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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Trouble deducing a dipole's scattering cross section (optics)

(I've already visited this post but it begins precisely with the formula I'm trying to derive). I'm trying to deduce the scattering cross section for an electron bound to a nucleus in the far field: $$...
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Poynting's theorem in dispersive media

I am reading Jackson's Classical Electrodynamics (3rd ed) Section 6.8 on Poynting's Theorem in linear dispersive media with losses. From what I understand, in the last equation, the term $[-i\omega \...
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Dot product in optics

(Before marking this question as a duplicate, please consider I've read this post but it I didn't find the answers to it quite satisfactory regarding my doubt). I'm trying to derive the expression of ...
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Confusion in Poynting's theorem

The total force on a charge is equal to $\mathbf {F}=q\mathbf {(E+ v×B)}$ where everything have their usual meanings . We can say that: $$dW= \mathbf {F\cdot dl} = {\mathbf{F}\cdot \frac{d \mathbf{l} ...
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Poynting's theorem and continuity equation

I have recently come to realise that many of the most fundamental theorems can be reduced to a continuity equation. Doing some research on the topic of said equations, I have found out they have ...
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Showing that Poynting’s theorem preserved with Proca Lagrangian

The Proca Lagrangian is $$\mathcal{L}=-\frac{1}{4\mu_0}F_{\mu\nu}F^{\mu\nu}-\frac{1}{2\mu_0\Lambda^2}A_{\mu}A^{\mu}+A_{\mu}J^{\mu}$$ Where $\Lambda=\frac{\hbar}{m_{\gamma}c^2}$. The symmetric energy-...
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Energy of Monochromatic Beam of Light

A monochromatic beam of light has energy $$ E_{\text{beam}} = N \hbar \omega, $$ $ N $ being the number of photons in the beam and $ \omega $ their frequency. Another way to evaluate this energy is ...
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How can I calculate the energy of Electromagnetic wave for specific range of wavelength?

I have captured a wide bandwidth of electromagnetic waves (E and B fields) in the simulation. I would like to calculate the energy within a specific bandwidth. How can this be achieved? Which method ...
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Is power through a surface Lorentz invariant?

I am trying to solve this problem from Griffiths, but my point is not really to ask the answer of this problem : A point charge $q$ is moving velocity $v$ parallel to $x$ axis. determine the total ...
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How to model power transmission along a power transmission line?

I am a bit confused on this matter. Suppose we have an alternating current power source. One can transmit electric power two ways Through radiation, e.g., via an antenna. Through a transmission (...
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Poynting vector and plane waves

Suppose the electromagnetic field at a point is a superposition to two plane waves $(\vec E_1, \vec H_1)$ and $(\vec E_2, \vec H_2)$. If the two plane-waves have different frequencies, the (time-...
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Showing that the power is $P=UI$ using the Poynting vector

If I have a circuit with a resistor I want to show that the power delivered to the resistor is UI using Poynting vector. To do this I must integrate the pointing vector over a surface that contains ...
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Is poyinting vector theorem somehow related to PE and KE?

I'm trying to understand a DC circuit with only battery and light bulb component. In this scenario, electric potential energy as electrons move from negative to positive terminal is converted to ...
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Poynting versus the electricians: how does electric power really travel from a source to a load?

Suppose I connect a battery to a lamp in the usual way. Obviously, electric power will go from the battery to the lamp, causing the lamp to light up. But exactly what path does the power take to get ...
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The Classical Theory of Fields: Surface Integral of Poynting Vector Vanishes at Infinity on page 76

I am reading the section Energy density and energy flux in Chapter 4. The Electromagnetic Field Equations of Landau's The Classical Theory of Fields (third revised English edition). On page 76 after ...
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Link between group velocity and Poynting vector EM?

Why poynting vector and group velocity have the same direction? In isotropic medium is obvious but in anisotropic medium it is more difficult to evaluate
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What is the "momentum density" of an electromagnetic field? How does the Poynting vector relate to the momentum "stored" in such field?

I'm taking introductory, undergraduate-level E&M, for which we're following Griffiths. In his chapter on the conservation laws, he gives the following as the statement for conservation of momentum ...
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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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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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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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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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