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Physical meaning of multipole moment

Is there a physical interpretation for multipole moments? For a quantity governed by the Laplace equation ($\nabla^2 \omega = 0$), I understand that the general solution is given by the multipole ...
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72 views

From your 2 point charges, does the electric field fall off like $\frac{1}{r}$ or $\frac{1}{r^2}$? [closed]

From your 2 point charges, does the electric field fall off like $1/r$ or $1/r^2$ , or somewhere in between. To determine the behavior, calculate the coordinates for several equipotential surfaces and ...
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20 views

strength of each dipole charge

If I have a two dimensional dipole whose line charges are located on the y axis, I know that the electric flux through a gaussian pill box containing both the charges will be zero, that is ...
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24 views

Series expansion of potential due to a dipole displaced from the origin

I learn that we can expand the electric potential in an infinite series of $\rho$ and $\cos(n \phi)$ when solving the Laplace equation in polar coordinates. The problem I want to consider is the ...
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1answer
25 views

Is the transition electric quadrupole or magnetic dipole?

If a nucleus makes a transition from 0$^+$ ground state to 2$^+$ excited state, then will the transtion have E2 character, or M1? Or partly, both? Should the matrix elements of both E2 and M1 be ...
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Why is the gravitational multipole expansion taken with the origin at the centre of mass instead of the centre of gravity?

Wikipedia's article on the multipole expansion of the gravitational potential expands it as $$ V(\mathbf{x}) = - \frac{GM}{|\mathbf{x}|} - \frac{G}{|\mathbf{x}|} \int ...
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155 views

What are the advantages of multipole expansion of potentials?

When I see the equations of multipolar expansions they "look" to me harder than the original expressions. For example: Multipole expansion - spherical form, in Wikipedia I bet that this is not ...
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1answer
21 views

Numerical computation of electric multipoles

I'm trying to do a plot of the first multipole terms in Mathematica. My plot isn't what I expected, so maybe my problem is in the mathematics. Following the Griffiths' book on Electrodynamics, the ...
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34 views

Where does the net charge on a hemisphere appear to act from?

I was wondering if, like centre of mass, there is anything called "centre of charge".
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21 views

find cylindrical multipole coefficients

How does one find the coefficients to the cylindrical multipole expansion? I have the harmonic function $\omega = \dfrac{f(\theta)}{\sqrt{r}}$ where $f(\theta)$ is function with a period of $2\pi$ ...
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2answers
117 views

Multipole expansion in cylindrical coordinates

I am seeking the general solution for the Laplace equation in cylindrical coordinates or $$\nabla^2 \omega = 0. $$ In several texts, the general solution can be found via separation of variables ...
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0answers
39 views

Positive/negative octupole moment of nuclei?

Does octupole moment of nuclear charge distribution show any positive/negative character, like the quadrupole moment does? Quadrupole moment has prolate and oblate types, but what about ...
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1answer
61 views

Introductory literature on the multipole expansions including toroidal moments

I wish to understand the general idea of the multipole expansion in the context of classical electrodynamics and, especially, the concept of the toroidal moments. All the papers on the subject I've ...
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23 views

Giant dipole resonance

Could anyone explain in simple words what exactly is meant by GDR? What does giant imply? I have read about collective excitations and am also familiar with the multipolar form of the charge ...
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0answers
53 views

Multipole expansion of Woods-Saxon potential?

When can a distribution be expanded in multipoles? What is the basic requirement? Can it be done for a potential like the Woods-Saxon form?
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1answer
145 views

Physical intuition for quadrupole source

In his Theory of Vortex Sound M. S. Howe defines sources "mathematically" (i.e. dipole is a source that could be described as a vector and than there is proved that it's equivalent to a two point ...
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69 views

How does the Wigner-Eckart theorem rule Multipole Expansion?

I am wondering why a spin-S particle have only the term up to $k=2S$ in his multipole expansion ? It seems that the Wigner-Eckart theorem shows the relation between spin and multipole expansion but I ...
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2answers
66 views

What determines the factors of the multipole expansion?

The multiple expansion of a potential V has contributing terms proportional to $\frac{1}{r^{n+1}}$ where $n=0,1,2...$. First, why are we interested only in integer powers of r? Second, why are we ...
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1answer
171 views

Find out gradient of electric potential at ${\bf r}$ created by eletric dipole of moment ${\bf p}$ [closed]

Suposing an electric dipole of moment ${\bf p}$ located at the origin which creates an electric potential at ${\bf r}$ given by ...
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1answer
118 views

The Electric Quadrupole

I've read the following sentence: "Every electric circuit with two pairs of accessible terminals is called a quadrupole." I was wondering why does it happen that the multipole expansion gives us a ...
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92 views

Higher order multipolar second harmonic generation in centrosymmetric materials

As is pointed in this question, second harmonic generation is forbidden in the bulk of the materials possessing centrosymmetry. In some papers it is said that in the dipolar approximation the SHG ...
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88 views

Transverse Trace-less quadrupole

In Gravitational radiation, it is convenient to work with "transverse traceless quadrupole tensor". However there are three terms: "quadrupole moments" , "reduced quadrupole moment" and "transverse ...
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0answers
67 views

Physical significance of toroidal moments

The electric field of a toroidal dipole moment $\vec t$ is the same as the electric field of a electric dipole moment $\vec p$, except that it is scaled with the factor $ik$. The $i$ makes the ...
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2answers
44 views

Is it inevitable to compute the quadruople tensor in components? Why? [closed]

I was trying to determine the quadrupole tensor for a given charge distribution in one go from this equation: $$\overleftrightarrow{D}=\int d^3r \varrho(\vec{r})\left(3\vec{r} \circ ...
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0answers
30 views

Approximating electrostatic grids as a multipole expansion

Is there a known good summary, or a succinct algorithm to compute the far-field approximations of an arbitrary set of electrostatic surfaces set at different potentials? I'm looking to model a ...
2
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1answer
57 views

Magnetic Multipole Tensor

When the electric scalar potential is expanded into spherical coordinates, one gets \begin{align} \phi (\vec r) = \frac{1}{4\pi\varepsilon_0} \sum_{l=0}^{\infty} \sum_{m=-l}^l ...
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1answer
240 views

Traceless multipole moments vs non-traceless moments

There are two different possibilities to define the electric quadrupole tensor: On the one hand, one can define \begin{align}Q_{kl} = \int \rho(\mathbf r') \cdot r'_k \, r'_l d^3r',\end{align} while ...
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3answers
138 views

Why monopole does not radiate energy in electodynamics?

Why there is no monopole radiation in Electromagnetic field? I read somewhere that it is impossible because it violates charge conservation. I don't understand how? How charge conservation gets ...
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0answers
107 views

Potential due to a Uniform Ring [closed]

Consider a uniform ring of mass $M$ and radius $a$ (?). I would like to prove that for $r > a$: $$\Phi(r) = \frac{GM}{r} \sum_0^\infty[P_n(0)]^2 \left(\frac{a}{r}\right)^n $$ Where $\Phi(r)$ is ...
2
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1answer
231 views

Why three families of multipole moments?

There are three families of multipole moments: The electric multipole moments, the magnetic multipole moments and the toroidal multipole moments. Is there any reason why there are this three families ...
2
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1answer
1k views

Existence of Tripoles?

With multipole expansions, we speak only of monopoles, dipoles, and $2^n$-poles. Why is there nothing like a tripole? So how would something like $rsin(3 \theta)$ be expressed with a multipole ...
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1answer
177 views

Magnetic multipoles in spherical harmonic

Does someone know explain me how to identify the multipoles magnetic terms of the multipolar expansion (Dipole, quadrupole, etc) in spherical harmonics?
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2answers
480 views

One question about sextupole

In multipole expansion, we use monopole, dipole, quadrupole or octupole to describe an electromagnetic field. But I saw someone use sextupole to describe transition states. If we expand an ...
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0answers
302 views

Electrodynamic multipole expansion

I am reading Jackson, Classical Electrodynamics, and I have a question regarding the electrodynamic multipole expansion (with page numbers I refer to the 3rd edition). So on page 409, he gives in ...
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2answers
249 views

Rotation of Taylor expansion of a scalar

I have a scalar magnetic field in a volume expressed by the formula $$B(x,y)=B_0 + \frac{\partial B}{\partial x}(x-x_0) + \frac{\partial B}{\partial y}(y-y_0)$$ which approximates the ...
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2answers
165 views

Potential generated by a hollow sphere with a hole

The sphere has radius $R$ and is missing its "pole" - meaning that in the area $\theta\leq\alpha$ there is nothing. The object has a homogenous charge density $\sigma=\frac{Q}{\pi R^2}$ I'm trying to ...
2
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0answers
238 views

The anapole moment, derivation from Dirac current density

Basically I am looking for a way to expand the electromagnetic interaction energy $W = A_{\mu}j^{\mu}$ (both $A$ and $j$ obtained from the Dirac equation) similar to the classical expansion in ...
3
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2answers
311 views

What is the first non-vanishing multipole moment of this configuration?

Imagine that you have a triangle where each side has the length $a$ and a charge $q$ sitting at every vertex. Additionally, we have a charge $-3q$ sitting in the center of the triangle. What is the ...
4
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1answer
107 views

Toroid moments tensor decomposition

I am currently working on my bachelor's thesis on the anapole / toroidal moment and it seems that I am stuck with a tensor decomposition problem. I have actually never had a course about tensors, so ...
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1answer
326 views

quadrupole moment and higher for simple current loop

I'm working on a field configuration that needs to die off rapidly and I got to a $1/r^5$ dependence with canceling the dipole moment of the system cleverly, but to go get better arrangements I need ...
1
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1answer
433 views

Clarification of multipole expansion for a point charge

In Griffith's electrodynamic: 3.4.2 He pointed out that the monopole term is the exact potential for a single point charge. However I was under the impression that different configuration of a ...
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2answers
257 views

What's the $\ell$ in the Bicep2 paper mean?

The BICEP experiment's recent announcement included the preprint of their paper, BICEP2 I: Detection of $B$-mode polarization at degree angular scales. BICEP2 Collaboration. To be submitted. ...
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0answers
67 views

Proton as superposition of hadrons: $\vert p\rangle = c_0\vert p_0\rangle+c_1\vert h\rangle+\cdots$

I have a question regarding hadron fluctuations. For instance on page 85 in Feynman's "Photon-Hadron Interactions" equation 15.2 reads: $$\tag1\vert \omega\rangle = \vert ...
3
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2answers
183 views

Objective measure of anisotropy

If we know a function $f(\phi, \theta)$ in $\mathbb R^3$ only over a convex surface (which for simplicity let's assume a sphere of radius $r$), is there any measure for the degree of anisotropy over ...
3
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1answer
131 views

Intuitive explanation of difference in $r$-dependence between dipole and monopole

For an electric monopole, its potential scales with $\frac{1}{r}$, where $r$ is the distance from the point of interest to the charge. However, for a dipole, its potential scales with $\frac{1}{r^2}$. ...
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1answer
202 views

How do aspherical gravitational monopoles look like?

I was recently pointed by laboussoleestmonpays to a beautiful paper from some time ago, Aspherical gravitational monopoles. Alain Connes, Thibault Damour and Pierre Fayet. Nucl. Phys. B 490 no. ...
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1answer
436 views

Does a pendulum necessarily emit gravitational waves?

A question about the behaviour of a pendulum in a frictionless vacuum recently made it back to the front page, and a few comments below John Rennie's excellent answer set me thinking about one ...
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2answers
106 views

Any quadrupole approximation? Any example?

In atomic and molecular physics we quite often encounter with electric dipole approximation. The dipole approximation we do when the wave-length of the type of electromagnetic radiation which induces, ...
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1answer
377 views

Density matrix and irreducible tensor operators

I'm reading those lecture notes on atomic physics. Yesterday I posed a question on reducible tensors, and today I have a question on their relation to the density matrix. If there's any information ...
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2answers
252 views

Why 3 dipole terms in a multipole expansion?

As can be seen on this page http://en.wikipedia.org/wiki/Multipole_expansion when we take a multipole expansion without assuming azimuthal symmetry we end up with $2l+1$ coefficients for the $l^{th}$ ...