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a system of charged particles whose total electric charge and electric dipole moment equal zero.
A quadrupole can be considered a set of two identical dipoles with the dipole moments equal in magnitude but opposite in direction and separated by a certain distance. At great distances R from the quadrupole, the field intensity of the quadrupole E decreases in inverse proportion to R to the fourth power (E∼ 1/R4). The relationship between E and the charges and their location is described in the general case by a set of five independent values that together constitute the quadrupole moment of the system. The quadrupole moment also determines the energy of a quadrupole in an external electric field. In the case described by Figure 1 the absolute value of the quadrupole moment is equal to 2ela, where e is the charge, 1 is the dimension of the dipoles, and a is the distance between the centers of the dipoles. A quadrupole is a second-order multipole.
REFERENCELandau, L. D., and E. M. Lifshits. Teoriia polia, 5th ed. Moscow, 1967, § 41.
G. IA. MIAKISHEV