What do you mean by multipole expansion?

A multipole expansion is a mathematical series representing a function that depends on angles—usually the two angles on a sphere. These series are useful because they can often be truncated, meaning that only the first few terms need to be retained for a good approximation to the original function.

What is multipole expansion of charge distribution?

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.

What does multi pole mean?

Definition of multipole : having or involving more than one pole (see pole entry 3) : multipolar sense 1 multipole particles multipole interaction a multipole magnet/connector.

What is electric multipole?

Multipole expansions are used frequently in the study of electromagnetic and gravitational fields, where the fields at distant points are given in terms of sources in a small region. A multipole moment usually involves powers (or inverse powers) of the distance to the origin, as well as some angular dependence.

What is monopole moment?

The monopole moment is the total quantity of whatever it is you’re considering. For example, if you’re looking at a 3-dimensional multipole expansion of the mass of the earth, the monopole moment would be the total mass.

What do you mean by electric quadrupole?

[i¦lek·trik ′kwä·drə‚pōl] (electricity) A charge distribution that produces an electric field equivalent to that produced by two electric dipoles whose dipole moments have the same magnitude but point in opposite directions and which are separated from each other by a small distance.

What is linear quadrupole?

A linear electric quadrupole can be created by superimposing two electric dipoles of opposite orientation so that their positive charges overlap. This case can be treated analytically and gives some insights into the nature of quadrupole fields.