Electrodynamics/Dipoles and Multipoles

Introduction
In the previous sections of the book, charges and charge distributions have been treated in a general fashion. In this section of the book, we will allow for ordered charge configurations of which molecular matter is actually comprised of. For the most part, ordinary matter is electrically neutral, but it is highly saturated with pairs of charges called dipoles. For us, dipoles will be the building blocks of dielectric and magnetic materials.

Electric Dipole
An electric monopole is a single charge, and a dipole is two opposite charges closely spaced to each other, or something which looks like that electrically. Dipoles are actually very abundant in nature. For example, a water molecule has a large permanent electric dipole moment. Its positive and negative charges are not centered at the same point; it behaves like like two equal and opposite charges separated by a small distance. Another occurrence happens to uncharged pith balls. In presences of a charged object, the uncharged pith ball will be attracted to the charged object because the little dipoles have responded to the electric field of the rod.

The Electric Potential due to a Dipole
As it turns out, it is better mathematically to not think of dipoles as a collection of positive and negative charges but as a separate object all together. Take a moment and imagine two opposite charges with magnitude  Q  and they are separated by a small distance  s . The question to ask then is, what is the potential at some distance  r  away from the configuration?