Physical meaning of electric dipole moment I am reading about the electric dipole moment. What I can't understand, and seems that no one cares to explain, is what is the physical meaning of it. To my understanding everytime that dipoles are "examined" the dipole moment is essential regarding to the understanding of their properties, but I don't understand what is its physical meaning and why it is so important to dipoles.
 A: The dipole moment is defined as a system of two charges that are very close to each other. In doing so, we find that there the potential now experimentally measured is inversely proportional to the square root of the distance between the centre of dipole to the measuring point and is directly proportional to the cosine of angle as measured from the line joining the two charges. Now barring the constants we have an extra term which dictates the strength of the electric field which is given by $p = q.d$ where d is the distance between the two charges.
The physical importance of the dipole moment term in the electric potential can now be easily understood to be the second order term $(0(1/r^2))$ in the electric potential, where the first order term has been cancelled out due to equal charges placed closely and so giving a net charge 0$(O(1/r))$. So physically the dipole moment is a measure of the residual electric potential that remains even if the the net charge of the system is zero. 
A: Imagine a dielectric is placed in an electrid field. We want to study its effect on electric field. It can be proven its electric effect can be described only with its charge (which is assumed to be zero) and its dipole vector density. So for instance it is important to know what is the electric potential of a dipole; because once you know the effects of a small charge and a small dipole, then you know the effect of all dielectrics with precision.
