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18
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2answers
1k views

Why there is no dipole gravitational wave?

I have read that "thanks to conservation of momentum" there is no dipole gravitational radiation. I am confused about this, since I cannot see the difference with e.m. radiation. Is this due to the ...
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 ...
11
votes
1answer
643 views

Magnets arranged in a sphere

If I was to take a bunch of magnets and arrange them in a sphere (And keep them there with glue or plastic or something) so that the north pole faces the outside of the sphere and the south pole faces ...
8
votes
5answers
2k views

Direction of rotation of proton in magnetic field--opposite to a dipole

Chatroom created by @pcr for discussing this: http://chat.stackexchange.com/rooms/2824/direction-of-rotation-of-proton-in-magnetic-field Here's a small paradoxical question I was asked a long time ...
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$...
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? ...
6
votes
2answers
1k views

Why is there a factor of 1/2 in the interaction energy of an induced dipole with the field that induces it?

In this paper, there's the following sentence: ...and the factor 1/2 takes into account that the dipole moment is an induced, not a permanent one. Without any further explanation. I looked ...
6
votes
1answer
66 views

How do temporary dipole-dipole interactions work in quantum mechanics?

The standard presentation of temporary dipole-dipole interactions (in high school at least) is classical: the electrons in an atom/molecule 'orbit' around its nucleus/nuclei. As a direct result of ...
6
votes
2answers
190 views

Near Energy In the Null of a Hertzian Dipole

Since $\mathbf E = -∇Φ - ∂\mathbf A/∂t$ one expects an oscillating $\mathbf E$ field even in the null of a Hertzian Dipole unless the two right hand side terms cancel -- which they do in the far field ...
5
votes
6answers
2k views

What is the origin of the Dirac delta term in the dipole electric field?

I am a bit lost how one has deduced the formula for electric field with electric dipole because of some inconsistency between different sources. The Wikipedia article contains a delta function in the ...
4
votes
2answers
1k views

Meaning of the phrase “dipole moment of the combination”

Here is a question I came across in a book: Three point charges $-q$,$-q$ and $2q$ are placed on the vertices of an equilateral triangle of side length $d$ units.What is the dipole moment of the ...
4
votes
2answers
708 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. ...
4
votes
2answers
260 views

How do you fit a dipole in an electron?

Experiments used to observe particle spin properties (such as Stern-Gerlach) rely on a varied magnetic field and a dipole-like reaction in the particle, deflecting it in one direction or another. In ...
4
votes
1answer
6k views

Force from point charge on perfect dipole

Have a point charge and a perfect dipole $\vec{p}$ a distance $r$ away. Angle between $\vec{p}$ and $\hat{r}$ is $\theta$. Want to find force on dipole. I'm having more than a little difficulty ...
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 ...
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 $\frac{1}{r^2}$. ...
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 ...
3
votes
1answer
1k views

Why is the geomagnetic north pole at a different location from the magnetic north pole?

According to this site Magnetic North, Geomagnetic and Magnetic Poles The Geomagnetic poles (dipole poles) are the intersections of the Earth's surface and the axis of a bar magnet hypothetically ...
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
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 ...
2
votes
3answers
6k views

Potential energy of a dipole in a uniform electric field convention?

When finding the potential energy of a dipole in a uniform electric field, I was told by my lecturer that the convention is that the potential energy is 0 when the dipole moment and electric field ...
2
votes
2answers
747 views

Why Does Dipole Moment Depend on Distance?

Why does the dipole moment of an electric dipole of different charges depend on the distance from the origin? Physically, I don't understand why something that measures how much of a dipole something ...
2
votes
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'})...
2
votes
1answer
158 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 ...
2
votes
3answers
409 views

Why does the Electric Field of a dipole have no $x$ component?

According to the solution $2E\sin(\theta) = E_{net}$. I understand how the dipole works but I don't understand why the x component would be 0?
2
votes
1answer
3k views

Force between two point dipoles

What would the force between two parallel point dipoles be? I was thinking of doing it the way force between two point charges is found out, by finding the field and then the force but I am not able ...
2
votes
1answer
655 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 ...
2
votes
1answer
652 views

Conservation of Angular momentum in the dipole selection rules

If the total angular momentum J of an atom is not changing during a dipole transition, where does the angular momentum for the photon come from?
2
votes
1answer
94 views

Is there an easy way to see that $\phi =\frac{\mu_0}{4\pi} \frac{\vec m \cdot \vec r}{r^3}$?

The scalar potential of an electric dipole is given by: $$\phi =\frac{1}{4\pi\epsilon_0} \frac{\vec p \cdot \vec r}{r^3}$$ The derivation of this is quick, however, is there an easy way to see that ...
2
votes
2answers
265 views

Physical meaning of electric dipole moment [closed]

I am reading about the electric dipole moment. What I can't understand, and seems that no one cares to explain, is what is the physical meaning of it. To my understanding everytime that dipoles are "...
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 ...
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 ...
2
votes
2answers
241 views

Power due to dipole radiation and time reversal symmetry in classical E&M

The dipole formula for the power loss emitted by a time varying electric dipole is (in natural units) $P = \frac{\dot d_i^2}{6 \pi}$. This is clearly even under time reversal symmetry $T$, but a ...
2
votes
4answers
629 views

Dipole in a spherical cavity in an infinite dielectric

In this example the assumption is made that inside a spherical cavity (with an infinite dielectric) with a dipole placed at its centre, the potential takes the following form: $$\phi_{in}= \frac{p ...
2
votes
0answers
46 views

Lorenz Gauge Dipole Potentials Formulation In SI Units? [closed]

After hunting in vain* for a documented closed form solution (ie: no integrals or differentiation in the formula) for $\phi$ in terms of A under the Lorenz condition, of an electrically short dipole (...
2
votes
2answers
89 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 ...
2
votes
1answer
273 views

Electric field in space created by intersection of spheres of charge [closed]

I am trying to calculate the electric field in space created by a body assembled by the intersection of 2 spheres. The upper sphere, its center is at $$\frac{d}{2}\mathbf{\hat{z}}$$ with radius $R$ ...
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(...
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 ...
2
votes
1answer
2k views

Minimizing potential energy of a dipole in an electric field

My test paper asked me which way a dipole should be orientated in an electric field to minimize its potential energy. My answer was that the dipole should lie parallel to the electric field with the ...
2
votes
2answers
430 views

What is meant by 'a perfect dipole'?

Question What is meant by a perfect (electric) dipole? Additional information I came across the term in this question Force from point charge on perfect dipole and also in a textbook (which does ...
1
vote
1answer
213 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?
1
vote
2answers
68 views

The Strength of the Tangential and Radial Components of a Dipole Magnetic Field

I am following along well several textbooks (Geophysics) that helps me understand the in-depth physics behind the magnetic field of a dipole magnet. I understand that the basic magnetic potential (...
1
vote
1answer
256 views

Why does the aligning of magnetic dipoles in a material cause its heat capacity to decrease?

This is with regards to adiabatic magnetisation.
1
vote
2answers
86 views

Entropy reversal in magnets

Entropy is an irreversible phenomenon without any energy supplied to reverse it. I was reading about paramagnetic substances and how dipoles align inside them on application of magnetic field. My ...
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
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?
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 ...
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
312 views

Explain the electric dipole moment vector

For a pure dipole situated at the origin, I don't understand why the dipole moment vector is $$ \vec{p} = p\cos \theta \hat{r} - p\sin \theta \hat{\phi} $$ Since the vector does not have any $r$ in ...