Questions tagged [dipole]

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Electric current dipole moment

Electrical Current Dipole of dipole moment $\mathbf{p_{EC}}$ has unit of $A\cdot m$. My knowledge of dipole moments unfortunately stopped in high school where I learned that dipole moment $\mathbf{p}$ ...
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How will a polar molecule affect another molecule nearby, why it feels a relatively large force?

Mean position of the negative charges and positive changes are not at the same point (polar molecule) how will that affect another molecule nearby, why it feels a relatively large force? Will the type ...
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Hard problem on dipole with $r^7 $ in denominator, I don't know how or why?

In an external electric field, a molecule is polarized. The dipole moment induced is given by $\vec P =\alpha \vec E$, where $\alpha$, is the polarizability constant and is a positive constant and $\...
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Understanding simulation output: should the total dipole moment be the sum of its components?

I am trying to understand output from a simulation. I want to calculate a total dipole moment. This is the output I have for an example time step (I assume the three columns correspond to x, y, and ...
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Mathematical rigorous definition for an electrical dipole

I've been reading Laurent Schwartz's Mathematics for the physical sciences, and in the chapter on distributions he makes many cool examples of ways to define in a mathematical rigorous way certain ...
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Integrating the dyadic Green function of a dipole source

I would like to ask if anyone know how to derive the equation (4) from this paper? I could not figure out how they derive the term $-\mathbf{P}_\mathrm{LO}(\mathbf{r})/3\varepsilon_0\varepsilon_B(\...
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Why is parallel dipole to electric field is stable equilbrium

For a dipole making $0$ degree angle with field and for making $180$ degrees it is stable and unstable equilibrium respectively. Why?
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Vectors, their representation and dipole moment

I know that the length of an arrow representing a vector gives represents the magnitude of that vector, now consider a force vector. $\vec{F}$=m$\vec{a}$ , therefore in space a force vector ...
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Divergence and rotation of ideal dipole field at d --> 0

I am working on an assignment in vector calculus where we are supposed to find the divergence and the rotation of the electric field caused by an ideal dipole when the distance d between the charges ...
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Dipole Inside Cavity of A Spherical Conductor

Consider the following case: There is a short electric dipole placed arbitrarily inside a spherical cavity inside a solid,uncharged conducting sphere We need to find electric field at a point ...
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What is dipolar charge distribution?

An electric dipole is a system of two opposite point charges when their separation goes to zero and their charge goes to infinity in a way that the product of the charge and the separation remains ...
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Nature of interaction of two magnetic dipoles

Is the force of interaction between two magnetic dipoles a conservative force? If not, how do we find that force?
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How to derive a force expression for dipole-dipole interaction

Background I recently asked a question about how to derive a force expression between a point charge and a dipole. This got me wondering whether I could extend this solution to dipole-dipole ...
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Is there an electric field in a poled piezoelectric crystal at rest?

From my understanding, after a piezoelectric crystal is poled, all the dipoles are roughly aligned inside it, so that the piezoelectric effect is not negligible. However, wouldn't that result in a ...
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How to cast dipole point charge force expression from cylindrical to Cartesian coordinates

Background I am currently building simulations of molecular dynamics and one thing I want to model is dipole interactions. I recently came across this post about calculating the force between a point ...
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57 views

Electric dipole moment of two infinite charged lines

Two parallel infinite opposite charged lines (of uniform density $\lambda$) are placed at distance $L$ from each other. Need to calculate the electric dipole moment of this system. How do you do such ...
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Integrand discontinuity of surface integral of electric field of dielectrics

I am reading an article here on dielectrics Equation $(4.10)$ is: $$\Phi(\mathbf{r})=\dfrac{1}{4\pi \epsilon_0}\int_{V} \dfrac{d^3r'}{|\mathbf{r}-\mathbf{r'}|} [\rho (\mathbf{r'})\ -\nabla'.\mathbf{...
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approximation to the dipole of 2 infinite line charges

This is the question: 2 infinite line charges are located at distance $l$ and charged with linear charge density $\lambda $ and $-\lambda$. Find the electric field and the electric potential away ...
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Perturbation theory for molecules, dipole approximation, chromophore

I am interesting in chromophore group and dipole approximation. For example, i have a molecule (acetone or any other ketone/enol) which is belongs to some symmetry group. Because of the symmetry ...
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Do neutral particles interact with EM radiation?

This question has been bugging me for a while. I asked my professor, I read a couple of posts here and from other sources and some people say that neutral particles interact with light and some people ...
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How a sphere can be assumed as dipole?

From the book introduction to electrodynamics by David Griffiths , fourth edition, page no 279, there is an example to find the magnetic field of uniformly magnetized sphere. It said the magnetic ...
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Adding Hertzian Dipoles

I want to add the electric fields of two Dipoles oscillating with 180° phase difference positioned at $(0,d,z)$ and $(0,-d,z)$. When I calculate the field in the origin, I wonder that my (bought) ...
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Spherical wavefronts from a linear electric dipole-antenna

We are given the equation \begin{equation*} \vec{E}=\hat{u}_\theta\ p_0 \sin{(\theta)}\frac{k^2}{4\pi\varepsilon_0r}\sin{(kr-\omega t)}~, \end{equation*} that describes the far field radiated ...
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Electric field and potential [duplicate]

Suppose we consider a point dipole i.e. an ideal dipole. At the origin the potential: $$ \phi(\mathbf r) = \frac{1}{4\pi\epsilon_0} \frac{\mathbf p\cdot\hat{\mathbf r}}{r^2}$$ is undefined due to ...
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How to determine the best-fit magnetic dipole Gauss coefficient in a shifted coordinate system?

Introduction A planetary magnetic field $\vec{B}$ can be described outside of the planet using Gauss coefficients $g_n^m$ and $h_n^m$ and a spherical harmonic expansion: $$\vec{B} \;=\; -\vec{\...
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Why is the singularity not taken into account?

In this article "Reflections on Maxwell’s Treatise", Section 4.2, it says: He replaces $\mathbf{m}$ with a volume element of magnetization $\mathbf{M}\ dV$ , integrates over $V$ , and lets the same ...
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If one divides the molecular dipole of HCl by the interatomic separation, the result is not a multiple of the electron charge. Why is that?

I'm having some trouble understanding the reasoning behind the final note in the following worked problem: An HCl molecule has a dipole moment of $3.4\times10^{-30}\:\rm C\:m$. Assuming that equal ...
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What is the force on a dipole in a uniform electric field?

For an electric dipole of dipole moment $\vec{p}$ placed in an electric field $\vec{E}$ experiences a force given by $$\vec{F}=-\nabla U=-\nabla(\vec{p}\cdot\vec{E})=(\vec{p}\cdot\nabla)\vec{E}.$$ So $...
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95 views

Dipole over a conductor plane

If we place a charge $q$ over an infinite grounded plane we can find the potential in all points of space using the method of images and find the induced surface charge on the plane. However, how ...
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Why is electric dipole moment represented by “p”?

I recently came across a text where the electric dipole moment was represented as "d" instead of the more commonly used "p". The reason behind using "d" here is probably that "dipole moment" begins ...
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Is it necessary that, in $q$ dipole charges should be equal and opposite?

When I read about multipole expansion in Griffith book, i saw that "if total charge is zero, dipole moment is independent of origin." I have some doubts about this. I learned that the dipoles are two ...
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1answer
359 views

Torque on dipole in a non-uniform electric field [duplicate]

What happens when an electric dipole is kept in a nonuniform electric field?
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162 views

Radial vs tangential component of electrical field due to dipole

I was wondering that why should the maximum magnitude (with respect to $\theta$) of radial component of electrical field of an electric dipole, $$E_r=-\partial V/\partial r=\frac{2p \cos\theta}{4\pi\...
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Electric field of two equal charges of the same sign [closed]

Two equal positive charges are at distance d, -d from the origin on the y axis. What is the distance on the x axis beyond which a small perturbation in y will move a particle away from the x axis? ...
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Can I replace a multipole expansion by a combination of separate dipoles?

If I want to be able to model a magnetic field flux density $\mathbf{B}$ from a magnetic source located at the origin at a position $\mathbf{r}$, it is my understanding that I can represent $\mathbf{B}...
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How is total angular momentum conserved in electric dipole transitions for ΔJ = 0 in a multi-electron atom?

One of the selections rules is that ΔJ=0,±1 for an electric dipole transition in a multi-electron atom, where J is the total angular momentum. Since ...
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Electrodynamics confusion - Hertzian dipole

I am studying a course in Electrodynamics and we are just covering retarded potentials and the Hertzian dipole. In my lecture notes, we have calculated the magnetic vector potential $A$ in the ...
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Paradox in conservation of energy

Let us assume there is a constant electric field in an interested region (finite volume)and a non-conducting object is thrown into it with speed $v$ and now take the second scenario with the same ...
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Deriving the electric displacement field ($D$ field)

I am trying to derive the $D$ field (or electric displacement field): $$D=\varepsilon _{0}E+P$$ I am using the following relationships: $$\rho=\rho_{f} + \rho_{b}$$ $$ \rho_{b} =-\nabla \cdot P$$ ...
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Question on force between dipoles [closed]

Two point dipoles of dipole moment $p_1$ and $p_2$ are at a distance $x$ from each other, and $p_1$ is parallel to $p_2$. The force between the dipoles is? I’m not understanding what does point ...
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Isn't magnetism governed by the inverse square law? [duplicate]

Why does magnetism appear to decay much faster than gravity with distance? A clear indication of this is the fact that a magnet that in short distance able to overcome gravity and pick up some object,...
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1answer
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How to derive the $\frac{4\pi}{3}\vec{p}\delta^3(\vec{r})$ element for the dipole field, from its potential?

This might be a bit more general question about how to figure out what is the appropriate (delta) expression in singular points, but e.g. for the dipole, we can derive its potential by a taylor ...
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Optical tweezers : dipole force or radiative pressure?

Two types of forces are usually considered to describe light-matter interaction. On the one hand, the radiative pressure, which corresponds to absorption - spontaneous emission cycles, is proportional ...
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408 views

What is the physical significance of Dipole moment?

What does dipole moment physically signify? I know it is the product of 2 charges and distance between them. Like momentum is the product of mass and velocity, but physically it shows the quantity of ...
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Why does a ionic crystal polarize more at low frequencies rather than at high ones?

And if there was a difference if the propagational mode of the electric field in the crystal is longitudinal or transverse.
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Working principle of an optical stretcher

I understand that while using an optical stretcher experimental apparatus we attach a small dielectric ball to the specimen of study which can either be a DNA molecule, a Biological cell or any ...
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1answer
57 views

Question about Optical tweezers working principle

Why do particles on the periphery of the laser beam in optical tweezers apparatus drift to the center of the beam? What force pattern causes this pull to the center?
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What is the mechanism by which light induce polarity in tiny particles?

I understand that the electric field in light induces polarity in tiny microparticles for example. Can someone explain the mechanism of how the vibrating electric field in light induces a dipole ...
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Expression for electric potential around an electric dipole in Cartesian coordinates

I'm trying to find the equation of the electric potential of a electric dipole in Cartesian coordinates. The equation should take the form of something looks like this: $$z = x\exp(-x^2-y^2)$$ ...
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796 views

How to calculate the dipole potential in spherical coordinates

I want to calculate the dipole potential in spherical coordinates. I know that the potential can be calculated with $$ \phi = - \int \mathbf E \cdot\mathrm d\mathbf r,$$ but I don't know the electric ...