1
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1answer
28 views

Poynting vector plain 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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0answers
24 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 $B$ ...
1
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1answer
140 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 ...
0
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0answers
32 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 ...
1
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0answers
60 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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votes
1answer
136 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 ...
2
votes
1answer
103 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 ...
1
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1answer
107 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 ...
5
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1answer
115 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 ...
1
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1answer
323 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 ...
3
votes
1answer
159 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 ...
1
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1answer
48 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 ...
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0answers
93 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 ...
2
votes
3answers
323 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
votes
2answers
419 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
736 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 ...
0
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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} ...
2
votes
3answers
289 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 ...
1
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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} = ...
0
votes
0answers
235 views

Intensity of unpolarized light

If the electromagnetic field of an unpolarized plane wave is written as $$\bar{E}(t,\bar{x})=(\bar{E}_{0x}+\bar{E}_{0y}e^{i\delta(t)})e^{i(\bar{k}\bar{x}-\omega t)}$$ ...
1
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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 ...
4
votes
2answers
640 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) ...
3
votes
1answer
470 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 ...