Electric Quadrupole

A general distribution of electric charge may be characterized by its net charge, by its dipole moment, its quadrupole moment and higher order moments. An elementary quadrupole can be represented as two dipoles oriented antiparallel.

One of the most common uses of the electric quadrupole is in the characterization of nuclei. The nucleus has charge, but not dipole moment since it is all positive. But if the nucleus is not spherically symmetric, it will have a quadrupole moment.

Quadrupole and higher order multipoles are not important for the characteriztion of dielectric materials. Dipole fields are much smaller than the fields of isolated charges, but in dielectrics where there are no free charges, the dipole effects are dominant. There is no such circumstance favoring the quadrupole effects, since they must arise from the same number of molecules as the dipole effects. Scott says that the macroscopic quadrupole effects are smaller than dipole effects by about the ratio of atomic dimensions to the distances of experimental observation.

Linear Electric Quadrupole

A linear electric quadrupole can be created by superimposing two electric dipoles of opposite orientation so that their positive charges overlap. This case can be treated analytically and gives some insights into the nature of quadrupole fields. The electric field from any collection of charges can be obtained from Coulomb's law by vector addition of the fields from the individual charge elements.

This has shown that the distant electric field perpendicular to the quadrupole drops off like 1/r⁴. This 1/r⁴ dependence applies to other directions as well. In fact, it is characteristic of quadrupoles in general, although we have not shown that here. It is also a general characteristic of quadrupoles that the electric field depends upon the magnitude of one of the charges times the square of the dimension of the quadrupole, qd².