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2
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1answer
99 views

Do Dipole Moments Obey Superposition?

Essentially, I have two surfaces which I know how to find the dipole moments for. I realize that $V_{dip}(r) = \frac{1}{4\pi \epsilon_0 r^2} \mathbf{\hat{r}} \cdot \int \mathbf{r'} \rho{(\mathbf{r'})...
7
votes
5answers
7k views

What is the physical sense of the transition dipole moment?

So if the states are the same we achieve the expectation value of the dipole moment for a given state. I mean $ \langle \mathbf{\mu} \rangle = \langle \psi \vert \hat{\mathbf{\mu}} \vert \psi \rangle$...
0
votes
1answer
105 views

Spontaneous radiative decay due to electric dipole radiation

In my textbook, we calculated the rate at which an electric dipole radiates energy to be $Pwr = \frac{1}{4\pi \epsilon_0}\frac{2}{3c^3}\left(\frac{d^2 p}{dt^2} \right)^2$ where p is the dipole ...
2
votes
1answer
157 views

Vector Potential Oscillating E Field of the “Null” Field of a Hertzian Dipole?

The vector potential of a Hertzian dipole falls off spherically as $1/r$. The polar axis of the dipole is a "Null" field -- meaning no electric and magnetic field. The absence of magnetic field is ...
15
votes
1answer
2k views

In the Lennard-Jones potential, why does the attractive part (dispersion) have an $r^{-6}$ dependence?

The Lennard-Jones potential has the form: $$U(r) = 4\epsilon\left[ \left(\frac{\sigma}{r}\right)^{12} - \left(\frac{\sigma}{r}\right)^{6} \right]$$ The (attractive) $r^{-6}$ term describes the ...
0
votes
1answer
35 views

Help with this question (Eletric Fields, Dipole) [closed]

The answer in the textbook in the solutions manual is the following: I didn't undestand the last step. He said he did a binomial expansion, I just can't figure out! Appreciate any help.
0
votes
0answers
36 views

forces between two dipoles, one of them oscillating

so, imagine we have two dipoles A and B, A is fixed at the origin and B is free to move on the X axis. Suppose we make the dipole A oscillate, say reversing it's direction every one second, then B ...
0
votes
0answers
135 views

Finding Magnitude and Direction of Dipole's Electric Field at a Point

This question pertains to finding the magnitude and direction of a dipole's electric field. Specifically, I am trying to figure out why we are using both the hypotenuse and $\sin\theta$, and not the ...
1
vote
1answer
209 views

Why does the field of an electric dipole drop off as $1/r^3$?

Electric field of a point charge drops off inverse squarely but that of a dipole varies as $1/r^3$. Why the field drops off more quickly for a dipole?
0
votes
1answer
395 views

dipole field on axis twice the field on perpendicular bisector

Why is the dipole field on axis twice the field on perpendicular bisector? For the perpendicular bisector: Lets assume -q is right from of the origin and +q is left from the origin, both a distance a ...
1
vote
1answer
132 views

How does one calculate or even approximate the force observed by a magnet as its dropped inside of a diamagnetic cylinder?

How does one calculate or even approximate the force observed by a magnet as its dropped inside of a diamagnetic cylinder? Wikipedia and Google does not provide much information on this topic. ...
2
votes
2answers
88 views

Why is there no electric dipole term in the Hyperfine Hamiltonian?

I have been looking a several discussions of hyperfine structure. (For example: here and in the explanation for eq. 2.1 here It seems that the hyperfine interaction can be explained almost entirely ...
3
votes
1answer
1k views

Derivation of Interaction energy of Dipole - Induced Dipole Interaction

I see that the formula giving the potential (interaction) energy of a dipole and an induced dipole is $$V=-\frac{C}{r^6}$$ where $$C=\frac{\mu_1^2 \alpha'_2}{4 \pi \epsilon_0}$$ and that the formula ...
2
votes
1answer
652 views

Difference between a “source dipole” and a “force dipole”

I know quite well what a dipole is and in general what multipole moments are (in the context of, for instance, electrodynamics). What I find myself confused by is something called a "force dipole" in ...
0
votes
1answer
92 views

Ignoring spin, what is its orbital magnetic moment of an electron in a hydrogen atom in the 2p orbital?

I know that a magnetic dipole moment is given by $$\mu=\frac e{2m}I$$ and that the angular momentum is $$\frac {m_jh}{2\pi}.$$ However, I have also seen that angular momentum $I$ is given by $$I=\frac ...
0
votes
1answer
216 views

What do we mean with magnetic monopole and dipole?

What do we mean with magnetic monopole and dipole? I can not find a way to relate magnetic monopoles and dipoles with electric ones. I do not understand their outcomes. Also,what is their role in ...
0
votes
0answers
53 views

Why doesn't a quantum pairwise Hamiltonian couple states in which more than one interaction occurs?

This question is about the standard quantum mechanical pairwise interaction Hamiltonian. I'll phrase it in terms of an example using Rydberg atoms, but you could just as well imagine spins (for ...
1
vote
1answer
121 views

Born approximation and dipole approximation

I'm having some trouble really understanding when it's okay to use these approximations and why. I've been looking myself blind on equations, but I'm not even sure I understand it qualitatively. So I ...
1
vote
1answer
651 views

What is retardation effect?

I have in my book a passage which states: "We also remark that the dipole approximation (obtained by setting $\exp(i \textbf{k} \cdot \textbf{r}) = 1$ in the matrix element Eq. #) yields the leading ...
0
votes
1answer
77 views

Dielectric heating - does EM field transfer energy to polar molecules?

In AC field, polar molecule are trying to align with external field. At high freguencies, changes of field are so quict, that molecules cannot align with it. This leads to increasing kinetic energy of ...
0
votes
1answer
62 views

Change in work done by dipole

How would you explain the intuition behind the equation $dW = -\tau d\phi$ for an electric dipole?
1
vote
0answers
23 views

What makes an insulator good for polarizing?

Water in an electric field become polarized easily, since the natural dipoles twist and turn to align with the field. In non-polar insulating materials, a redistribution of charge can happen in the ...
0
votes
1answer
94 views

Dipole approximation in solids

I have seen the use of dipole approximation (where the extent of the wave function is assumed to be much smaller than the wavelengths of the transitions or that of the electromagnetic field applied) ...
0
votes
1answer
219 views

Sound power radiation of two monopole sources

For a fixed given electrical power to two monopole sources, producing the same frequency. Which mode, either in-phase or out of phase, will radiate the most sound power into the far-field?
0
votes
0answers
25 views

If an common metal is induced with a static dipole moment, won't the the positive side be weaker?

To my knowledge, common metals with metallic bonding is formed through free electrons within its lattice structure. If say we are to shift the free roaming electrons to one side and therefore minutely ...
0
votes
1answer
163 views

Finding direction of electric force of 2 particles [closed]

A molecule has its centre P of positive charge situated a distance of 2.8 × 10–10 m from its centre N of negative charge, as illustrated in Fig. The molecule is situated in a uniform electric ...
0
votes
1answer
228 views

Phase difference between incident plane wave incident on a dipole and radiation fields from dipole

i have an incident plane wave and a dipole, consider that plane wave incident on dipole. at this moment what happens to dipole? We know that after incident of plane wave on dipole, the radiation has ...
3
votes
1answer
124 views

Power loss due to dipole antenna position mismatch

If we have two dipole antennas, it is well known that in order to transfer maximal power, two dipole antennas should be parallel and on the same height, which means that line that connects their ...
0
votes
0answers
18 views

Can we build an ideal hexadecapole? [duplicate]

I'm just curious about whether it is possible to build an ideal hexadecapole (16-pole) from point charges in 3D. My intuition tells me no, because the point charge of a (electric) monopole "bound" a ...
0
votes
0answers
307 views

Calculation of Magnetic Field Lines

I am doing some research on how to calculate magnetic field lines for a bar magnet. So far I have found the following equations: \begin{align} \frac{B_r}{B_\theta} &= \frac{d_r}{rd_\theta}\\ B_r&...
2
votes
0answers
59 views

Connection: Work on dipole <-> optical absorption

If I consider a two-level system with a ground and an excited state, I can compute the instantaneous rate at which work is being done on the dipole $\mu(t)$ by an electric field $E(t)$: $\dot{W} = E(...
1
vote
2answers
471 views

Does the intensity of dipole radiation fall as $1/r^2$ or $1/r^3$?

I have seen this derivation: I want to estimate what is the intensity of the electrical field as function of $r$ the distance from the radiated source ? I think it is can modled as pointed source ...
0
votes
2answers
154 views

Electric field of a dipole

I'm trying to find the electric field due to an electric dipole $\mathbf{d}$. There are plenty of approaches to doing this online, but I want to do it "my way," which doesn't seem to be working (and I ...
0
votes
1answer
165 views

Magnetic field of a Herzian dipole antenna

If I am given the dipole moment of very short dipole antenna as $P = P_0 sin (\omega t)$, what will be the magnetic field and polarization of far field radiation? Do I need to consider the time ...
0
votes
0answers
47 views

Are there examples of “loss-less” Forster Resonance Energy Transfer (FRET)?

When I think of a Forster Resonance Energy Transfer (FRET) process, I typically imagine the initial excitation of an absorbing chromophore with a photon followed by the subsequent emission of a lower ...
2
votes
2answers
1k views

Does field line concept explain electric field due to dipole?

Consider an electric dipole consisting of charges $-q$ and $+q$, separated by a distance $2a$ and placed in free space. Let $P$ be point on the line joining the two charges (axial line) at a distance ...
3
votes
1answer
491 views

Are the axial electric field lines of a dipole the only ones that extend to infinity?

Consider an electric dipole and its electric field lines. There will be many field lines that do not extend to or originate from infinity, but rather begin at the positive charge and loop back ...
3
votes
2answers
3k views

Motion of a dipole in an electric field

Assume that we have some non-constant electric field $E(x,t)$ and a point-dipole at a position $q$ with a constant dipole moment $\vec{p}$. How would you describe the time evolution, i.e. the motion ...
3
votes
1answer
146 views

Intuitive explanation of difference in $r$-dependence between dipole and monopole

For an electric monopole, its potential scales with $\frac{1}{r}$, where $r$ is the distance from the point of interest to the charge. However, for a dipole, its potential scales with $\frac{1}{r^2}$. ...
-1
votes
1answer
125 views

Can an EM wave be represented in terms of dipole? [closed]

The direction of propagation is represented by a line. A positive charge moves along this line at velocity c. A negative charge moves along a line that is perpendicular to the direction of propagation ...
2
votes
2answers
2k views

Comparing effect of electric and magnetic dipoles on their fields

So at the end of one of my prof's lectures he gives us something to think about: Both electric and magnetic dipoles tend to line up with their respective fields. Materials made out of ...
4
votes
2answers
705 views

Will there be any force of attraction or repulsion between an electrified body and a non-electrified body?

Up to my knowledge an electrified (charged) body can attract a non-electrified (neutral) body. I thought this because, when we bring a charged (suppose negatively charged) body near a neutral one. ...
1
vote
0answers
86 views

Why do “virtual states” in Raman spectroscopy have absorbance profiles distinct from either the ground or excited states of an absorbing material?

Do virtual states in Raman spectroscopy have distinct and observable dipoles that can interact with and/or induce dipoles in other molecules (over extremely short femtosecond timescales)? This notion ...
7
votes
2answers
1k views

What is the “direction” of the transition dipole moment? (Understanding Eq. 9.29, Charge and Energy Transfer 3rd Ed, May & Kuhn)

For a real vector $\mathbf{r}$, the direction is given by: $\hat{\mathbf{n}}=\mathbf{r}/\left|\mathbf{r}\right|$. The transition dipole moment is a complex vector. How do you define its direction? ...
1
vote
1answer
318 views

Potential of a dipole with actual physical extension?

I think everybody here knows the equation that gives the potential of a point like dipole, but how does the field look like if you have e.g. a metal sphere with radius $R$ and a certain dipol moment, ...
1
vote
1answer
1k views

Dipole moment induced in a spherical particle

Consider a spherical metal particle made out of gold. If there is an external charge somewhere near the gold particle, is there a way to calculate the resulting dipole moment that is induced by the ...
1
vote
1answer
2k views

Equation for the equipotential lines? [closed]

What is the equation for the equipotential lines in $x$-$y$ plane for a dipole oriented along the $x$ axis?
2
votes
0answers
95 views

Mie Scattering for spheres with constant dipole moment

I was wondering whether there exists a theory that describes Mie Scattering for spheres that have a constant dipole moment. Since there are theories that describe Mie scattering in the case of a ...
1
vote
2answers
129 views

potential energy of a dipole?

The very popular from of potential energy of the dipole is $-P.E$. But in the derivation of it, we have negelected the potential energy of the pair of charges constituting the dipole. will this not ...
0
votes
1answer
677 views

Electric dipole moment, which charge is the $q$ for?

Electric dipole moment says $p = qd$. Which charge does the $q$ equal to?