Multipole expansions are related to the underlying rotational symmetry of the physical laws and their associated differential equations.
12.
The distortion potential \ psi ( r, \ theta ) in Eq ( 10 ) is given by the multipole expansion
13.
The spherical Hankel functions appear in problems involving spherical wave propagation, for example in the multipole expansion of the electromagnetic field.
14.
A magnetic dipole is something whose magnetic field is predominantly or exactly described by the magnetic dipole term of the multipole expansion.
15.
It can be shown that, if the charge distributions of the two monomers overlap, the multipole expansion is formally divergent.
16.
This finds use in multipole expansions of the vector potential in electromagnetism, or the metric perturbation in the description of gravitational waves.
17.
If observation is confined to regions sufficiently remote from a system of charges, a multipole expansion of the exact polarization density can be made.
18.
This term appears as the second term in the multipole expansion of an arbitrary electrostatic potential ? ( "'r "').
19.
The " higher orders " correspond to further terms of the multipole expansion of a function on the sphere in terms of spherical harmonics.
20.
Very close to the source, the multipole expansion is less useful ( too many terms are required for an accurate description of the fields ).
