Questions tagged [dipole-moment]

Dipole moment is the electrostatic moment generated by two opposite charges taken together, far away from the charge's locations

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How to prove resonant medium $\frac{d^2P}{dt^2} + \gamma\frac{dP}{dt} + \omega_0^2P = \omega_0^2 \epsilon_0 \chi_0E(t)?$

I need to show the equation from a resonant medium $$\frac{d^2P}{dt^2} + \gamma\frac{dP}{dt} + \omega_0^2P = \omega_0^2 \epsilon_0 \chi_0E(t)$$ where $$\omega_0 = \sqrt{\frac{k}{m}}$$ and $$\chi_0=\...
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+100

Dielectric constant of crystals: Feynman's mistake?

Feynman mentioned in his lecture that we can, in some way, obtain dielectric constant of crystals by summing up the electric field due to dipoles. For example, equation (11.33) from above link shows ...
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Behavior of a Pointlike Dipole

I have a practice problem in my textbook that I'm not sure how to approach. It asks to find the force of an electric field created by an infinitely long line of charge of density $+\lambda_0$ (which I ...
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40 views

Is the dipole moment of a polarized particle supposed to be a constant?

Problem $4.4$ A point charge $q$ is situated a large distance $r$ from a neutral atom of polarizability $\alpha$. Find the force of attraction between them. Source: Griffiths, Electrodynamics ...
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GUI for DFT calculations

I am a beginner in DFT. Can someone suggest a good DFT software with a GUI for simulating dipole moment directions and optical absorption spectra in an organic crystal? I have tried Burai. But it ...
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80 views

If dipole moment is a vector $q×d$, then is charge a vector?

If I am right you can only do vector product for vectors. Here you have dipole moment $= q×d$. Then are we assuming charge is a vector? But how then does charge obey the triangle law of vector ...
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Electric dipole moment, formula derrivation

I want to derive the formula for the potential energy of an electric dipole $$ U = - \overrightarrow{p} \cdot \overrightarrow{E} $$ where $\overrightarrow{p}$ is the electric dipole moment and $\...
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98 views

What is the physical significance of defining the dipole moment as a vector?

I don't know why do we need to assign a direction to some quantity which is a product of the charge and the distance bewteen charges. What is the physical reason of defining the dipole moment as a ...
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+150

Definition of electric polarisation and the potential due to a polarised body

I've two questions, the second one depends on the first. $\mathbf{1}$ How exactly is polarisation defined? Griffiths says $\mathbf{P} \equiv$ dipole moment per unit volume How exactly do we go about ...
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Dipole moment of non-uniformly charged cylinder — direction

If we consider a cylinder along the $z$-axis, with charge density $\rho(z)$ [varying linearly according to$\rho = az + b$, from the positive value $\rho_1=-ha+b$] at $-h$ to the also positive $\rho_2=...
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Understanding of oscillating charge in oscillating dipole

During the derivation of oscillating dipole radiation, two retarded potentials for a point P are written: due to the positive charge $+q$ and negative $-q$. The potentials $V_{1}$ and $V_{2}$ imply a ...
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Why are electronic transitions in atoms modelled as oscillating electric dipole radiation?

Sources such as Eugene Hecht and Griffiths claim that oscillating electric dipole radiation is a great approximation for radiation generated from atoms and molecules during electronic transitions. I ...
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Can neutrons be manipulated with magnetic fields? Can neutron particle accelerators be built?

Neutrons have no electric charge and do not respond to electric fields as in a conventional particle accelerator. However, they are magnetic and do have a small magnetic dipole moment. So it should ...
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How to understand the relation of the two representation of dipole moment?

On one hand, the dipole moment is define as $$\vec{\mu} = q\vec{r},$$ where q is the charge and $\vec{r}$ is a position vector. On the other hand, I know the transition dipole operator of a two level ...
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What are the potential of a volume charge and potential of a surface charge?

I have encountered two terms called: the potential of a surface charge the potential of a volume charge In this context: ${\bf P}$ is the The dipole moment per unit volume This terms came up in ...
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1answer
133 views

Why does the neutron have an electric dipole moment?

As I understand it, the neutron is believed to have an electric dipole moment (the so-called "$nEDM$"), the precise value of which hasn't been pinned down, although we've been able to place ...
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35 views

How to rewrite the Lagrangian density for the Pauli moment in Dirac theory

I am trying to follow a derivation in a paper (DOI: 10.1119/1.2710486). It defines the Lagrangian density for an ananomalous magnetic moment (Pauli moment) in the Dirac theory as, $$\mathcal{L}_{Pauli}...
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Transition dipole moment of electronic states in $H_{3}$ molecule

I have some questions regarding statements about transition moments of $H_{3}$ molecule in the article ...
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39 views

Confusion over Gauss' law for an ideal electric dipole

To find the charge density of an ideal electric dipole centred at the origin, I can evaluate the divergence of $\vec{E}(\vec{x})$ which equates to evaluating the laplacian of the potential. Working ...
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29 views

Electric field due to group of dipoles

We know that an electric dipole (having no net charge) produces electric field around it, which means net charge is not a compulsory condition to make electric field. Now if in a region a group of ...
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70 views

How is the magnetic dipole moment operator defined?

In quantum mechanics, the electric dipole moment operator is defined as $$\hat{\vec D}=q\hat{\vec r}$$ where $q$ is the electric charge of the distribution. This is directly obtained by promoting ...
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136 views

Divergence of electric field of point dipole

Am I correct to say that since the divergence of the following E field $$ \mathbf{E} = \frac{1}{4\pi\epsilon_0}\left[ \frac{3(\mathbf{p_0}\cdot\hat{r})\hat{r}-\mathbf{p_0}}{r^3} \right] - \frac{1}{3\...
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Finding electric dipole moment

For a ideal electric dipole we have $$\rho (\mathrm{\mathbf{x}})=-\mathrm{\mathbf{p_0}}\cdot\nabla\delta^{(3)}(\mathrm{\mathbf{x}}-\mathrm{\mathbf{x_0}})$$ The electric dipole moment formula is given ...
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46 views

Electric field of electric dipole and gradient properties

I am trying to work out whether there is a way to calculate the electric field of a dipole from the following formula: $$\phi(\vec{r}) = -\vec{p} \cdot\vec{\nabla}\phi_0$$ Where $\phi_0$ is the ...
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48 views

Relation of bound charges and polarization

In this Wikipedia article the polarization $$ \vec P = \rho_\mathrm{b} \vec d $$ is determined from the density of bound charges $\rho_\mathrm{b}$ and the displacement vector $\vec d$, which denotes ...
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A question on dipole approximation

In the Feynman Lectures on Physics, Volume 2, Chapter 6, Section 6-4 Feynman derives the electric potential due to a sphere with a surface charge distribution proportional to the cosine of the polar ...
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How to formulate the magnetic dipol moment and field in a line geometry instead of a point

In classical physics, the magnetic field of a dipole is calculated as the limit of a current loop as the source shrinks to a point while keeping the magnetic moment $m$ constant. Because I come from a ...
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46 views

Direction of dipole moment? [duplicate]

Why is the direction of dipole moment taken from negative to positive charge when the field is directed in the opposite direction ?
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116 views

Magnetic dipole moment of volume current derivation

The multipole expansion of the magnetic potential yields the dipole term : $$\mathbf A_{dipole}(\mathbf{r}) =\frac{\mu_0}{4\pi r^{2}}\int (\hat {\mathbf r} \cdot {\mathbf r}') \mathbf J {dV}'$$ How do ...
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Magnetic dipole moment because of spinning electron

We always consider only the spin of electron. But protons are spinning charges as well. So what about the magnetic dipole moment caused by them?
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Why electric field symmetry along $z$-axis implies vanishing of odds multipole moments

In the Jackson exercise 6.4, we have the following electric field inside a rotating sphere, $$ \vec{E} = -\frac{2}{3} \mu_0 M \omega r \hat{r} $$ Where $r$ is the radial coordinate in cylindrical ...
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328 views

Selection rules in the harmonic oscillator

If I have a molecule with two different atoms and this molecule gets excited by EM radiation, we can only see transitions with $\Delta n=\pm1$ in the molecule spectrum. I found this in my physics ...
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How possible is using complex variables to model the electric field system of a dipole? [duplicate]

If one considera a dipole system, is it possible to model the system using complex variables and if ao, how can we use complex analysis to model it? I have the idea that we can model dipole moment as ...
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What does the dipole moment really represent?

Wikipedia gives the most general expression for the $n^{\rm th}$ moment $\mu_n$ of a physical quantity $\Lambda$ as: $$ \mu_n = \int {\bf x}^n \space \lambda({\bf x}) \space \rm d^3 x$$ provided that ...
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318 views

Average field inside a sphere

Griffiths, problem 3.47: show that the average field inside a sphere of radius R, due to all the charge within the sphere, is $$\langle {\bf E} \rangle = - {1 \over 4 \pi \epsilon_0} {\bf p_{\tt tot}\...
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How to search for an atom electric dipole moment

I read some papers about searching for induced atomic EDM. Finding such an EDM would imply a violation of the P and T-invariance (and hence CP). The way the derivation works (very roughly) is by ...
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68 views

Force on a Magnetic Dipole due to Another Dipole

I'm trying to find the force on a magnetic dipole $m_2(r,0,0)$ on the x-axis due to the magnetic field $\vec B_1$ produced by a another dipole $m_1(0,0,0)$ which is at the origin. Both magnetic points ...
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Electric Field and Dipole Moment Synthetization (Attempt)

Based on the setup of the electric field between two equal charges, you end up getting the equation labeled 5.5. I am wondering if the term $qz$ from equation 5.5 can be stated $\vec p = qz\hat k$ ...
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Dipole moment in primary polarization mechanism in a dielectric

The question I have is regarding material from an old University book I am currently reading, Chapter 13, "The Solid State", Third Edition, H.M Rosenburg. And it states that the first ...
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Orientation of an electric dipole in an external magnetic field

I am wondering the following situation: Assume you have an atom in an external magnetic field. You can choose the direction of the external magnetic field as the quantization axis. Now, the external ...
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98 views

Mechanical properties of electric point dipoles

Point electric dipoles are usually introduced as two charges $\pm q$ at a distance $d$, then taking the simultaneous limit $d \to 0$ and $q \to \infty$ keeping the product $qd = p$ constant. In this ...
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Torque on an arbitrary shaped object having some dipole moment in a uniform electric field

Can anyone show me a proof that the torque on an arbitrary shaped object having a dipole moment $\vec{P}$ in a uniform electric field $\vec{E}$ is given by $\mathbf{N}=\mathbf{p} \times \mathbf{E}$. I ...
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58 views

Proof of the formula for the atomic polarizability of a simple linear molecule

For an atom Griffiths says $$ \mathbf{p}=\alpha \mathbf{E} $$ The constant of proportionality $\alpha$ is called atomic polarizability. And $\mathbf{E}$ is the external applied field Then he goes on ...
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A Classical model for diamagnetism

I'm trying to derive a classical model to describe diamagnetism, and I'd like to understand if it is possible to understand the basic properties of diamagnetic materials with it i.e.: ''A diamagnetic ...
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Does a rotating magnetic monopole have an electric dipole?

Does a rotating magnetic monopole have an electric dipole? It is known that a rotating electrically charged sphere possesses a magnetic dipole, so for symmetry I guess that also a magnetic monopole ...
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Problem from dipole moment which involves perimeter of elipse

An ellipse has a uniform linear positive charge density in upper half (total upper half part charge $+Q$ ) and a uniform linear negative charge density in lower half (total lower half part charge $-Q$ ...
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Forcing freezed water to become a ferroelectric?

I got answers a long time ago about the possibility to make of iced water a permanent ferroelectric.This means put the water in a box and apply a strong electric field and in that condition let the ...
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Coordinates for coupled transition dipole moments

I am working on some calculations on coupled transition dipole moments interacting with light pulses with different polarisations. I am currently trying to find a way of writing $\theta_{\beta}$ and $\...
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1answer
87 views

Can electrons be electrically polarized, i.e., can they acquire an induced electric dipole moment?

A comment on a recent question raises an interesting point: Neutrons can have intrinsic electric dipole moments. Neutrons also have a nonzero electric polarizability, i.e., they acquire an induced ...
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41 views

Forbidden transitions from triplet to singlet states in the deuteron?

The dipolar moment for the deuteron is $$\vec{\mu}_{d}=\frac{\mu_{N}}{2 h}\left\{\left(g_{s}^{(p)}+g_{s}^{(n)}\right) \vec{S}+\left(g_{s}^{(p)}-g_{s}^{(n)}\right)\left(\vec{s}_{p}-\vec{s}_{n}\right)+\...

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