Is the Quadrupole Moment Non-Zero?

Thread starter ispivack
Start date Mar 18, 2020
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Moments Multipole

In summary, multipole moments are mathematical quantities used to describe the distribution of electric charge or mass in a system. They are calculated using integrals over the charge or mass distribution, and are important in understanding the shape and structure of molecules, atoms, and other physical systems. They have significance in many areas of physics and can be experimentally measured using techniques such as electric or magnetic field measurements, providing valuable insights into the structure and properties of a system. They are closely related to the symmetry of a system, with different symmetries resulting in different combinations of non-zero multipole moments.

Mar 18, 2020

ispivack

Homework Statement: Given ##\rho=(k/r)sin(\theta)cos(\phi)## for a sphere of radius R, find the lowest non-vanishing multipole moment.

Relevant Equations: General multipole expansion equation, as well as spherical harmonics (I think).

I have been throwing everything I can at this. I believe that both the monopole and dipole are zero, but I have no clue as to how to evaluate the quadrupole moment.

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Mar 18, 2020

DrClaude

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What is the formula to calculate the quadrupole moment?

Mar 18, 2020

kuruman

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If I did it right, the dipole moment has one non-zero component.

Last edited: Mar 18, 2020

What is the concept of multipole moments?

Multipole moments are a mathematical tool used to describe the distribution of charges or masses in a system. They are represented by a series of terms that indicate the strength and orientation of the charges or masses.

Why is finding multipole moments important?

Finding multipole moments allows scientists to understand the structure and behavior of complex systems, such as atoms, molecules, and celestial bodies. It also helps in the calculation of electric and gravitational fields and the prediction of their effects.

How are multipole moments calculated?

Multipole moments are calculated using integrals of the charge or mass distribution over a volume. These integrals are then used to determine the coefficients of the terms in the multipole moment series.

What are the different types of multipole moments?

The most commonly used types of multipole moments are the electric multipole moments, which describe the distribution of electric charges, and the gravitational multipole moments, which describe the distribution of masses. Other types include magnetic multipole moments and higher-order multipole moments.

How do multipole moments relate to other physical concepts?

Multipole moments are closely related to other physical concepts, such as the dipole moment, which is the first term in the multipole moment series. They are also connected to the concepts of symmetry and conservation laws, as well as to the properties of electric and magnetic fields.