What is a multipole in physics?

What is a multipole in physics?

A multipole expansion is a mathematical series representing a function that depends on angles—usually the two angles on a sphere. Multipole expansions are very frequently used in the study of electromagnetic and gravitational fields, where the fields at distant points are given in terms of sources in a small region.

What is the use of multipole expansion?

Multipole expansions are widely used in problems involving gravitational fields of systems of masses, electric and magnetic fields of charge and current distributions, and the propagation of electromagnetic waves.

What is octupole moment?

An extreme generalization (“point octopole”) would be: Eight alternating point charges at the eight corners of a parallelepiped, e.g. of a cube with edge length a. The “octopole moment” of this arrangement would correspond, in the “octopole limit” to a nonzero diagonal tensor of order three.

What is electric multipole?

In physics, the electric potential Φ, caused by—and outside—a non-central-symmetric charge distribution ρ(r), can be expanded in a series, the multipole expansion of Φ. This expansion is in terms of powers of 1/R, where R is the distance of a field point R to a point inside ρ.

Which polynomial series is multipole expansion?

Legendre polynomials
Legendre polynomials form the basis for multipole expansion of spatially varying functions. The technique allows for decomposition of the function into two separate parts with one depending on the radial coordinates only and the other depending on the angular variables.

What is multipole expansion of electric field?

What is electric Tripole?

In the multipole terminology, a “tripole” would correspond to a triplet (e.g. vertices of a triangle) of charges. If their total charge would be nonzero, there would be a leading “monopole” term. If the total charge cancelled, the system of 3 charges would still have a dipole moment.