# Questions tagged [multipole-expansion]

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### What would the multi-pole expansion of a spherical shell of magnets look like?

A singular magnet can be expanded in terms of the dipole term, while a set of four magnets with alternating sides facing the inside is described in terms of the quadrupole term. What would happen if ...
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What information does the quadrupole provide? I've seen many definitions on the internet, but I don't understand the relation between them. What is the relation between knowing that the quadrupole ...
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### Calculating multipole expansion outside uniformly charged sphere

When calculating the potential outside a uniformly charged sphere with charge density $\rho$ and radius R using the multipole expansion, it makes sense that only the monopole term survives (since it ...
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### What do moments of inertia do in the potential terms of Lagrangians?

I am struggling to understand the Lagrangian computed in this paper. In particular, a binary spacecraft-debris system is assumed as below. The analysis goes as follows. 1- I am in trouble to ...
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### Why is quadruple moment zero for spherically symmetric charge distribution about centre?

How can we show that for a spherically symmetric charge distribution, the dipole, quadrupole and all higher moments about the centre of the distribution are identically zero. As we already know that ...
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### Multipole moment of an octupole

I have a cube with each side of length a centered on the origin. Each of the corners carries a charge of magnitude q, but the sign of the charge alternates such that no edge connects corners with the ...
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### 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 ...
48 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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### Difference between monopole moment and charge or mass itself?

I'm trying to understand the difference between monopole moment and charge or mass itself. What I found is related to magnetic monopole that is irrelevant. I want to know in multiple expansion of ...
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### 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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### Electric quadrupole and octupole moments for nuclei

I am getting slightly confused as to which nuclei cab exhibit quadrupole and octupole excitations. In This link it says closed shell nuclei cannot exhibit quadrupole oscillations because if their ...
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### 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....
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### Quadrupole moment of Kerr spacetime

In this paper this paper, the Kerr black hole is described as having quadrupole moment of $q=J^2/M$ (which means $q=a^2M$ using $J=aM$) whereas in this paper it says in the abstract that the limiting ...
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### Griffiths Multipole Expansion and $Q$ going to zero

Griffiths states that given the multipole expansion: $$V(\vec{r})=\frac{1}{4\pi\epsilon_o}\sum_{n=0}^\infty\frac{1}{r^{(n+1)}}\int(\vec{r}')^nP_n(cos(\theta')\rho(\vec{r}')d\tau'$$ for large $r$ the ...