This article does not cite any sources. Please help improve this article by adding citations to reliable sources. Unsourced material may be challenged and removed. Find sources: "Spherical multipole moments" – news · newspapers · books · scholar · JSTOR(October 2010) (Learn how and when to remove this message)
In physics, spherical multipole moments are the coefficients in a series expansion of a potential that varies inversely with the distance R to a source, i.e., as Examples of such potentials are the electric potential, the magnetic potential and the gravitational potential.
For clarity, we illustrate the expansion for a point charge, then generalize to an arbitrary charge density Through this article, the primed coordinates such as refer to the position of charge(s), whereas the unprimed coordinates such as refer to the point at which the potential is being observed. We also use spherical coordinates throughout, e.g., the vector has coordinates where is the radius, is the colatitude and is the azimuthal angle.
and 27 Related for: Spherical multipole moments information
In physics, sphericalmultipolemoments are the coefficients in a series expansion of a potential that varies inversely with the distance R to a source...
A multipole expansion is a mathematical series representing a function that depends on angles—usually the two angles used in the spherical coordinate system...
Axial multipolemoments are a series expansion of the electric potential of a charge distribution localized close to the origin along one Cartesian axis...
\end{aligned}}} The orthogonality relations allow one to compute the sphericalmultipolemoments of a vector field as E ℓ m r = ∫ E ⋅ Y ℓ m ∗ d Ω , E ℓ m ( 1...
the structure is unknown or complicated. Multipole analysis offers a way to separate the radiation into moments of increasing complexity. Since the electromagnetic...
Cylindrical multipolemoments are the coefficients in a series expansion of a potential that varies logarithmically with the distance to a source, i.e...
terms are given by the toroidal multipolemoments as well as time derivatives of the electric and magnetic multipolemoments. While electric dipoles can be...
ordering constituted by high rank multipoles, e.g. quadruple, octople, etc. Due to the strong spin-orbit coupling, multipoles are automatically introduced...
sources using another type of multipole, which generalize the Weyl moments to mass multipolemoments and momentum multipolemoments, characterizing respectively...
longstanding of these is the low-ℓ multipole controversy. Even in the COBE map, it was observed that the quadrupole (ℓ = 2, spherical harmonic) has a low amplitude...
The Multipole Density Formalism (also referred to as Hansen-Coppens Formalism) is an X-ray crystallography method of electron density modelling proposed...
from electromagnetism, consisting of the interaction of the nuclear multipolemoments (excluding the electric monopole) with internally generated fields...
importance. They appear, for example, in the form of spherical atomic orbitals and real multipolemoments. The explicit Cartesian expression of the real regular...
spherical functions are replaced by polynomials that have been well known in electrostatics since the time of Maxwell and associated with multipole moments...
crystallographic point groups, the inclusion of higher order moments, i.e. multipolemoments of the charge density might be required. It is shown by electrostatics...
produced by a finite source, but external to it, can be represented by a multipole expansion. Each term in the expansion is associated with a characteristic...
relativistic bodies, including the influence of the coupling of their multipolemoments to the spacetime curvature of nearby objects, as well as writing down...
the interactive forces between instantaneous multipoles in molecules without permanent multipolemoments. In and between organic molecules the multitude...
system's magnetic dipole moment, which produces the first term in the multipole expansion of a general magnetic field. Both the torque and force exerted...
polarization), which is the attractive interaction between a permanent multipole on one molecule with an induced (by the former di/multi-pole) 31 on another...
Reynolds numbers. Faxén's laws are direct relations that express the multipolemoments in terms of the ambient flow and its derivatives. First developed...
fields are being developed to utilise multipolemoments, as opposed to point charges, given that multipolemoments can reflect the charge anisotropy of...
caused by polar moments within molecules. Multipoles could account for attraction between molecules having permanent multipolemoments that participate...
situation with the atomic electric dipole. Higher electric and magnetic multipolemoments cannot be predicted by this simple version of the shell model for...
Global Information
