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Questions tagged [poynting-vector]

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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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1answer
37 views

Is the direction of energy flux arbitrary for the poynting vector?

So for the poynting vector, we have $\vec S=\vec E\times\vec B$, which would give us a vector (energy flux) that is perpendicular to both the electric field and magnetic field. The problem for me is ...
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1answer
31 views

What happens with the divergence of maxwell stress tensor when EM fields in vacuum?

The conservation momentum can be derived from the total electromagnetic force on the charges in volume $V$ and is written in this way: $$ \frac{d\vec{p}_{mech}}{dt} + \frac{d}{dt} \int_V (\vec{E}\...
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2answers
108 views

Is a “classical” electron surrounded by 31,6 GW electromagnetic energy-vortex? [closed]

Electromagnetic energy-momentum circulation around the dipole-axis of a "classical" electron can be substantiated by determination of the amount of passive power [W] assignable to such energy-...
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1answer
107 views

The fields of Liénard and Wiechert and Poynting vector

EDIT: I know that the electric and magnetic fields depend not only on speed but also on acceleration and can both be expressed as the sum of two contributions: \begin{equation} \overline{E} (\bar{r},...
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0answers
45 views

Questions about the energy density and momentum density in linear media

Precisely which energies are accounted for in the energy density of a linear medium given by $$u = \frac{1}{2}\left(\epsilon E^2 + \frac{1}{\mu}B^2\right)?$$ For example, is there a kinetic energy ...
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5answers
296 views

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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3answers
106 views

Is Poynting vector conserved or Intensity conserved for reflection and transmission of electromagnetic wave?

When an electromagnetic wave meets a boundary, does energy conservation mean Poynting vector of reflected + Poynting vector of the transmitted wave is equal to Poynting vector of incident wave or just ...
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1answer
62 views

Computing Poynting Vector from phasors

The Poynting Vector is defined as: $$\mathbf{N} = \mathbf{E} \times \mathbf{H}$$ With $\mathbf{N}$, $\mathbf{E}$ and $\mathbf{H}$ being vector fields. I'm working with monochromatic plane waves, so ...
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50 views

Relationship between poynting vector and radiation pressure

I know that When an electromagnetic wave is absorbed or reflected by a surface, the momentum of the wave is transferred to the surface. I also know that for absorption the radiation pressure is 〈S〉/c ...
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2answers
62 views

Momentum density of the EM field - Classical field theory

The Lagrangian density of the EM field is given by $$ \mathcal{L} = \frac{1}{8\pi}\left(E^2-B^2\right) $$ Let $\vec{A}$,$\phi$ be such that $$ \vec{E} = -\frac{1}{c}\frac{\partial\vec{A}}{\partial t} -...
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3answers
132 views

Can a wave's Poynting vector be in the opposite direction compared to its direction of propagation?

Can a wave's Poynting vector be in the opposite direction compared to its direction of propagation, and if so, what physical implications does it have? As I understand, the poynting vector s can be ...
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1answer
66 views

How is the electric field of light related to its wavelength?

Light is an electromagnetic field. At the same time light is composed of photons; each one carries an energy given by $E=\frac{hc}{\lambda}$. The electromagnetic energy of light is expressed by its ...
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1answer
187 views

Poynting's vector and its application to circuits

If I had a circuit as shown in the figure with the battery and the capacitor being covered completely, save for a passage for the conducting wire, by a hypothetical material that doesn't allow ...
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0answers
31 views

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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0answers
47 views

Visualizing a scenario where wave vector's direction is different from Poynting vector's one

Can someone help me visualize how the direction of the wave vector can be different from the one of the poynting vector in a scenario like a lossy medium? I'm not seeing it.
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424 views

Energy and Poynting vector in a solenoid

We have the following scenario. A long (ideal) solenoid, with $n$ turns per unit lenght, is carrying a current $I$. At the beginning, the current is constant and we have a magnetic field $$\mathbf{B}...
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1answer
102 views

why do we use poynting vector in poynting theorem but not just it's magnitude?

We all know that poynting vector points in the direction of the wave propagation and it's value of power supplied to a unit area. So while deriving poynting theorm, the energy flown out of the system ...
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1answer
95 views

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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1answer
74 views

Instantaneous radiated EM power, integrate over an open or enclosed surface?

It's about the propagation of an EM wave in the vacuum. The instantaneous radiated power outcoming the volume $v$ is expressed as $$p=-\iiint_v \frac{\partial w}{\partial t} \text{d}v=-\iiint_v \...
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1answer
420 views

Do Maxwell's equations conserve energy? [closed]

I was wondering if Maxwell equations conserved energy. Jackson is not really convincing about the whole Poynting theorem (neither currently google found articles which just assume a bunch of stuff). ...
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Poynting theorem on an example?

I understand the basic statement of Poynting theorem of conservation of energy relative to electromagnetic field. However, I fail to apply it to an example. Consider this classical case: ...
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2answers
225 views

Is the angular momentum vector of a photon in the same direction as the magnetic field?

From what I understand, when you have linearly-polarized light, the angular momentum vector is perpendicular to the poynting vector. Does this mean that the angular momentum vector is always in the ...
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1answer
918 views

light intensity through a double slit [closed]

When a light source with a given intensity I emit through a double slit (or triple slit) how does the intensity of the first maxima change in regard with the initial one?
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267 views

Poynting vector in static electromagnetic fields

What would Poynting vector mean physically if there is plane-parallel electric and magnetic field perpendicular to each other, like what we do in Hall Effect experiment? Or, in general, what would it ...
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1answer
946 views

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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1answer
268 views

On a derivative of the Poynting vector's derivation

I'm studying the Poynting theorem (the mathematical proof). It starts considering the energy held by the electromagnetic field inside a surface $S$, which is: $$ U_{em} = \int_{\tau}\frac{1}{2}(\vec{...
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2answers
171 views

Help finding an alternative to the time average of the Poynting vector

The time averaged Poynting vector is: $$\langle \vec{S} \rangle = \frac{1}{T}\int_0^T\frac{1}{\mu_0}(\vec{E} \times \vec{B}) dt$$ But I am not given the total time of the event. Is there another way ...
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1answer
69 views

Derivatives and integrals in the Poynting theorem

Many derivations of the Poynting theorem follows the same approach: The work done by the electromagnetic field is: $dW = dq(\vec E + \vec v \times \vec B)\cdot d\vec l = dq(\vec E + \vec v \times \...
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1answer
177 views

How can the power density term (E·J) be negative in the Poynting vector theorem equation?

The $\displaystyle\iiint_V \vec E \cdot \vec J dV$ term in the Poynting theorem equation can indicate the Joule's power dissipation when that integral is greater than zero, because $\vec E \cdot \vec ...
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1answer
200 views

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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1answer
836 views

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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1answer
2k views

How do you find the direction of magnetic field given the electric field?

Say you're asked to find the poynting vector of a wave and you're given an electric field component of the E M traveling wave. You will need to find B using E=cB, but how would you find the ...
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1answer
526 views

Find poynting vector (understanding solved example)?

An electromagnetic wave in the free space satisfy the following relationships: $\vec{K}\times \vec{E}=Z\vec{H}$ $\vec{E}=Z\vec{H}\times \vec{K}$ $Z=\sqrt{\frac{\mu}{\epsilon} } $ Find local ...
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1answer
327 views

Energy of the electromagnetic wave

The energy(density) of an electromagnetic wave is described by the Poynting vector. This is the function of the $E$ and $B$ field. (the exact formula is well known). The magnitude of the $E$ and $B$ ...
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1answer
163 views

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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1answer
680 views

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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0answers
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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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2answers
3k views

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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3answers
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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}{\...
2
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1answer
487 views

In a waveguide, where does the energy in attenuated waves go?

In an electromagnetic waveguide, there is generally a "cutoff frequency." Electromagnetic waves with a frequency that is lower than this cutoff frequency will not propagate at all -- i.e., they will ...
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3answers
641 views

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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1answer
70 views

Poynting vector and electric shock

As an explanation to Poynting vector(P), I read the following example: A DC source is connected to a bulb (receiver) by means of 2 conductors. The direction of the electric field between the ...
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2answers
353 views

Photoelectric effect and energy of light

I have a doubt about photoelectric effect and the nature of light in general. From what I understood, in order to ionize a piece of some material, I need an electromagnetic wave with a frequence ...
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1answer
193 views

Poyting theorem for a plane wave

I would like to apply and verify the Poynting theorem for a uniform plane wave but there is obviously something wrong in my demonstration. The Poynting theorem expresses the conservation of energy: ...
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2answers
337 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 ...
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1answer
581 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 ...
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1answer
215 views

What is the meaning of $\vec{E}\times\vec{B}$?

Consider that for a single $\mathbb{R}^3$ point-source emitter of RF, the $\mathbf{E}$ and $\mathbf{B}$ fields (when treated as transverse sinusoids and ignoring interference properties) are always ...
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3answers
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Question about intensity of EM waves

For electromagnetic wave if it's reflected from a perfect conductor standing wave can be form. I wonder why Poynting vector can be used to describe the intensity of standing EM wave. (see p.19 of http:...
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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 ...