# Quadrupole

(redirected from*Electric Quadrupole Radiation*)

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## quadrupole

[′kwä·drə‚pōl]## Quadrupole

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/*R*^{4}). 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.

### REFERENCE

Landau, L. D., and E. M. Lifshits.*Teoriia polia*, 5th ed. Moscow, 1967, § 41.

G. IA. MIAKISHEV