What is meant by quadrupole moment?

What is meant by quadrupole moment?

The quadrupole moment of a nucleus is usually defined1 as “the quantity (3z2 — r2)Av, where the average is taken over the nuclear charges for the state which has the maximum component of spin I in the z direction”.

What is monopole and dipole?

A dipole is a symmetrical device with two identical halves The equivalent monopole comprises one of the halves positioned over a groundplane such that its image in the groundplane replaces the second half.

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 do you mean by multipole expansion?

What is dipole and quadrupole?

3.8: 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. It has no net charge and no net dipole moment. Unlike a dipole, it will experience neither a net force nor a net torque in any uniform field.

What is the difference between electric dipole and dipole moment?

Now, the dipole moment definition is given as the product of the magnitude of charges and the separation between them. The dipole moment determines the strength of an electric dipole to produce the electric field. The direction of the dipole moment is always from the negative charge to the positive charge.

How does a monopole work?

The monopole is often used as a resonant antenna; the rod functions as an open resonator for radio waves, oscillating with standing waves of voltage and current along its length. Therefore the length of the antenna is determined by the wavelength of the radio waves it is used with.

Which is the correct definition of the dipole moment?

Dipole Moment The electric dipole moment for a pair of opposite charges of magnitude q is defined as the magnitude of the charge times the distance between them and the defined direction is toward the positive charge.

What is the goal of a multipole expansion?

A multipole expansion provides a set of parameters that characterize the potential due to a charge distribution of finite size at large distances from that distribution. The goal is to represent the potential by a series expansion of the form:

How is the moment of inertia of a point mass defined?

The moment of inertia of a point masswith respect to an axis is defined as the product of the mass times the distance from the axis squared. The moment of inertia of any extended object is built up from that basic definition. The general formof the moment of inertia involves an integral.

Why does the product of moment of inertia remain constant?

This is because the product of moment of inertiaand angular velocitymust remain constant, and halving the radius reduces the moment of inertia by a factor of four. With the appropriate balance of force, a circular orbit can be produced by a force acting toward the center.

https://www.youtube.com/watch?v=QNGYKWVOV54