side of the collection, and an electric field attractive to negative charge on the other side of the collection, then your collection has a dipole moment. It is, in essence, the form of electric field that is next most "complicated" than the field of a single point charge.

Another way to think of it is that you can arrange "basic" types of electric field by their angular symmetry, and this has close mathematical connections to the elecrtron orbitals of an atom. If the field has the symmetry of an s orbital (spherically symmetric) then it is a monopole field. If the field has the symmetry of a p orbital (positive on one side, negative on the other) then it is a dipole field. If the field has the symmetry of a d orbital it is a quadrupole field, and so forth.

It can be shown that ANY electric field can be written as a combination of monopole, dipole, quadrupole....et cetera...fields, multiplied by appropriate coefficients, which should remind you, if you have studied quantum mechanics of the way you can build up any wavefunction from a set of eigenfunctions, or, if you have studied electrodynamics (or even radio) of the way you can build up any electromagetic wave from sine waves of various frequencies. It's all the same idea, the superposition principle. It's just with multipole moments what you're building up is an angular dependence -- a way in which a field changes in different directions -- and the math for that is a bit more complicated. The coefficients of the various multipole fields necessary to build up any actual field are called the multipole moments of the field. The monopole moment is just the total charge, and the next higher is the dipole moment.