Questions tagged [poynting-vector]

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Complex Poynting vector and energy loss

Consider continuum medium (no boundaries) and the electromagnetic wave Poynting vector $$ \mathbf{S} = \mathbf{E}\times \mathbf{H}^*$$ with $^*$ the complex conjugate. When there is a phase difference ...
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19 views

Energetic balance from differential Ohm's law

Before talking about Poynting vector, my book considers a region of space in which there are batteries, resistors and electromagnetic waves. To find the expression of the Poynting vector, the book ...
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94 views

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 ...
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32 views

In wave equation, what is the meaning of poynting vector, compare to the amplitude vector?

I'm looking at this equation: $$\tilde{\vec E}(\vec r,t)=\tilde{\vec E}_0e^{i(\vec k\cdot r-\omega t)}\hat n \tag{1}$$ I thought that $\tilde{\vec E}_0$ was the polarization vector, but then he added $...
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Poynting vector exists only in vacuum?

The Poynting vector is defined as $\vec{S}=c^2\epsilon_0 \vec{E}\wedge \vec{B}$ in vacuum. Can we replace $\epsilon_0$ by $\epsilon$ when we consider dielectric ?
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38 views

Why do these two ways of thinking about current seem to be contradictory?

I was studying for my electrodynamics exam and came across two questions which seemed to require conflicting models of how power is transferred in a current carrying wire. The first question: A ...
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112 views

Is the Poynting vector in a DC circuit mathematically correct, but representing potential energy and not the delivery of energy?

There are magnetic and electric fields outside the DC circuit wire. The fields are static and separate. Energy is stored in the fields. There is a low amount surface charges, and to detect the ...
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66 views

Is applying the Poynting Vector to a DC circuit incorrect?

The Poynting vector can be defined as: the Poynting vector magnitude is the rate of energy flux in watts per square meter and whose direction is the direction of propagation of the electromagnetic ...
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346 views

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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1answer
62 views

Meaning of zero Lagrangian and connection to Poynting theorem

I have an electromagnetic field system for a cavity with a current source, whose Lagrangian has the form $$ L=\int_V dV (w_{e}+w_{h} +i(E\cdot J)/\omega)+ \oint_A dA (E\times H)\cdot \hat{n}, $$ ...
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77 views

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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100 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 ...
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57 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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44 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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40 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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66 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 ...
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1answer
120 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 dA ...
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263 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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30 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 ...
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1answer
65 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 ...
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1answer
228 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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140 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
46 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 ...
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1answer
82 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 ...
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28 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 ...
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1answer
129 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 ...
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3answers
106 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 ...
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1answer
69 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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269 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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116 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
144 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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61 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
365 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
340 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
195 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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86 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
612 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
120 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
404 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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1answer
47 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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61 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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1k 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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127 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
179 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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88 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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606 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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502 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
313 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 ...