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### 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 ...
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### 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 ...
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### 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 ...
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### multipole moments of dipole with finite spacing

Can a dipole with finite spacing between poles be represented by pure multipoles centered at the origin? Say for example that I have a dipole with finite spacing $2\epsilon$ between the poles. I ...
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### General expression for electromagnetic toroidal moments

I'm reading about this third family type of multipole moments (independent from the usual electric and magnetic moments), called "toroidal multipole moments". The first multipole term in the expansion ...
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### What is the affection of stress tensor of spacetime by the energy/mass density moment of a photon? [closed]

First of all what kind of moment exhibits the photon under its propagation to spacetime continium -quadrupole,dipole or monopole! Please, explain me- why. Do Give some arguements! When it propagetes ...
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### 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 ...
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I've been doing some exercises in my workbook and every time I came across a problem involving a quadrupole moment it was always assumed that it was traceless without providing any proof (at least ...
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### Method of image charges (hemisphere on metal) (2) [duplicate]

This is a continuation from Method of image charges (semisphere on a metal) . nbubis helped me a great deal concerning this problem and in this post I want to address my problem with the computation ...
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### Method of image charges (semisphere on a metal) (2)

This is a continuation from Method of image charges (semisphere on a metal) . nbubis helped me a great deal concerning this problem and in this post I want to address my problem with the computation ...
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### 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 ...
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### What is the location of point charge with respect to the original charged body?

we say if distance between two charged bodies is large as compared to its size then we take them as point charges and assume all its charge content to be concentrated at one point in space. What is ...
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### Quadrupole and Multipoles in Physics

I am a little confused over the notion of quadrupole and higher moments in physics in general. The first time I saw it was in electromagnetism, when we did multipole expansion to analyze higher ...
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### External and internal multipole expansion for axisymmetric potential - the region of convergence

Say, we have a system of electrodes exhibiting symmetry around a certain axis. We know the explicit expression for the potential on the axis $\phi (z)$. We want to find the potential for any point in ...
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The general solution to the 2D Laplace equation, $\nabla^2 \psi = 0$ is \begin{align} \psi(r,\theta) = P_0 \ln r + \sum_{k = 1}^\infty \dfrac{Q_k \cos(k\theta)+R_k\sin(k\theta)}{r^k} \end{align} The ...
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### 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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### 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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### 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 \begin{...
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### 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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### 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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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}|}\... 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 ... 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}... 1answer 28 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 ... 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, ... 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". 0answers 23 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 ... 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 ... 0answers 55 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 ... 0answers 54 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? 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 ... 2answers 76 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 ... 0answers 78 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 ... 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 ... 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). ... 1answer 284 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$$\psi(\textbf{r})=\frac{\textbf{p}\centerdot\textbf{r}}{4\pi\epsilon_0r^...
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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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### 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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### 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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### 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 \vec{r}-r^2\hat{I}...
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### 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 ...
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### 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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### 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 ...
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. ...