Questions tagged [poynting-vector]
The directional energy flux of an electromagnetic field. In conjunction with Poynting's theorem and the continuity equation, it used to express the conservation of electromagnetic energy, and to calculate the power flow in electric and magnetic fields.
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Meaning of the Poynting vector
In a book I am studying, the Poynting vector is defined as:
$$ \mathcal{P} = \mathbb{E} \times\mathbb{H} $$
and it is described the Poynting's theorem, that states that the flux through a surface ...
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Does a lightbulb glow due to the interaction with electromagnetic waves or due to the interaction between its atoms and the moving electrons?
Today I learned that energy is transferred to a lightbulb through electromagnetic waves produced by the movement of electrons and according to Poynting's law, the direction of this energy is ...
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Does the Newtonian gravitational field have momentum analogous to the Poynting vector?
We can define the total energy of the electromagnetic field as:
$$\mathcal{E}_{EM}= \frac{1}{2} \int_V \left(\varepsilon_0\boldsymbol{E}^2+\frac{\boldsymbol{B}^2}{\mu_0}\right)dV$$
which satisfies the ...
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Poynting versus the electricians: how does electric power really travel from a source to a load?
Suppose I connect a battery to a lamp in the usual way. Obviously, electric power will go from the battery to the lamp, causing the lamp to light up. But exactly what path does the power take to get ...
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Is there something like the Poynting vector for hydraulic circuits?
The Poynting vector is a representation of the energy flux in electromagnetics, showing the amount and direction of power flow at different points in space. In electric circuits, the energy is not ...
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What is the Poynting vector of an electron?
On chapter 27 of "The Feynman Lectures on Physics Volume II: Mainly Electromagnetism and Matter", Richard Feynman says:
Finally, in order to really convince you that this theory is obviously nuts,
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Does a nonzero Poynting vector mean that there is propagation of energy?
I don't know how this "paradox" can be solved. I'm given the following system: A permanent magnet with a magnetic field given by ($\hat{a}$ are unit vectors in the x and y directions)
$$\vec{H}=H_0\...
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Why is the Poynting Vector Symmetric in E and H?
Why is the Poynting Vector symmetric in E and H? I always thought that E and B were the analogous fields, so I would think that any equation using magnetic and electric fields should be symmetric in E/...
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Transmitted Power and Poynting's theorem contradiction?
I was reading Chapter 12.1 in Hayt & Buck "Engineering Electromagnetics" 8-th edition. Here they discuss the reflection of uniform plane waves at normal incidence.
They derived the following ...
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When (or what is the meaning of) $I \propto E^2$?
For a monochromatic plane wave: $$\mathbf E = \mathbf E _0e^{i(\mathbf k \cdot \mathbf r -\omega t)},\qquad \mathbf H = \dfrac{\mathbf B}{\mu _0}= \mathbf H_0e^{i(\mathbf k \cdot \mathbf r-\omega t)},$...
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Interpretation of Poynting Vector
Short Version
How exaclty can the Poynting vector be physically interpreted for static electric and magnetic fields?
I know that it describes the magnitude and direction of energy flow in EM-waves. ...
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Is the additional term in the canonical momentum exactly equal to the momentum of the electromagnetic field?
The canonical momentum of a particle in an electromagnetic field is given by $$\textbf{P}=m\textbf{v}+q\textbf{A}$$ Is the term $q \textbf{A}$ equal to the momentum of the electromagnetic field (which ...
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Intuition behind Poynting's theorem: relative sign between the electric and magnetic contributions to the energy
The standard derivation of Poynting's theorem for EEs uses sinusoidal complex time dependence $e^{\mathfrak{j} \omega t}$, that is $\mathbf{E}(t)=\Re [ \hat{\mathbf{E}}e^{\mathfrak{j} \omega t}]$ and ...
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Veritasium Electricity videos: where does the majority of energy really flow? [duplicate]
After watching Veritasium second video on electricity (references at the end), I have some doubts about where the majority of the energy flow actually happens. The reference experiment is the simple ...
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Magnetic monopoles and the Poynting vector
Assume that magnetic monopoles exist. Let us have one charge(for example, an electron) of electric charge $q_e$ at the origin and one magnetic monopole particle of magnetic charge $q_m$ separated by a ...
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What does the magnitude of the Poynting vector mean in practice?
I have recently found out that word "intensity" is somewhat ambiguous for electromagnetic waves. I always thought of it as the magnitude of the Poynting vector (field), but this is not ...
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Relativistic momentum of the E.M field vs Poynting momentum questions
I come somehow to the following thoughts:
The energy of the EM field is $$\mathcal{E} = {\epsilon_0\over 2} (E^2 + c^2 B^2).$$
Associate to $\mathcal E$ the relativistic mass $$m_r = {\mathcal{E}\over ...
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Near energy In the null of a Hertzian dipole
Since $\mathbf E = -∇Φ - ∂\mathbf A/∂t$ one expects an oscillating $\mathbf E$ field even in the null of a Hertzian Dipole unless the two right hand side terms cancel -- which they do in the far field ...
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Understanding Poynting's Theorem intuitively
I understand that, broadly speaking, Poynting's theorem is a statement of conservation of energy.
Energy density of a volume of current and charge decreases proportionally to work done on charges ...
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Poynting theorem and entering power
I refer to the time-domain version of the Poyinting theorem in electro-magnetism:
$- \displaystyle \oint_S (\mathbf{E} \times \mathbf{H}) \cdot d\mathbf{S} - \int_V \mathbf{E} \cdot \mathbf{J}_i \ dV ...
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Explanation of the Angular Momentum of the Electromagnetic Field [closed]
The fact that the EM field carries angular momentum is a well-accepted fact, and I've been trying to look into ways of showing it. I have two: One using Noether's Theorem, other using the Poynting ...
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Is it the Poynting Vector Flux or the Electric Field Flux that creates a Diffraction pattern on the back screen?
As we know the diffraction pattern from a circular hole looks something like
Intuitively I would think the "bessel function like" pattern on the right would be due to poynting flux through ...
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Poynting's theorem - energy conservation
Poynting's theorem:
$$\int_V\left(\vec{E}\cdot\vec{J}\right)\,\mathrm dV = -\dfrac{\partial}{\partial t}\int_V\dfrac{1}{2}\left(\epsilon_0 E^2 + \dfrac{1}{\mu_0}B^2\right)\,\mathrm dV - \dfrac{1}{\...
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Concerning the energy stored in electromagnetic fields
How do we know that $$u = \frac{1}{2}\left(\epsilon_0E^2 + \frac{1}{\mu_0}B^2\right)$$ gives the energy density of electromagnetic fields? Is it a postulate of classical electrodynamics? Griffith ...
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How does the Poynting vector know who is the primary and who is the secondary of a transformer?
I've read in several places that the Poynting vector is directed from the primary to the secondary of a transformer (we assume here that the primary is the winding that provide the AC energy, while ...
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Poynting vector in a simple DC circuit
This image
I took from Wikipedia shows the directions of E(red) and B(green) and poynting vectors(blue) at different locations on the circuit. I don't seem to understand why the E fields(red) are ...
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z-component of angular momentum for classical light
Given an electric field and magnetic filed in the forms of
$$
\begin{aligned}
\vec{E}(\vec{r},t) &= \Re \left[ E_{0}^{2} \exp(i(kz - \omega t)) \left(E_{x}\hat{e}_{x} + E_{y} \hat{e}_{y} \right) ...
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Momentum density and Poynting vector
In Feynman lectures vol 2 chapter 27 he says there is a theorem which says whenever there is a flow of energy per unit time per unit area the momentum density in the volume is found by multiplying it ...
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Is there any other momentum besides the Poynting momentum stored in an electromagnetic field?
I am having some conceptual difficulties with energy and momentum stored in the EM field.
The force density at a point is
$\rho E + j\times B$
Because of conservation of momentum, and because the ...
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Is the Poynting vector continuous?
Helmholtz equation for the magnetic field is
$$∇^2 \mathbf{H} + k^2 \mathbf{H} = \mathbf{0}$$
Assuming time-harmonic waves Ampere's law can be rearranged
$$\mathbf{E} = \frac{∇\times\mathbf{H}}{σ+...
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Lateral momentum of Gaussian beam
A beam of light carries momentum. What fraction of this is lateral rather along the propagation direction if we assume something like a Gaussian beam?
Wikipedia claims in the entry on Gaussian beams ...
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Orthogonality between $\vec{E}$ and $\vec{H}$ waves with space-dependent amplitudes
I am able to prove in a few lines that the electrodynamic field vectors $\vec{E}$, $\vec{H}$ and $\vec{S}$ are all orthogonal to each other considering that $\vec{E}$ and $\vec{H}$ are coherent plane ...
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What experiments confirmed Poynting's Theorem?
Actually, I have two related questions. The fist is the above question. The second is, what experiments confirmed that $\varepsilon_0\left(\frac{E^2}{2} + c^2 \frac{B^2}{2}\right)$ is the ...
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On Poynting vector and electric circuits
Consider the following setup.
The answer is $(3)$ - spoiler alert - and it's explained here, using Poynting vector. The thing is though
How can the electromagnetic energy flux even reach the light ...
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Linearity (or lack thereof) of the Poynting vector
Maxwell's equations are linear. If we have a solution for the electromagnetic fields $\vec{E},\vec{H}$, and another solution $\vec{E}',\vec{H}'$, then $\vec{E}+\vec{E}',\vec{H}+\vec{H}'$ is also a ...
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Poynting vector of a scalar wave
Consider a scalar wave (of sound for example) of the form $\psi(\vec{r},t)$. Which is its Poynting vector? I mean, the vector that takes account for the energy flux in the same sense as for the case ...
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Relation between intensity of light and refractive index
The intensity of light (as calculated from time average of the poynting vector) is given by $I = (1/2) \epsilon v E_0^2$. Here the intensity is dependent on the velocity of light in the medium. The ...
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What does the Poynting flux represent?
I know that the Poynting flux is the cross product between $\vec E$ fields and $\vec B$ fields, but I'm wondering, are the field lines of the Poynting flux considered as electromagnetic energy? Let's ...
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Poynting's Theorem simplified?
How can I apply Poynting's theorem to any system that has a magnetic field & electric field, to state conservation of energy?
How does Poynting's theorem state conservation of energy in EM? I ...
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Imaginary components of Poynting vector in rectangular waveguide
Consider a rectangular wave guide, as in the example of Jackson - Classical Electrodynamics
The Poynting vector turns out to be
$$\vec{S}=\epsilon c^2 \vec{E_0} \times \vec{B_0} e^{2i(kct-\alpha z)}...
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Why does the divergence of the Poynting vector have energy flux density?
The poynting vector is defined as
$\vec{S}=\mu_{0}^{-1}\vec{E}\times \vec{B}$
Taking the divergence of the poynting vector, one arrives at
$\vec{\nabla} \cdot \vec{S}=-\frac{\partial u}{\...
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X-ray diffraction from crystals and time-averaging
To calculate the elastically scattered intensity of x-rays from crystals, one classically considers scattering from a free electron first and then one sums up the scattered em-fields of all electrons ...
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Veritasium Electricity Follow-Ups: Insulators, Switch Location, larger gap
This question is similar to:
Doesn't Veritasium's Recent Video About Circuits Violate The Speed Of Light?
In what order would light bulbs in series light up when you close a long circuit?,
...
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What is the connection between the Poynting vector (EM transverse wave) and the description of photons with $E=h*f$ and $c=f*\lambda$?
I think for radio antenna transmitters, if the AC current's frequency is at the frequency of radiowaves, EM waves in the radio frequency will be emitted? Then the frequency has something to do with ...
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Understanding the meaning of (and using) Maxwell Stress Tensor
From reading Griffiths, I understand that the total EM force on a set of charges in volume $\mathcal{V}$ can be found as
$$ \textbf{F}=\oint_{\mathcal{S}} \overleftrightarrow{\textbf{T}} \cdot d\...
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Why doesn't a uniformly moving particle radiate?
When considering a uniformly moving charged particle, we have the following fields:
$$\vec E = \frac{q(1-\beta^2)}{4\pi\epsilon R_a}\vec R$$
$$\vec B = \frac{1}{c^2}\vec u \times \vec E$$
With $\vec ...
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Physical Interpretation of Poynting Vector
I'm looking for a physical interpretation of the Poynting Vector. I understand that it should be thought of as an energy flow due to the electromagnetic field, but would I be correct in saying that in ...
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Radiation Pressure derivation
Radiation pressures mathematical expression according to Wikipedia is,
$\frac{1}{\mu_0 c}\vec{E} × \vec{B}$
"Radiation pressure is the mechanical pressure(force/area) exerted upon any surface due ...
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Joule effect in Poynting theorem
I came across two different statements of the Poynting theorem. In one of them the power dissipated through Joule effect is made explicit.
The one without explicit Joule effect is:
$\frac{dW}{dt} = \...
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Superposition of two electromagnetic waves and momentum
Electromagnetic waves follows superposition principle. So that we can simply add the fields of waves to calculate the final field. Then let's think there are two waves that are moving through x-axis ...