A quadrupole is one of a sequence of configurations of electric charge or gravitational mass that can exist in ideal form, but it usually just part of a power series representation of a more complex structure reflecting various orders of complexity.

Electric multipoles

In the theory of electricity there are two signs of charge. The net total charge is the monopole moment. If there are charges of two signs, separated, for example along some line, then there is a dipole moment along that line. If there is no net charge, the lines of force resemble those of bar magnet, though they are electric, not magnetic. If there are charges of both signs, but separated in a more complicated way, an electric quadrupole, but not a monopole or dipole may be present. A simple configuration of that kind could be modeled with an insulating weathervane having letters N, E, S, and W as indicators. If there are, for example, four equal charges present, two of each sign, with the two positive charges on the N and S letters, and the two negative on the E and W letters, we have an electric quadrupole but no dipole or monopole! Configurations of electric charges of dipole and higher multipolar nature that change in time radiate electromagnetic radiation, whose character is named dipole, quadrupole, etc. according to a specific pattern generated by such sources. (There is no monopole radiation due to the conservation of electric charge, or Gauss' Law.) Time changes can be exemplified by oscillating or by rotating configurations.

Magnetic multipoles

Because magnetic monopoles have never been observed (though there was one contested observation), they are often assumed not to exist; certainly they cannot at the present time 2005 be made in the laboratory or put to any known use. Thus, the magnetic sequence, though similar to the electric one, begins with the dipole case. In terms of the above weathervane example, we would have a single bar magnet as a dipole. To make a quadrupole we could take two identical bar magnets, putting the North pole of one on North and its opposite end on East (sic!), while the other magnet would have its North pole on South (sic!) and its South pole on West (sic!). Such a configuration would have no dipole moment, and its field can be proven to decrease at large distances faster than that of a dipole - see below. Again, a changing dipole or quadrupole moment will lead to the production of electromagnetic radiation.

Gravitational multipoles

The situation here is similar in some ways to the magnetic case and in one way different. We do have gravitational monopole configurations and field; they are very commonly represented by ideal, stationary, spherically symmetric suns, planets, and so on. But, because no negative gravitational mass has ever been found, we have no possibility for a dipole moment. A gravitational quadrupole can be represented by two massive balls (say, lead) on opposite ends of a light rod, or, more simply, just as a long massive rod or a thin massive disk. A football shaped (prolate) or spheroidal (oblate) mass has a quadrupole moment. For example, the Earth is flattened at the poles, so it has a quadrupole moment. If a quadrupole (or higher order multipole ) of mass rotates or oscillates (in vibration) it will emit gravitational radiation.

Distance dependence of multipole fields

The sequence monopole, dipole, quadrupole. can be extended to higher orders. A simple quadrupole is constructed by placing two opposing dipoles near each other, an octupole by adding another opposing quadrupole displaced from the one just made, and so on. The static fields of electric and magnetic multipoles fall off more and more rapidly as one moves away to an increasing radius r from the center. A monopole field (as for a single electric charge, or a single mass in Isaac Newton's law of universal gravitation, falls off with the inverse square law. A dipole field falls off as the cube of the distance, an octupole as the inverse fourth power, and so on.

When varying configurations of charges, currents, or masses are present, however, radiation is generally produced, and the radiation field falls off only as the first power of the distance, at large distances.

• Multipole expansion