# What is the point of multipole expansion?

## What is the point of multipole expansion?

Point multipole expansions are widely used to gain physical insight by providing a simplified expression for a complex distribution of sources of potential fields, such as electrostatic potential due to a charge distribution.

Which polynomial series is multipole expansion?

Legendre polynomials
Legendre polynomials form the basis for multipole expansion of spatially varying functions.

### How do you calculate quadrupole moment?

While a single charge is a scalar quantity, and a dipole moment is a vector quantity, the quadrupole moment is a second order symmetric tensor. px=∑Qixipy=∑Qiyipz=∑Qizi.

Why do we need 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 the significance of quadrupole moment?

The nuclear electric quadrupole moment gives a measure of the deviation of the nucleus, or more precisely of its charge distribution, from a spherical shape and hence is an important source of information about nuclear structure.

What is the significance of electric quadrupole moment?

## What is meant by quadrupole moment of nucleus What information do you get from it about the charge distribution of nucleus?

The nuclear electric quadrupole moment is a parameter which describes the effective shape of the ellipsoid of nuclear charge distribution. A non-zero quadrupole moment Q indicates that the charge distribution is not spherically symmetric.

What is meant by multipole radiation?

Multipole radiation is a theoretical framework for the description of electromagnetic or gravitational radiation from time-dependent distributions of distant sources. Multipole analysis offers a way to separate the radiation into moments of increasing complexity.