Questions tagged [dipole]

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Energy of Dipole Configuration [closed]

This is a Problem from Electricity and Magnetism by Purcell. I am giving the whole problem as mentioned in the Textbook below. We want to find the energy required to bring two dipoles from infinite ...
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2answers
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Conflicting answer for potential of dipole at midpoint

If I have a dipole of two opposite charges separated by a distance $d$, then by taking the leading non-zero term in multipole expansion centered about their midpoint, I find the potential to be: $$ V= ...
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3answers
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$H$ field formula

For a permanent bar magnet is there a formula for the magnetic field strength $H$? Just like the electric field strength $E$ can be calculated at a point in space, can we do the same for the magnetic ...
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1answer
63 views

Is grain really a dipole?

Yesterday I was solving some electric field from resnik book and one of the solutions assumed a bee to be a sphere of charge $60 \;\text{pC}$ and the grain which sticks to it as a dipole due to ...
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1answer
97 views

How is the work done along an equipotential line zero?

If a charge is brought from some distance to a point which lies on the equatorial line of an electric dipole, the work done is 0 and so is the electric potential. But how should I imagine this?
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Spin Transition operator

What interaction Hamiltonian operator should one use when we consider photon emission through change in spin states?
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2answers
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Direction of electric field

We say when we place a positive test charge near + it moves away from the charge following a curved path when there is also a ~ charge. That is the field of + charge Originates from + and terminate in ...
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2answers
58 views

Electric field due to a dipole at large distances

It says $$ E= \frac{1}{4\pi \epsilon_0} \frac{p}{r^3} $$ so by this this eqn, if we measure electric field at a distant point then we can never find $q$ and $d$ separately. $q$ and $d$ are charge and ...
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1answer
52 views

Magnetic flux of a dipole through a sphere

I wish to calculate the magnetic flux of a dipole placed at the center of a sphere through the sphere. From Gauss's law, I know that it is zero. However, how do I verify it mathematically without ...
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1answer
37 views

How to deal with Dipole in a cavity?

Consider a conducting solid sphere having a spherical cavity. Centre of the cavity and centre of the sphere coincide. A point sized dipole [negligible separation and cavity is large] is placed at ...
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Energy of dipole using the electrostatic energy of all of space

I was watching my online lecs, and we were considering the electrostatic energy of a dipole. First, doing the torque-in-uniform-field calculations, and derived that $U_{rot}= - \vec{p} \cdot \vec{E}$. ...
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Polarization density

Is the polarization density term in the electromagnetic wave equation the density of static electric dipole moments or transition dipole moments?
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1answer
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Help to understand this equation $\frac{dw}{d\omega\,d\Omega} = \frac{1}{4\pi\epsilon_0} \frac{|p|^2\sin^2\!\theta\>\omega_0^2}{4\pi c^3\gamma^2}$

I'm looking for the name of this equation. $$\frac{dw}{d\omega\,d\Omega} = \frac{1}{4\pi\epsilon_0} \frac{|p|^2\sin^2\!\theta\>\omega_0^2}{4\pi c^3\gamma^2} \left[\frac{\gamma^2/4}{(\omega-\omega_0)...
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4answers
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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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1answer
35 views

Constellation of charges in a quadrupole

I’d like to know if any constelation of 4 charges is a quadrupole. I have a task where there are 2 positive and 2 negative charged particles in the corners of a rectangle. And this is a quadrupole. Is ...
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Force on a magnetic dipole

How to deduce the force on a magnetic dipole given by $F = \nabla(m \cdot B)$ from the Lorentz force?
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1answer
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The physics behind DC voltage derating of capacitance

I don't understand this phenomena pointed out in LDO's Capacitor vs. Capacitance where it says: Given the dynamic nature of capacitors (storing and dissipating electric charge in a nonlinear fashion),...
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3answers
111 views

Energy of magnetized vs not magnetized ferromagnet?

A ferromagnet conststs of many, many microscopic magnetic dipoles that can be pointed in different orientations. If the ferromagnet is not magnetized by applying an strong external magnetic field, the ...
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1answer
22 views

Magnetic field around a magnetic dipole and circular current loop

Qualitatively, how does the magnetic field around an ideal dipole compare with the magnetic field around a circular current loop?
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1answer
82 views

Why is the external torque not taken as -$pE\sin\theta$ in the derivation of the Potential energy due to an external field

So in the derivation of the Potential energy of a dipole due to an external field, we consider a dipole with charges $q_1= +q$ and $q_2= –q$ placed in a uniform external electric field. We know that ...
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2answers
86 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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1answer
25 views

Do EM waves produced by a dipole antenna propagate along 1 plane?

The plane would be perpendicular to the dipole and passing through it. Do em waves propagate in all directions of that plane or in any direction of any plane?
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1answer
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Doubt in the interaction energy of the dipole in an electric field

Consider a dipole ($\vec{p}$) in an electric field ($\vec E$) making an angle $\theta$ with the field. We can see that $V_1-V_2=Ed\cos\theta$ In books, the derivation for the interaction energy of ...
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25 views

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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1answer
37 views

Why does the dipole-dipole interaction scale with $r^{-6}$?

I often see the formula $$V \propto \frac{-C}{r^6}$$ for the interaction energy of two electric dipoles. However there interaction energy of an electric dipole in an electric field generated by an ...
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Voltage distribution around a dipole for different wavelengths [closed]

It is well known that the alternating current distribution in a center-fed dipole antenna (black line) is as follows: Despite the different wavelengths, the current distributions depicted above all ...
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1answer
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Surface charge due to electric polarisation

We've a piece of dielectric parallel to the polarisation $P$ , in two cases as in the figure we take a slice of it, one a perpendicular cut the other an oblique one. The charge on the surface $q$ is ...
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Torque on a system of dipoles [duplicate]

I know that the net force on a system of dipoles is zero because internal forces cancel out, but the same is not true for the torque. I wanted to know why does this happen. And is it related to any ...
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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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1answer
33 views

Potential of a continuous charge distribution and it's dipole term

I've a charge distribution, whose potential will be given as $$\begin{aligned} V(\mathbf{r})=& \frac{1}{4 \pi \epsilon_{0}}\left[\frac{1}{r} \int \rho\left(\mathbf{r}^{\prime}\right) d \tau^{\...
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2answers
78 views

What is the diff in operational range underwater between a dipole trimmed to resonate @2.45GHz versus a dipole tuned to resonate using a pi network?

(Sorry about the use of "diff", but I needed the characters.) In air, a half-wave dipole can be physically trimmed to resonance and will radiate well. It can also be tuned using a pi network ...
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3answers
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Why is the half-wave dipole the most used antenna design?

When producing em waves using a dipole antenna (of length L), you could theoretically use any L and adjust the frequency of the oscillating voltage to get the desired wavelength. Then why are most ...
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1answer
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What does “weak-field limit” mean when it refer to dipole and atomic polarization?

In Griffiths' book, Introduction to Electrodynamics 3rd, problem 4.3,it requires me to find the condition on ρ(r) such that equation $p = αE$ will hold in the weak-field limit. The answer gives $ρ(r)=...
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Can a dipole keep rotating with increasing angular velocity?

Let's say, we have a dipole and we know if we keep it in uniform electric field it allines it self along the electric field direction.so can we some how make an arrangement to rotate it indefinitely ...
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Why are electrons inherently magnetic? [duplicate]

I read that permanent magnetism is caused by electrons orbiting in a way which produces a net magnetic field. but how can a particle with no dimensions have a magnetic dipole? also I read that photons ...
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Understanding the physical interpretation of bound charges in a polarized material

I'm reading Section 4.2.2 of Griffiths' Introduction to Electrodynamics (Third Edition): "Physical Interpretation of Bound Charges". He explains where the bound "surface charge density&...
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37 views

What does this variable coefficient represent of electric field of dipole?

$V:=\text{potential at point P}$ $V=\frac{2Qd\cos(\theta)}{4\pi \epsilon_{0}r^{2}}$ $E_{r}=-\frac{\partial V}{\partial r}$ $E_{\theta}=-\frac{1}{r}\frac{\partial V}{\partial \theta}$ The problem for ...
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How to interpret bound charges geometrically?

Conceptually, it makes sense to say that when there is an electric field along $E=E\hat{n}$, then given a polarization $P$, the amount that $P$ aligns with the electric field is simply the dot product ...
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Field of an infinitely wide magnetic dipole

Students commonly wonder about the near-analogies between electricity & magnetism. One such: The field of an electric dipole in the limit of an infinitely wide plane tends to 0 outside the plane (...
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(Special relativity) A tilted dipole composed of $+q$ and $-q$ point charges moves at a horizontal velocity. Will it rotate?

Two point charges $+q$ and $-q$ are connected with a rigid insulating stick: This dipole moves at a velocity $v$ to the right. Therefore, the charges should exert a magnetic Lorentz force $F_B$ on ...
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1answer
41 views

Electric Diople potential derivation [closed]

I was looking into the potential created by two point charges at a point $r$ away, as shown in the diagram below and it is given as $$V(r) = \frac{q}{4 \pi \epsilon_o} \left(\frac{1}{|\vec{r} - \vec{d}...
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1answer
23 views

Selection rules for electronic transitions in dipole approximation

I saw this video which provides a clear, though simple, introduction to the argument. I think the main thing missing is a proof for: $\Delta \ell = \pm 1 $ $\Delta m_\ell = 0, \pm 1$ $\Delta m_s = 0$...
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Gravitational Waves, Dipole Radiations and Momentum

I am trying to understand Gravitational Waves and and going through MTW's book. They state that there can be no dipole radiation because of the conservation of momentum but gravitational waves also ...
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1answer
139 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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1answer
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Uniform electric field formation in motional emf induction

Why is the electric field $E$ across the ends of a conducting rod, when it's moved with a uniform velocity $v$ in a magnetic field $B$, uniform? Wouldn't it vary non-linearly, since there are opposite ...
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1answer
66 views

Finding the equilibrium angle for a dipole when another dipole in the vicinity is held fixed

Panofsky and Phillips' Exercise 11 of Chapter 1: Consider two coplanar electric dipoles with there centers a fixed distance apart. Show that if the angles the dipoles make with the line joining their ...
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Electric field due to a dipole sheet

The potential due to a dipole sheet, $S$, having dipole moment density, $\vec\tau$ (per unit area), is given by $$ \phi(\mathbf r) = \frac{1}{4\pi\epsilon_0}\int_S\frac{\vec\tau(\mathbf r')\cdot(\...
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Finding torque on dipole from the force on it

The force on an electric dipole $\mathbf p$ due to field $\mathbf E$ is given by $\mathbf{F=(p\cdot\nabla)E}$. We should then be able to find the well-known torque $\mathbf{\tau=p\times E}$ by using ...
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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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