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# Questions tagged [multipole-expansion]

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124 views

### What is the minimal number of point charges required to model an electric octupole?

In an answer to this question, I showed that a general electric quadrupole can be modeled by a combination of seven point charges (or possibly less if one or two of the principal quadrupole moments is ...
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### How does a electric quadrupole oscillate?

I know that in static a electric quadrupole is made of two positive charges and two negative charges, distributed as in the following figure: What I don't understand is when it oscillates and ...
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### 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 ...
127 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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### 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 ...
628 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 ...
66 views

### Why gravitational waves can only be generated by a time-varying quadrupole moment of the mass distribution?

The (rather old) source I dispose of "Sexl, Urbantke : Gravitation and Cosmology" describes the radiation of gravitational waves only rather sketchy. So why gravitational waves are only generated by ...
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### Electrostatic polarization of an axially symmetric conductor

A single point charge at the origin induces charge onto a grounded Z-axis symmetric conductor. The induced charge is given in cylindrical coordinates as $\sigma(r, z)$ since the Z symmetry means there ...
54 views

### 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 ...
69 views

### 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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### 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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### 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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### Multipole expansion

consider a charge distribution say q, 2q, 3q, kept on the vertices of an equilateral triangle. There exist monopole, dipole ,qudrupole etc terms in the potential expression. these 3 charges are ...
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I was wondering if the $n=2$ term in the potential of a multipole: $V(r)= \dfrac{1}{4 \pi \epsilon_0} \sum \dfrac{1}{r^{(n+1)}} \int (r')^n P_n(cos \alpha) \rho(r')dv'$ was the same as this ...
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### What is the nature of the multipoles used to shape/re-direct an e-beam?

Imagine having an electron beam, just like in an electron microscope. Now imagine that we have some multipoles prepared in the beams path to influence the shape/path of the beam. My question is: ...
38 views

### Does a uniformly moving charge induce electric quadrupole moment densities in surrounding space?

The electric field of a uniformly moving charge is cylindrically symmetric around an axis parallel to its velocity vector. It varies inversely to the square of the distance. The electric field of a ...
42 views

### Is there a way to know the non-zero coefficient of $\cot(\theta)$ expansion in spherical harmonics?

I'm currently trying to find an analytical solution to the Poisson equation for a given distribution using a multipole expansion. During this task, I found the radial expansion and everything else, ...
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This is a very interesting problem that I've been struggling to solve for a week, so I decided to ask for some orientation, as I think it could also be of interest for the community. Let's consider a ...
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### The magnetic and electric dipole moment 'popping out' from multipole expansions

I interpret electric dipole moments and magnetic dipole moments as intrinsic properties of certain materials, but in Griffiths it's literally picked out of expressing the potential and magnetic vector ...
23 views

### How to extract quadrupole moment and its error from $\chi^2 < \chi^2 + 1$ surface?

I have following info: plot of $\chi^2$ minimization of 208-Rn Coulomb excitation data, Surface corresponds to regions $\chi^2 < \chi^2 + 1$ with error bars of 1$\sigma$, mean lifetime is 8 $\pm$ 0....
31 views

### Relevance of electromagnetic multipole transitions

In what kind of systems higher electromagnetic multipole transitions (like electric quadrupole transitions) become important or at least measurable? Is it for antennas in radiofrequency? Is it in the ...
I am trying to compute the polarisation moments in the tight coupling limit which is an exercise from Dodelson's Modern cosmology where the evolution equation is given by \dot{\Theta}_p+ik\mu\...