Questions tagged [poynting-vector]

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4
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1answer
59 views

Is the extra 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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2answers
83 views

Interpreting discontinuity in the Poynting vector

An infinite cylinder of radius R has a uniforme current distribution through its surface $\vec \kappa (t)=\kappa(t)\vec \phi$. Find a) the magnetic field generated by the distribuition, b) the induced ...
2
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2answers
53 views

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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0answers
32 views

Poynting vector & power flow

I'm trying to understand why the Poynting vector coincides with the power flow. Firstly, the general "conservation theorem" of electrodynamics or the so called Poynting's theorem is: $${\displaystyle ...
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0answers
35 views

Angular distribution formula & Poynting's vector

I'm looking for a derivation of the Angular distribution formula of the "Bremsstrahlung" for radiated power as a function of angle (Bremsstrahlung is german for "deceleration radiation"): $${\...
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0answers
62 views

Analogue for $E$ and $H$ in mechanics

I'm playing with mechanical analogues for current/voltage (force/velocity) and passive elements $RLC$ (damper, spring, mass). In order to define and analogue for Poynting vector... what should be the ...
2
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1answer
90 views

About electromagnetic work in first principle of thermodynamics

Reading L. E. Reichl, A Modern Course in Statistical Physics, first principle of thermodynamics is stated as $$dU = \delta Q − \delta W + \sum_{j=1}^{v} μ_j dN_j$$ with $$\delta W = P dV − J dL − σ ...
5
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1answer
245 views

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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0answers
29 views

Mechanics / electrodynamics borderline

In classical mechanics we use a simpler approach than in electrodynamics: the forces are supposed to be exchanged directly among the bodies, no notion of field is needed, and conservation laws (energy ...
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1answer
41 views

Electrodynamic wave energy momentum transfer

if a point charge Q is vibrating in some mechanical way along the X axis with respect to a certain point xQ, then the value of electromagnetic energy density(which is a point function like E) on the ...
0
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1answer
52 views

How to show that imaginary part of complex power is reactive power?

Suppose I have a voltage across an element $V(t) = A \cos(\omega t)$ and the current through it given by $I(t) = B \cos(\omega t + \phi)$. The instantaneous power is $$P(t) = V(t)I(t) = AB \cos(\...
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1answer
29 views

If the $E$ component of an EM wave interacts with another $B$ field (from other source), can they generate Poyting vector (or photon flux)?

As shown in the figure, a planar EM wave propagates in the $z$-direction, and its electric component is in the $x$-direction. Meanwhile, in the whole region, there is a static magnetic field B ...
0
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1answer
128 views

Calculating average of normal Poynting vector for evanescent wave

The Poynting vector (in Gaussian units) is given by $\mathbf{S} = \frac{c}{8\pi}\left(\mathbf{E}\times\mathbf{H}^*\right)$, and the magnetic field is given by $\mathbf{H} = \frac{c}{\mu\omega}\left(\...
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1answer
99 views

Interpretation of real and imaginary parts of the Poynting vector in a vacuum

It is known that the flux of the Poynting Vector through a certain surface represents the total electromagnetic power flowing through it. Then, its real part is the active power, while its imaginary ...
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2answers
43 views

On work by a electric field in a electric circuit

If the electric circuit is complete, then one can say that the net average displacement of the electrons is $0$. Then consequently the work done by the electric field is also $0$. So how is energy ...
0
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1answer
65 views

Poynting vector flux on a closed surface

What does the flux of the Poynting vector through a closed surface represent? I know that the flux of the Poynting vector on a certain surface represents the power flowing through it. But if the ...
3
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0answers
27 views

Poynting vector flux in a tube (geometrical optics)

Let's consider the following tube (defined as the solid described by two arbitrary surfaces dA1 and dA2, and by all the rays which connect their boundaries): I read in a textbook that, because of ...
0
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1answer
104 views

How Is Induction Energy Transferred From a Toroidal Solenoid To An External Conductor During Linear Current Change?

It is widely understood that $\nabla \times \vec A =\vec B = 0$ outside a toroidal solenoid with constant current, $I=k$ ($I = \vec J$ in the below illustration). It is not so widely understood that ...
2
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3answers
99 views

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 ...
1
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1answer
58 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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2answers
225 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
114 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-...
1
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1answer
137 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},...
2
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0answers
56 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
346 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 ...
1
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3answers
290 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 ...
1
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1answer
169 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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2answers
83 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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4answers
484 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 ...
1
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1answer
105 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
352 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 ...
3
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0answers
42 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
56 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.
3
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1answer
905 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}...
0
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1answer
124 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 ...
2
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1answer
133 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 ...
0
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1answer
86 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
562 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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0answers
497 views

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
302 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
1k 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?
2
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0answers
379 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 ...
3
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1answer
1k 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
349 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
675 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 ...
0
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1answer
72 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 \...
0
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1answer
198 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 ...
4
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1answer
252 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
1k 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
3k 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 ...