# Questions tagged [multipole-expansion]

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### Exploring Quantum Wiggles with AI: Gravitational Waves and the Double-Slit Mystery [closed]

I would like to preface this by stating that I am by no means a physicist, but I am an engineer who can't stop thinking about how similar the macrocosmic universe is to the quantum realm. I asked ...
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### Meaning of electric dipole moment

what is the meaning of electric dipole moment? Or why do we need to define electric dipole moment?
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### Multipole expansion, same charges

I know dipole is defined with 2 opposite charges. That's why in EM dipoles exist, while in gravity they do not. However, I view multipole expansion as a way to describe how the distribution of charges ...
1 vote
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### Multipole expansion and spectral decomposition

We can always write a Hermitian operator in the form of its spectral decomposition: $\hat{A}=\sum_i \lambda_i | \chi_i(\boldsymbol{r})\rangle\langle\chi_i(\boldsymbol{r}')|$ where $\lambda_i$ are the ...
1 vote
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### Conservation of angular momentum in electric quadrupole transition

I know that We can classify radiative transitions of electrons between different energy levels as electric multipole transitions or magnetic multipole transitions. My question is: In electric ...
1 vote
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1 vote
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### Can ideal dipoles be associated to a covariant four-current?

I am trying to check if the classical electromagnetic sources from a point electric/magnetic dipole do form a true four-current. In this SE post, it is shown that a point electric charge do transform ...
1 vote
118 views

### Star with quadrupole in binary system violates Newton's 3th law?

Suppose that, in a binary system of two stars, the star A (and only the star A) has a non-zero quadrupole moment $Q_A$. Then, the star B feels the usual gravity force plus an additional force, ...
44 views

### Using spherical harmonics for the charged interaction of particles

I am currently inversitgating a system consists of positive and negative point particles satisfying charge neutrality condition. They have a unit charge +1 and -1. In most case, we deal with coulomb ... 39 views

### Product of rank-2 spherical tensors

I have been reading up a lot of material on spherical tensors to try and help me with a calculation of the electric quadrupole energy shift of an atom, and have run into a block due to my lack of ...
64 views

### How are multipolar expansion of earth magnetic field computed?

In the study of the geomagnetic field, an expansion in spherical harmonics is used to represent the scalar magnetic potential: the first terms give the dipole approximation, then the quadrupole, etc. ...
1 vote
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### Multipole Expansion of Point Charge at Origin

The multipole expansion for the potential of some collection of point charges can be written as $$V=\frac{1}{4\pi\epsilon_0r}\sum_{i}q_i\sum_{n=0}^{\infty}(\frac{r_i}{r})^nP_n(\cos\alpha)\,,$$ where ...
27 views

I read that, the principle of the magnetic quadrupole trap confining is that an atom, with a magnetic dipole moment, subjected to a inhomogeneous magnetic field, is driven towards the point where the ...
1 vote
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### Why is the quadrupole moment of a spherical object equal to zero (when looking at the formula in cartesian coordinates)?

Is there a simple way to understand why $$\int \rho(x,y,z) (2z^2-x^2-y^2) dxdydz$$ is equal to zero if the density has spherical symmetry?
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### Is it true that an electric monopole does not radiate? [duplicate]

In the third edition of Griffith's Introduction to Electrodynamics, in section 11.1.4, he says that an electric monopole does not radiate because the electric charge is conserved. But we do know that ...