Final answer:
In the multipole expansion of the electric potential, the quadrupole term involves the off-diagonal terms of the quadrupole moment tensor. It is related to electrostatics and arises from the multipole expansion, not directly from Coulomb's law. Coulomb's law relates to the electric force between point charges or spherical charge distributions.
Step-by-step explanation:
To address the student's question regarding the multipole expansion and the quadrupole term: the quadrupole term is part of the multipole expansion of an electric potential, which is used to describe the potential of a distribution of electric charges at points far from the charge distribution itself.
Returning to the student's question, we should start by clarifying that the term 'i ≠ j' means that the terms considered in the quadrupole expansion are those where the indices i and j are not equal, which refers to the off-diagonal terms in the quadrupole moment tensor.
This tensorial approach to the quadrupole moment becomes relevant when discussing the multipole expansion in the context of electrostatics, under the framework of Coulomb's law. However, the quadrupole itself is not directly derived from Coulomb's law, but rather from the multipole expansion of the electric potential.
Coulomb's law is the fundamental principle that describes the force between two point charges, and it's applicable for point-like charges or spherical charge distributions. In contrast, the multipole expansion, which includes the quadrupole term, is a tool that allows for the electric potential of more complex charge distributions to be described.
Meanwhile, Gauss's law, another key concept from Maxwell's equations, states that the electric flux out of a closed surface is proportional to the enclosed electric charge, which is also relevant to the idea of electric fields created by charge distributions.