Is a capacitor a dipole? A few more questions about understanding dipoles

Question

I recently learned about dipoles, according to its definition I was wondering if a capacitor can be considered also as a dipole? Also I was wondering what is the physical meaning of the dipole moment $\vec{p}=qd$? And my last question is what is the motivation of studying dipoles? What is so special about it? From what I have learned it is just 2 equal and opposite charges that are a distance $d$ apart and they create an electric field according to what expected.

Answer 1

Capacitors are technically dipoles, but the two things are usually studied in opposite approximations. With a capacitor, you want to look at it up close, and calculate the electric field between the two plates, because it stores the most energy, and it's the quantity we want to manipulate.

Now, while a dipole is technically just two opposite charges, we are usually interested in what happens when we are far away from the two charges, at distances much larger than the distance between them. This is just a different approximation we can do; and in this approximation, the electric field depends only on the combination $q\, \mathbf{d}$, and not on $q$ and $\mathbf{d}$ separately, which is why we call that a dipole moment. This regime is interesting simply because it occurs often: for example, many molecules can be analyzed as dipoles. And if the approximation is too rough you can use the full multipolar expansion, of which the dipole term is just one part.

So in other words, you could take a capacitor to be a dipole with a certain dipole moment $\mathbf{p}$ and write its electric field using the dipole formula. But this is an approximation that applies far from the capacitor, where its electric field is very small. The interesting behavior (or at least the one that is relevant for circuits) happens inside the capacitor, where the dipole approximation doesn't work at all.

Answer 2

I will answer your first question. A capacitor is not necessarily a dipole. For example, a conducting wire surrounded by a conductor separated by an insulator is a capacitor but not a dipole.

Answer 3

No capacitor is not a dipole it is combination of oppositely charged plates so that electric fireplace within then is zero . The value of electric for any other system is different from that a dipole . The basic motivation for it's study is to understand the change in values of electric field and potential when a system consists of two oppositely charged bodies.

Answer 4

Since we believe that the universe is electrically neutral, any separation of positive and negative charges can be considered as a combination of electric dipoles.