Fr.: multipôle électrique
An electric → charge distribution consisting of more than four → positive and → negative → electric charges located at a small distance from each other. The multipole concept is an extension of the → electric quadrupole. For the generalized multipole characterized by the letter l, the potential at a distance r varies as 1/rl + 1 and the field intensity as 1/rl + 2.
An entity consisting of several poles.
Fr.: indice multipolaire
A variable used in → spherical harmonic expansions. Each spherical harmonic is characterized by its multipole index l: l = 0 for a → monopole, l = 1 for a → dipole, and so on. It is used in particular to describe the → cosmic microwave background anisotropy: ΔT/T0 (θ,φ) = Σ almYlm(θ,φ), where θ and φ are the → spherical polar coordinates, Ylm is the → spherical harmonic functions, and the sum runs over l = 1, 2, ..., ∞ and m = -l, ..., l, where the multipole index l corresponds to angular scales ≅ 180°/l.
Fr.: moment multipolaire
The quantity that gives the electric potential field due to a distribution of charges, such as a → dipole, → quadrupole, → octupole, etc. A multipole moment usually involves powers of the distance to the origin, as well as some angular dependence.