Quadrupol

Quadrupol, also known as quadrupole, is a concept used across physics and engineering to describe a configuration or property associated with the second-order term in the multipole expansion of a field produced by a localized distribution of charge, mass, or current. In simple terms, the quadrupole moment measures how much a distribution deviates from spherical symmetry beyond a net charge (monopole) and a dipole moment.

In electrostatics, the potential of a localized charge distribution can be expanded in multipoles. If the net charge is zero and the dipole moment vanishes, the leading term is the quadrupole. The quadrupole moment is described by a rank-2 tensor Q_ij = ∫ ρ(r) (3 x_i x_j − r^2 δ_ij) d^3r. The resulting potential falls off as 1/r^3 at large distances and determines angular patterns of the field in the near region.

In chemistry and molecular physics, the molecular quadrupole moment is a measure of the charge distribution’s shape and influences intermolecular forces, dielectric properties, and spectral selection rules. It is particularly relevant for neutral molecules with zero dipole moment.

In nuclear physics and solid-state NMR, nuclei with spin I > 1/2 can have an electric quadrupole moment due to non-spherical charge distribution. In a nonuniform electric field gradient, the quadrupolar interaction splits nuclear energy levels, affecting NMR and Mössbauer spectroscopy.

In gravitational physics, the time-varying mass quadrupole moment is the leading source of gravitational waves in general relativity; changes in the quadrupole moment of an astrophysical system radiate energy, observed by detectors such as LIGO and Virgo.

In devices, quadrupole configurations appear in quadrupole antennas and quadrupole mass filters, which use specific field arrangements for directional radiation patterns or mass selection.