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18
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2answers
1k views

Why there is no dipole gravitational wave?

I have read that "thanks to conservation of momentum" there is no dipole gravitational radiation. I am confused about this, since I cannot see the difference with e.m. radiation. Is this due to the ...
11
votes
2answers
265 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. BICEP-...
10
votes
2answers
812 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 $$ \mathbf{r}_c=\frac{1}{Q}\...
10
votes
1answer
543 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 ...
9
votes
2answers
896 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. ...
9
votes
2answers
178 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 ...
5
votes
1answer
215 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. 1-...
5
votes
2answers
189 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: $$ \phi({\...
5
votes
2answers
179 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 ...
4
votes
2answers
524 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 ...
4
votes
3answers
3k views

What is the physical meaning of the terms in the multipole expansion?

I have a few questions on multipole expansions and I have read about the topic in many places but could not find an answer to my questions, so please be patient with me. The electrostatic potential ...
4
votes
1answer
66 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 ...
4
votes
1answer
117 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 ...
3
votes
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 ...
3
votes
3answers
147 views

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 \left(\frac{r}{|\mathbf{x}|}\...
3
votes
2answers
345 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 ...
3
votes
3answers
865 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). ...
3
votes
1answer
1k 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 ...
3
votes
3answers
174 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 ...
3
votes
1answer
146 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 $\frac{1}{r^2}$. ...
3
votes
1answer
98 views

Method of image charges (semisphere on a metal)

I'm currently trying to study ahead for the upcoming semester since I'm on break and I'm stuck on the method of image charges. I've tried watching some youtube videos on that topic and I thought I ...
3
votes
2answers
201 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
2answers
109 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, ...
3
votes
2answers
259 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
1answer
81 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 ...
3
votes
0answers
45 views

Can gravitational waves observed far from a black hole tell us anything about the multipole moments of a dynamical horizon?

In a paper by Ashtekar et al in 2013 on the approach to the final state to a stationary black hole they study the evolution of the multipole moments of dynamical horizons, which relax away (except for ...
3
votes
2answers
188 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 ...
3
votes
0answers
357 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
270 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 non-...
2
votes
1answer
65 views

Do gravitational waves radiate isotropically?

Do gravitational waves radiate equally in all directions? If so, is this an inherent property of all gravitational waves or is it just due to how they are normally produced? In other words, in a ...
2
votes
1answer
683 views

What is the magnetic quadrupole operator?

To find magnetic or electrical moments in quantum theory we must calculate the expectation value of an appropriate operator. The dipole operators are similar and are easy to find but I couldn't find ...
2
votes
1answer
180 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 \...
2
votes
1answer
61 views

Dipole moment of a single point charge

Kindly refer to the Multipole Expansion section (chapter 3) of David Griffith's Introduction to Electrodynamics. Let us first discuss about why multipole expansion is needed. As far as I understand, ...
2
votes
1answer
297 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
0answers
97 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 ...
2
votes
0answers
73 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 ...
2
votes
0answers
32 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
1answer
63 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 \sqrt{\frac{4\pi}{2l+1}...
2
votes
0answers
282 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 ...
2
votes
0answers
69 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 \omega_0\rangle+\frac{\...
2
votes
0answers
88 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 ...
1
vote
1answer
71 views

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 ...
1
vote
1answer
363 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 ...
1
vote
1answer
167 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
1answer
43 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".
1
vote
1answer
229 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?
1
vote
1answer
384 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
510 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 ...
1
vote
1answer
407 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 ...
1
vote
1answer
318 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, ...