The tag has no usage guidance.

learn more… | top users | synonyms

0
votes
0answers
15 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 ...
0
votes
0answers
39 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?
1
vote
1answer
113 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 ...
1
vote
0answers
57 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 ...
1
vote
2answers
45 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 ...
1
vote
1answer
64 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 ...
-1
votes
1answer
68 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 ...
2
votes
0answers
75 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 ...
0
votes
0answers
54 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 ...
2
votes
0answers
60 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 ...
0
votes
2answers
39 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 ...
2
votes
0answers
26 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
votes
0answers
46 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 ...
1
vote
1answer
128 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 ...
3
votes
3answers
109 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 ...
1
vote
0answers
84 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 ...
1
vote
1answer
169 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
votes
1answer
861 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 ...
1
vote
1answer
120 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?
4
votes
2answers
430 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 ...
3
votes
0answers
239 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 ...
2
votes
2answers
223 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 ...
5
votes
2answers
137 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
votes
0answers
189 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
votes
2answers
230 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
votes
1answer
94 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 ...
1
vote
1answer
257 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
vote
1answer
298 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 ...
10
votes
2answers
237 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. ...
2
votes
0answers
62 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
votes
2answers
142 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
votes
1answer
112 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 $\frac{1}{r^2}$. ...
5
votes
1answer
180 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. ...
9
votes
1answer
389 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 ...
1
vote
0answers
82 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, ...
1
vote
1answer
330 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 ...
3
votes
2answers
236 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 $l^{th}$ ...
3
votes
3answers
579 views

How does the gravity of a massive non-spherical object act on things around it?

Firstly, not sure if this question ought to be in the space SE site. Please let me know if it should. (Posted in both for now) Secondly, I don't know a whole lot about physics (I'm just inquisitive). ...
1
vote
0answers
71 views

Question about “quadrupole radiation” vector potential formula derivation

I tried to get an expression for $\mathbf A (\mathbf x )$ in quadrupole approximation. After some transformations of Liénard–Wiechert vector potential I got, as in many books, $$ \mathbf A \approx ...
1
vote
1answer
240 views

Potential of a dipole with actual physical extension?

I think everybody here knows the equation that gives the potential of a point like dipole, but how does the field look like if you have e.g. a metal sphere with radius $R$ and a certain dipol moment, ...
3
votes
1answer
818 views

Meaning of terms and interpretation in the electric multipole expansion

In section 3.4.1 of Griffiths' Introduction to Electrodynamics, he discusses electric multipole expansion. He derives the formula or the electric potential of a dipole, which I follow, but right ...
1
vote
1answer
220 views

Are multipole fields, multipole expansion, and multipole radiation the same thing?

Interaction between electromagnetic radiation and nuclei can be written in terms of multipole radiation. Are multipole fields, multipole expansion and multipole radiation the same thing? I have found ...
9
votes
2answers
597 views

Hexadecapole potential using point particles?

We can get monopole $1/r$, dipole $1/r^2$, quadrupole $1/r^3$ and octupole $1/r^4$ potential falloff by placing opposite point charges at the corners of a point, line, square and cube, respectively. ...
0
votes
0answers
499 views

What is the magnetic quadrupole moment of a nucleus in cylindrical coordinates?

What is the magnetic quadruple moment of a nuclei in cylindrical coordinates? The quadrupole moment of a nucleus is zero in spherical coordinates but in the cylindrical coordinates it can't be ...
10
votes
2answers
637 views

Forcing quadrupole moments to vanish for a neutral system

For a system of electric charges $q_i$, at positions $\mathbf{r}_i$, with a nonzero net charge $Q=\sum_i q_i$, one can define a "centre of charge" in the obvious way as $$ ...
0
votes
1answer
943 views

Simple quadrupole moment

I have a very simple problem: There is a charge $-q$ at $(0, 0, d)$ and $(0, 0, -d)$ as well a charge $2q$ at $(0, 0, 0)$. I have to calculate the quadrupole moment using spherical coordinates. I use ...
2
votes
1answer
159 views

Center of charge in quadrupol tensor

In theoretical classical electrodynamics we defined the quadrupol tensor of $n$ charges $q_k$ at positions (from origin or center of charge, see below) $\vec r_k$ like so: $$Q_{ij} = \sum_{k=1}^n q_k ...
5
votes
2answers
168 views

Computing a “best-fit” of discrete points from a multipole expansion, i.e. invert the multipole moments

Take a field $\phi(\bf{x})$ created from a charge distribution contained within a radius $R$. The multipole expansion in spherical harmonics $Y_{\ell,m}$ outside of $R$ is approximated by: $$ ...
3
votes
1answer
62 views

all multipolar terms of nuclear fields must be confined?

When usually speaking about QCD confinement, one refers to the fact that color charges over lengths above the hadron size are fully neutral, which implies that monopolar charges over an extended ...
2
votes
0answers
86 views

quadripolar moment in curved space

So, i'm going over the Thorne's derivation of the quadrupolar radiation term, and they write the core term as: $$ \frac{3 r_i r_j - 2 r^2 \delta_{ij}}{4 r^5} $$ But if i try to obtain this term by ...