# Tagged Questions

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### Near Energy In the Null of a Hertzian Dipole

Since $\mathbf E = -∇Φ - ∂\mathbf A/∂t$ one expects an oscillating $\mathbf E$ field even in the null of a Hertzian Dipole unless the two right hand side terms cancel -- which they do in the far field ...
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### What experiments confirmed Poynting's Theorem?

Actually, I have two related questions. The fist is the above question. The second is, what experiments confirmed that $\varepsilon_0\left(\frac{E^2}{2} + c^2 \frac{B^2}{2}\right)$ is the ...
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### Derivation of Poynting theorem in matter

In most textbooks I have read they derive the Poynting theorem using the Maxwell's Equation in vacuum and the fact that the force density $f=\pmb{E} \cdot \pmb{J}$. Then they just generalize it ...
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### What does the Poynting flux represent?

I know that the Poynting flux is the cross product between $\vec E$ fields and $\vec B$ fields, but I'm wondering, are the field lines of the Poynting flux considered as electromagnetic energy? Let's ...
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### Absorbance by using Poynting vector

How should I compute the amount of energy of an EM wave absorbed by a material? Can I just use the divergence of the Poynting vector?
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### Transmitted Power and Poynting's theorem contradiction?

I was reading Chapter 12.1 in Hayt & Buck "Engineering Electromagnetics" 8-th edition. Here they discuss the reflection of uniform plane waves at normal incidence. They derived the following ...
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### What is the Poynting vector of an electron?

On chapter 27 of "The Feynman Lectures on Physics Volume II: Mainly Electromagnetism and Matter", Richard Feynman says: Finally, in order to really convince you that this theory is obviously nuts, ...
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### Is there something like the Poynting vector for hydraulic circuits?

The Poynting vector is a representation of the energy flux in electromagnetics, showing the amount and direction of power flow at different points in space. In electric circuits, the energy is not ...
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### Poynting vector and electric shock

As an explanation to Poynting vector(P), I read the following example: A DC source is connected to a bulb (receiver) by means of 2 conductors. The direction of the electric field between the ...
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### Photoelectric effect and energy of light

I have a doubt about photoelectric effect and the nature of light in general. From what I understood, in order to ionize a piece of some material, I need an electromagnetic wave with a frequence ...
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### Poyting theorem for a plane wave

I would like to apply and verify the Poynting theorem for a uniform plane wave but there is obviously something wrong in my demonstration. The Poynting theorem expresses the conservation of energy: ...
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### Vector Potential Oscillating E Field of the “Null” Field of a Hertzian Dipole?

The vector potential of a Hertzian dipole falls off spherically as $1/r$. The polar axis of the dipole is a "Null" field -- meaning no electric and magnetic field. The absence of magnetic field is ...
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### What is the meaning of $\vec{E}\times\vec{B}$?

Consider that for a single $\mathbb{R}^3$ point-source emitter of RF, the $\mathbf{E}$ and $\mathbf{B}$ fields (when treated as transverse sinusoids and ignoring interference properties) are always ...
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### Poynting vector of a wire between capacitors

A capacitor made of two circular plates of radius $L$ separated by $d$, initially the plates carry $\pm$ Q charge. Then a wire of resistance R is placed between them, how do I go about deriving a ...
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### Question about intensity of EM waves

For electromagnetic wave if it's reflected from a perfect conductor standing wave can be form. I wonder why Poynting vector can be used to describe the intensity of standing EM wave. (see p.19 of ...
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### Ratio E/B and power in rectangular cavity

I would like to know if the relation $E=B*c$ still holds in a rectangular cavity Let's consider this rectangular cavity where the wave is travelling along the z direction ...
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### Is there any other momentum besides the Poynting momentum stored in an electromagnetic field?

I am having some conceptual difficulties with energy and momentum stored in the EM field. The force density at a point is $\rho E + j\times B$ Because of conservation of momentum, and because the ...
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### How do I calculate the energy flux for this toroid?

My question is how do i calculate the total energy flux through the walls of the torus in this situation? The Poynting flux is given by $\vec{N} = \frac{1}{\mu} ( \vec{E} \times \vec{B})$ but the ...
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### In a system with a decaying magnetic field, is the induced E-field around the wire constant?

Below is an example problem that I know how to solve, particularly when the current is switched off and the magnetic field is allowed to decay. However, in systems typically like these, is it a far ...
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### Understanding Poynting's Theorem intuitively

I understand that, broadly speaking, Poynting's theorem is a statement of conservation of energy. Energy density of a volume of current and charge decreases proportionally to work done on charges ...
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### Does a nonzero Poynting vector mean that there is propagation of energy?

I don't know how this "paradox" can be solved. I'm given the following system: A permanent magnet with a magnetic field given by ($\hat{a}$ are unit vectors in the x and y directions) ...
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### Poynting's Theorem simplified?

How can I apply Poynting's theorem to any system that has a magnetic field & electric field, to state conservation of energy? How does Poynting's theorem state conservation of energy in EM? I ...
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### Total Momentum From a Standing Electromagnetic Wave

How does one show the momentum imparted to a perfect conducting resonance cavity (boundary) of any shape by a classical standing electromagnetic wave inside is zero? It should be by conservation of ...
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### Poynting vector plane wave

I'm calculating the poynting vector for a plain wave and I have some doubt. $$\bar S = \frac 1 2 \bar E \times \bar H^* = ... = \frac {| \bar E|^2} {2 \zeta} \hat i_k$$ Now if I consider a ...
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### Rate of work done by fields in a finite volume

In Jackson's Classical Electrodynamics, the rate of work done by fields in a finite volume is defined as $$\int _{v}\vec{J}\cdot\vec{E}\,d^{3}x^{'}$$ How?
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### Poynting Vector Volume Integral Inside a Cavity

Given an electromagnetic wave in resonance mode in a vacuum cavity inside a perfect conductor, on the boundary, the parallel component of $E$ field vanishes, and the perpendicular of component of $B$ ...
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### Poynting Vector for a Laser

How do you calculate the Poynting vector for a laser given it's power? I know for a sphere you can just take the power, and divide it by 4$\pi R^2$, but I don't know what I would do for a laser. Would ...
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### Determine the particle velocity of a pressure wave

I am using constant density wave propagators to model seismic waves in the subsurface. What I want with these acoustic waves is to estimate the energy of them at a certain grid point at a given time. ...
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I am trying to derive the Poynting theorem. So far, I've only been able to narrow down which equations I think I'll need to do so. These are the equations: Maxwell's Equations: $$\nabla\times{\bf E} ... 1answer 1k views ### Physical Interpretation of Poynting Vector I'm looking for a physical interpretation of the Poynting Vector. I understand that it should be thought of as an energy flow due to the electromagnetic field, but would I be correct in saying that in ... 1answer 237 views ### Orthogonality between \vec{E} and \vec{H} waves with space-dependent amplitudes I am able to prove in a few lines that the electrodynamic field vectors \vec{E}, \vec{H} and \vec{S} are all orthogonal to each other considering that \vec{E} and \vec{H} are coherent plane ... 1answer 51 views ### Is there a heuristic argument for the expression  \textbf{g} = \frac {\mathbf{S}}{c^2}? Electromagnetic momentum density and the Poynting vector are related by the simple expression:$$ \textbf{g} = \frac {\mathbf{S}}{c^2}$$It can be rigorously derived from Maxwell's equations, but is ... 0answers 139 views ### Angular momentum contained in E&M fields I am trying to do this question as a prep for my quals and find my solution too simplistic. I fear I am missing something important. "Iron atoms (atomic mass 56) contain two free electron spins that ... 1answer 879 views ### Difference between Poynting vector and energy flux density? Are those two terms the same, or...? My book says that the Poynting vector is an energy flux density given by:$$\mathbf{S} = \frac{1}{\mu_{0}}(\mathbf{E} \times \mathbf{B}) So that alone should ...
Just a quick question if I may. The Poynting vector, or the energy flux density, is given by: $\mathbf{S} = \frac{1}{\mu_{0}}(\mathbf{E} \times \mathbf{B})$ So it's the cross product between the ...