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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Electric field strength $d$km from a television transmitter of power $P$kW, assuming isotropic radiation

I think I need to use the Poynting vector to do this, as it is equal to the power per unit area flowing through a surface. At a distance $d$km from the transmitter, the surface will have a surface ...
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Poynting vector and intensity of a signal

Given a plane monochromatic electromagnetic wave propagating in $x$ direction, with associated electric and magnetic fields of the form: $\overrightarrow{E}(x,t)=\overrightarrow{E_0}\cos(kx-\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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Poynting Vector Perpendicular to Surface

In Spherical coordinates if we have a source at the origin generating $E$ in the $\hat{r}$ direction and $H$ in the $\hat{\phi}$ direction then our Poynting Vector will be in the $\hat{\theta}$ ...
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How does a Poyinting vector act on a neutron?

How does a Poyinting vector act on a neutron? As I understood a photon action on a charged particle this action is purely electromagnetic where the electric component shake the particle perpendicular ...
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AC power, EM waves and Poynting vector

Question: Does electric energy propagate as electromagnetic waves and if that is the case, how? This is clearly not the same as propagating EM waves by an antenna whatsoever. If that was the case we ...
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Fourier transform of the Poynting vector

One of the ways to define the instantaneous Poynting vector in the time domain is as follows: \begin{equation} \mathbf{S}(\mathbf{r}, t) = \mu_0^{-1} \big( \mathbf{E}(\mathbf{r}, t) \times \mathbf{...
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Validity of $E$ field energy density equation

As far as I'm aware, the most popular/rigorous way of deriving $E$ field energy density is starting with the potential energy of a continuous charge distribution (which itself has some flaws that I ...
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Near and far field EM radiation

When we talk about radiation, we often talk about the near and far field radiation. For the near field, the Poynting vector falls off like $1/r^3$ and the far field Poynting vector falls off like $1/r^...
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Energy carried by Electromagnetic Waves

The energy density carried by monochromatic planar Electromagnetic Waves is defined as: $ u = \epsilon_0 E_0^2 cos^2(kz-\omega t + \delta)$ As this wave travels, it carries this energy along with it. ...
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Doubt in Poynting's theorem

In Griffiths's Electrodynamics, to explain Poynting's theorem, he writes: Suppose we have some charge and current configuration which at time t produces fields E and B. In the next instant dt the ...
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Poynting vector in metamaterials

Poynting vector in a material with magnetic permeability $\mu$ is defined as $\mathbf{S}=\frac{1}{\mu}(\mathbf{E} \times \mathbf{B})$ In certain media $\mu$ can be negative. In that case, $S$ will ...
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Is the Poynting vector always perpendicular to the plane a circuit lies in?

The Poynting vector is the cross product of electric and magnetic field (divided by $\mu_0$). Given an electric circuit that lies on the plane of a circuit board, the magnetic field is usually "...
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Poynting vector for a plane wave in a medium with relative permittivity $\varepsilon_r$

The time-averaged Poynting vector can be written: $$\tag{1} \langle \boldsymbol{S}(\boldsymbol{r})\rangle=\frac{1}{2} \operatorname{Re}\left\{\boldsymbol{E}(\boldsymbol{r}) \times \boldsymbol{H}^{*}(\...
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Radiations in static fields by poynting Vector

Why Poynting vector $\vec S=\frac{1}{\mu_0}(\vec E\times \vec B)$ is not able to produce radiation when fields are static?
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Computing total power from $x$, $y$, $z$ components of Poynting vector

I have (real parts) of $x$, $y$, $z$ components of Poynting vectors on the surface of a sphere. Since the total outward power flow from the sphere involves integrating the normal component of a ...
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Energy dissipation due to displacement current

Consider the following problem: An isolated capacitor made of parallel circular plates of radius $a$ separated by a distance $d \gg a$ is charged such that there is a potential difference $V$ between ...
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Conservation of Energy / Poynting vector

On this page, it states: "The only fields' couples (a,b) for which we can get a non-zero value of the Poynting vector for a large distance r₀ over the sphere are (R, R); (radiation, radiation) ...
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How do minimum scattering antennas extract energy

In our antennas and fields course, we had one task where we simulated a line antenna in an incident plane wave. There, we specifically looked at the fields produced by scattering from the antenna. ...
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What is the force direction of the radiation of the electromagnetic field

We know the radiation waves are transversal wave. That means the electric field $\boldsymbol{E}$ is perpendicular to the radiation direction $\boldsymbol{r=x-x'}$. Here $\boldsymbol{x}$ is the ...
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Isn't the direction of propagation wrong in this diagram from wikimedia commons?

The direction of propagation of an electromagnetic wave is given by the Poynting Vector \begin{equation} \boldsymbol{S} = \frac{1}{\mu_0} \boldsymbol{E} \times \boldsymbol{B}. \end{equation} This ...
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Why do electromagnetic waves detach from the antenna?

In most explanations of how antennas work they say that because of kinks in the electric field of an antenna meets at one point and detaches... I looked up reasons for why this happens but all I got ...
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Units of Poynting vector after Fourier transform

Suppose the electric and magnetic fields $e(x)$ and $h(x)$ with units $\left[\frac{V}{m}\right]$ and $\left[\frac{A}{m}\right]$ and their Fourier transforms $E(k)$ and $H(k)$ with units $\left[V\right]...
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Poynting vector for a whole spectrum

Considering an electric and magnetic plane wave, $E(t)=E_p(\omega)e^{i\omega t}$ and $H(t)=H_p(\omega)e^{i\omega t}$, where $E_p(\omega)$ and $H_p(\omega)$ represent the frequency dependent peak ...
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Poynting vector on the surface of an isolated system

We've an isolated system inside which currents and charges reside. If the Poynting vector on the surface of the system is non zero, then there is energy exchange between the system and the ...
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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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+...