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257 views

Why is the Poynting Vector Symmetric in E and H?

Why is the Poynting Vector symmetric in E and H? I always thought that E and B were the analogous fields, so I would think that any equation using magnetic and electric fields should be symmetric in ...
5
votes
1answer
106 views

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, ...
5
votes
1answer
137 views

Poynting theorem and entering power

I refer to the time-domain version of the Poyinting theorem in electro-magnetism: $- \displaystyle \oint_S (\mathbf{E} \times \mathbf{H}) \cdot d\mathbf{S} - \int_V \mathbf{E} \cdot \mathbf{J}_i \ dV ...
4
votes
2answers
728 views

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) ...
4
votes
1answer
519 views

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 ...
3
votes
2answers
165 views

X-ray diffraction from crystals and time-averaging

To calculate the elastically scattered intensity of x-rays from crystals, one classically considers scattering from a free electron first and then one sums up the scattered em-fields of all electrons ...
3
votes
1answer
191 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 ...
2
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3answers
380 views

Surface integral of Poynting vector around static sources

Consider fields $\rho \left( \vec{r} \right)$, $\vec{J} \left( \vec{r} \right)$, $\vec{E} \left( \vec{r} \right)$ and $\vec{B} \left( \vec{r} \right)$ in $\mathbb{R}^3$, with their usual meaning as ...
2
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3answers
332 views

What makes Poynting's theorem consistent for a charge moving in a static electric field?

Poynting's theorem is given by $$\frac{\partial}{\partial t}\int_{v}Udv + \oint_{A}\vec S\cdot \vec {dA} +\int_{v}\vec E\cdot\vec J dv =0 $$ Where, the total electromagnetic energy inside the ...
2
votes
2answers
63 views

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 ...
2
votes
2answers
818 views

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 ...
2
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1answer
264 views

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 ...
2
votes
1answer
109 views

Energy estimation of an acoustic wave

I have an issue with 2D acoustic wave field modelling. In order to estimate the energy propagation direction of an acoustic wave I use Poynting vectors $S$ which can be described by $$ \vec{S} = - ...
2
votes
2answers
506 views

Irradiance (or intensity) of an electromagnetic wave

Is the irradiance (or intensity) of an electromagnetic wave given by \begin{equation} I = \left<\|\mathbf{S}\|\right>_{T} \end{equation} or by \begin{equation} I = ...
2
votes
2answers
178 views

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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vote
1answer
49 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 ...
1
vote
1answer
380 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 ...
1
vote
1answer
449 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 ...
1
vote
1answer
102 views

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 ...
1
vote
1answer
128 views

Relation between intensity of light and refractive index

The intensity of light (as calculated from time average of the poynting vector) is given by $I = (1/2) \epsilon v E_0^2$. Here the intensity is dependent on the velocity of light in the medium. The ...
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vote
1answer
669 views

Derivation of the Poynting Vector without the Poynting Theorem

My professor worked out the Poynting Vector without using the Poynting Theorem-I can't remember how. I can't seem to figure out where the cross product would come in.
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vote
1answer
2k views

Computing the Poynting vector?

Approaching the following problem: A plane monochromatic electromagnetic wave with wavelength $\lambda = 2.0 cm$, propagates through a vacuum. Its magnetic field is described by $ > \vec{B} = ...
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2answers
1k views

Conservation of Energy and the Poynting Theorem

Conservation of energy in an electrical circuit can be expressed by Ampere's law $$\nabla \times \textbf{B} = \mu_o \textbf{J} + \epsilon_o \mu_o \frac {\partial \textbf{E}} {\partial t}$$ when ...
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0answers
65 views

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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0answers
16 views

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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0answers
70 views

What is the necessary condition on EM field for vanishing Poynting vector?

It is well known fact that both static and dynamic EM fields can give $E\times B \not=0$. What can we say about EM field if $E\times B =0$ ? Can previous equation still hold in case of dynamic EM ...
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vote
1answer
157 views

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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0answers
33 views

Intensity Poynting

Take a plane wave propagating in the $\hat{z}$ direction in a non-magnetic linear dielectric. The real electric field is then given by $$\vec{E}(r,t) = E_0\, e^{-k_i z}\cos(k_R - \omega t)\, \hat{x} ...
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0answers
172 views

Using the Poynting Vector in Coaxial Cables for Power

Why is it that we can use the Poynting Vector to find the power dissipated in a Coaxial Cable? Unlike the situation with light, where the c makes sense, inside the coaxial cable I see no reason why ...
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votes
3answers
1k views

Deriving the Poynting Theorem

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} ...
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1answer
21 views

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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1answer
82 views

Angular momentum of the electric field of a point-like electric charge and the magnetic field of a monopole

I am currently reading "Magnetic Monopoles" of Ya. Shnir. My problem is I can not retrieve a result the author provides in the first chapter of the first part. In this chapter, he studies the ...
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0answers
35 views

Finite rod aligned with a time varying magnetic field

A finite length rod is aligned parallel with a magnetic field that has a changing magnitude (let's say a sinusoidal change), given the conductivity and permeability of the rod and assume a large ...
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0answers
40 views

Poynting Vector between Capacitor - With electrons in between!

Consider a capacitor with voltage $V = V_0 cos(\omega t)$, radius $a$ and separation $d$. Electrons are distributed uniformly with number density $n$. I want to find the poynting vector between the ...
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votes
1answer
162 views

Can we draw analogy between em power flow through free space and ac power flow through a transmission line?

Knowing that the free space has a characteristic impedance (which is purely resistive, measured in ohms) I was wondering if I can model the free space as an infinitely long transmission line- ...
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0answers
106 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 ...
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0answers
168 views

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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0answers
267 views

Intensity of unpolarized light

If the electromagnetic field of an unpolarized plane wave is written as $$\bar{E}(t,\bar{x})=(\bar{E}_{0x}+\bar{E}_{0y}e^{i\delta(t)})e^{i(\bar{k}\bar{x}-\omega t)}$$ ...
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votes
1answer
146 views

Poynting's theorem and escaping particles

I've edited my original question into horrible monstrosity (I apologize to all who spent their time on it). Here is rephrased version which hopefully will be clear. Lets have following model ...
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votes
1answer
703 views

Poynting vector direction

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 ...