multipole expansion

Any of these terms can be present in the multipole expansion of an electric field, for example.

This expansion is used to develop the normal multipole expansion.

This expansion is known as the multipole expansion of U.

The multipole expansion will no longer terminate, but the higher terms will be small.

In physics, this generating function is the basis for multipole expansions.

If the function being expressed as a multipole expansion is real, however, the coefficients must satisfy certain properties.

Very close to the source, the multipole expansion is less useful (too many terms are required for an accurate description of the fields).

See near and far field and multipole expansion.

Rather it means that if you write the distant electric field as a multipole expansion there is no monopole contribution.

The idea of using a multi-center multipole expansion was earlier proposed by Robert Rein.

Mathematically, the magnetic field of an object is often described in terms of a multipole expansion.

The multipole expansion is expressed as a sum of terms with progressively finer angular features.

A related approach is to divide the charges into those nearby the point of observation, and those far enough away to allow a multipole expansion.

However, in the multipole expansion of a magnetic field, the "monopole" term is always exactly zero (for ordinary matter).

The multipole expansion with angles is often combined with an expansion in radius.

Truncation of the multipole expansion to its first non-zero term is often useful for theoretical calculations.

In general, the fields of a source in a homogeneous isotropic medium can be written as a multipole expansion.

It can be shown that, if the charge distributions of the two monomers overlap, the multipole expansion is formally divergent.

This is the multipole expansion of the interaction energy of two non-overlapping charge distributions which are a distance R apart.

Multipole expansions are related to the underlying rotational symmetry of the physical laws and their associated differential equations.

Together, these approximate the sound field on a sphere around the microphone; formally the first-order truncation of the multipole expansion.

This term appears as the second term in the multipole expansion of an arbitrary electrostatic potential Φ(r).

Taylor expansion in d/R (see multipole expansion and quadrupole) allows this potential to be expressed as a series.

A toroidal moment is an independent term in the multipole expansion of electromagnetic fields besides magnetic and electric multipoles.

A multipole expansion is a mathematical series representing a function that depends on angles - usually the two angles on a sphere.