quadrupoles

A quadrupole is a system of four electric charges or magnetic poles. In electrostatics, a quadrupole consists of four point charges arranged in a specific configuration. The most common arrangement is two positive charges and two negative charges, with opposite charges placed diagonally to each other. Another configuration involves two charges of one sign and two charges of the opposite sign placed along a line, with the charges alternating in sign. The electric field produced by a quadrupole falls off more rapidly with distance than that of a dipole.

In magnetism, a quadrupole consists of four magnetic poles, typically arranged as two north poles and two south poles. Similar to the electric case, opposite poles are often placed diagonally. Magnetic quadrupoles are widely used in particle accelerators to focus and steer beams of charged particles. The magnetic field of a quadrupole has a specific symmetry, causing particles to be focused in one plane and defocused in the perpendicular plane. This alternating focusing and defocusing effect, when applied in sequence, results in a net focusing of the particle beam. Quadrupoles also find applications in nuclear magnetic resonance spectroscopy and mass spectrometry.