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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Intensity of a gaussian beam
Let's say a gaussian beam propagates along z-axis.
According to Wikipedia its intensity will be:
$I(r,z) = I_0 \frac{\omega_0}{\omega(z)}\exp(\frac{-2r^2}{\omega(z)^2})$
I think of the intensity as a ...
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Poynting vectors of perpendicular intersecting waves
Let us assume that wave $E_a(x,t)=Ae^{i(kx-wt)}$ is propagating along the $x$-axis and that wave $E_b(y,t)=Be^{i(ky-wt)}$ is propagating along the $y$-axis. The magnitude of the Poynting vector $\...
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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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Momentum conservation in classical electrodynamics
The partial of tensor is equal
$$\partial_{\mu}T^{\mu j} = \frac{\partial}{\partial t}T^{0j} + \nabla_{j} T^{ij} = -(\rho \vec{E} + \vec{j}\; \times \vec{B})^{j}$$
where does it come from?
In the ...
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Poynting vector
So I saw this video from the science asylum youtube channel and that guy said "momentum doesn't require velocity" and "if u have a constant perpendicular electric field and magnetic ...
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Poynting Vector from a Black Body
Suppose I have a cavity with rough walls that is close to an ideal Black Body. For simplicity, assume that it is a square box. I cut a small hole in the box of size $dA.$
Energy would radiate away ...
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Generalized Poynting Vector & Continuity in the Normal Direction
My E&M textbook states the equation (85.5) below as the generalized Poynting vector for any material. I have 2 questions:
In the 3rd sentence, did they mean to say DxH & DxB, instead of ...
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Direction of the wave vector
The following paragraph from Wikipedia about phase/group velocity and direction of propagation is confusing me:
"The direction in which the wave vector points must be distinguished from the &...
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Poynting vector and negative index of refraction
Why are the Poynting vector and the wavevector not pointing in the same direction in negative-index media?
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Relation between Rayleigh scattering intensity and Poynting vector of an oscillating dipole
In Rayleigh scattering by a molecule the intensity of the scattered light is:
$$I \propto I_0({1+\cos^2(\theta))}$$
while the time-averaged Poynting vector of an oscillating dipole is:
$$\langle S \...
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How do you explain that Poynting's theorem $P=E\times H$ is still valid for DC fields?
Poynting's theorem P = ExH is quite valid for DC circuits with stationary electromagnetic fields as well as for AC circuits and time varying EM fields. The question arises: Do Maxwell's 4 equations ...
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How does DC circuit deliver energy?
I don't understand how energy is being transferred in a DC circuit. For example here I have a simple circuit powered by a constant voltage. Some form of energy is being transferred from the source to ...
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Does the Newtonian gravitational field have momentum analogous to the Poynting vector?
We can define the total energy of the electromagnetic field as:
$$\mathcal{E}_{EM}= \frac{1}{2} \int_V \left(\varepsilon_0\boldsymbol{E}^2+\frac{\boldsymbol{B}^2}{\mu_0}\right)dV$$
which satisfies the ...
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Lorentz transformation of energy-momentum tensor of electromagnetic field
I wanted to calculate the power density of a moving antenna; it needs the Poynting vector, which is a part of the energy-momentum tensor of electromagnetic fields. My question is whether this tensor ...
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Relation between Radiance and Surface power density (i.e poynting vector intensity)
I am attending a microwave remote sensing course and I have same problem to understand the relation between the radiance and the intensity of poynting's vector.
The radiance is defined as:
$L(\theta,\...
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How does the Poynting vector know who is the primary and who is the secondary of a transformer?
I've read in several places that the Poynting vector is directed from the primary to the secondary of a transformer (we assume here that the primary is the winding that provide the AC energy, while ...
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Do optical tweezers provide conservative forces?
So, either it seems I am mislead with the idea of the conservative and non-conservative forces or I never knew/understood it. What exactly does the work in optical tweezers to make object levitating? ...
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Relativistic momentum of the E.M field vs Poynting momentum questions
I come somehow to the following thoughts:
The energy of the EM field is $$\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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Is it true that the Poynting theorem $P=E\times H$ is quite valid for DC circuits?
Can we assume that Poynting's vector theorem $P=E\times H$ is one of the universal laws of physics that applies to electromagnetic fields in AC and DC circuits.Is there A rigorous analysis of ...
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Fault/Technicalities with poynting theorem
When finding the force on a system of point particles $Q_{1}, Q_{2}$, we need to use the formula
$$\vec{F} = Q_{1} \vec{E_{2}}$$
Where $\vec{E}_{2}$ is the field ONLY due to the charge $Q_{2}$, since ...
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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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Where is the $\mu_0$ in this Jackson equation?
In Jackson's Electrodynamics, he derives a spherical harmonic expansion for the electromagnetic field in the radiation zone:
\begin{align}
\mathbf{B} &\rightarrow\frac{\mathrm{e}^{\mathrm{i( k ...
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Charged particle in crossed electric and magnetic fields
Suppose a particle with charge, mass $ q, m $ respectively is initially at rest and placed in a uniform crossed electromagnetic field as shown in the figure
The charge moves under the influence of ...
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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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Direction of energy flux in conducting wire confusion
From what I can read on the Internet, in a very simple electrical circuit consisting of a battery connected to a wire with finite resistance in a loop, the energy flux is given by the Poynting vector $...
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Role of Maxwell's stress tensor in the conservation of momentum of an EM wave
Defining the Wave:
Let's assume an electromagnetic wave exists in the form
$\vec{E}(x,y,z,t) = \vec{E}_0 \, cos(kx-\omega t)$
$\vec{B}(x,y,z,t) = \vec{B}_0 \, cos(kx-\omega t)$
How the wave interacts ...
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Why the intensity of a wave is $ \Psi \Psi^*$?
In here at the bottom, it says the intensity of a wave is the wave phasor times it's conjucate
$$ I(x) = \Psi \Psi^* = |\Psi |^2$$
But when I compute the intensity of an electromagnetic wave in c.g.s, ...
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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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Radiation of rotating spherical shell with constant angular speed
I know this has been asked twice here but none of the explanations made me realize why it is zero. One of the answers says dipole moment for constant angular velocity is also a constant vector and ...
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Is slower light darker?
Consider for example, electromagnetic waves inside conductors. The speed at which an EM wave travels at can be a considerable fraction lower than C
So my question is, If I were standing with my eyes ...
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Black body thermal radiation vs. the uniqueness of EM energy in Poynting's theorem
In this post Feynman is quoted stating that GR can potentially remove the inherent ambiguities implied by Poynting's theorem in the definition of EM energy density and energy flux.
Given $u=\frac{1}{2}...
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Poynting's theorem ambiguity
So in wikipedia for the Poynting's theorem we have:
$-\frac{\partial u}{\partial t}= \nabla \cdot\vec S + \vec j \cdot\vec E$
where:
$-\frac{\partial u}{\partial t}$ is the rate of change of energy ...
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General definition of a standing wave
Question "What is standing wave?" has already been asked. Intuitively we all know what it is, but how would we define such a wave in the most general way: for arbitrary geometry, dispersion, ...
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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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Poynting vector and $E = hf$
Energy flux for an Em wave is defined by the poynting vector $(1/\mu_0) E \times B$
The energy is also proportional to $E^2 $
If you take for example the simplest form of generating light, the ...
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Can current flow in a simple circuit if I enclose the battery in a faraday cage?
So suppose I have a regular circuit with a battery connected to a resistor and a lightbulb.
Suppose now somehow the battery is inside a metal box (faraday cage) but the rest of the circuit is outside ...
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Noether's Theorem and Poynting Theorem
For simplicity, let's assume the Lagrangian formulation of Noether's theorem, that is, our equations of motion can be derived from the Euler-Lagrange equations, or, simply, that we can use a ...
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Shouldn’t the net Poynting vector at a resistor or incandescent light bulb be zero?
I’ve read that the Poynting vector points into an incandescent light bulb at all instants of time, whether there is direct/constant or alternating current through the wire. This means the bulb is ...
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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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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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Experiment to detect Poynting Vector Angular Momentum
At the very end of this Feynman lecture: https://www.feynmanlectures.caltech.edu/II_27.html he says that static electric and magnetic fields can store angular momentum in the field itself. In the ...
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Intuition for energy density of electromagnetic fields
I have the following equations:
$U = \frac{1}{2}(\mathbf{E}\cdot\mathbf{D} + \mathbf{B}\cdot\mathbf{H})$ and
$\mathbf{S} = \mathbf{E} \times \mathbf{H}$
This is from the equation:
$$\frac{\partial U}{\...
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Does electromagnetic wave violates conservation of energy when passing between two dielectric mediums at oblique angles, is there a derivation?
how can we prove that poynting theorem works for an Electromagnetic waves which incident at an oblique angles between two dielectric medium?
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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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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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