Poynting vector Definition and 103 Threads

i need an interpretation for the poynting vector, and its derivation for EM waves (sinusoidal)

Homework Statement For an electromagnetic wave with an electric field given by \mathbf{B}=\mathbf{i} E_o cos (kz-\omega t)+ \mathbf{j} E_o sin (\omega t - kz) where Eo is a constant Find (a) its direction of propagation (b) the magnetic field (c) Poynting vector (d) energy density, i.e., the...

The power density of an electromagnetic wave is proportional to the absolute square of the electric field |E|^2 (assuming a plane wave). Here, E is a vector so the absolute square involves all three of Ex, Ey, and Ez. In homogeneous, linear media, it's easy to show that each component of E...

Hi, sorry if this is in the wrong forum but 2 Quick hopefully simple questions about Poynting vector and EM waves. Q1) Say I have two antenna (antenni?)...dipoles maybe, both with say, 50W going into them, one oscillating on the kHz range, one on the MHz range (GHz, whatever). But for this...

After reading Griffiths' book, I find the explanation from poynting vector to sinusodial EM wave pretty blurred. EM wave has two requirements. 1. E / B = c 2. E and B are sinusodial How could we ensure the Poynyig vector ultimately will produce the form satisfying the two points mentioned? Or...

Homework Statement I am trying to understand why, in an example in Griffiths E&M (3rd ed, 8.1) says that the Poynting vector of a current carrying wire that is being heated via resistance (Joule heating), has a Poynting vector pointing radially inward. The E field is parallel to the wire, B...

Homework Statement Show that for plane waves, the following result holds: \oint \textbf{S}\cdot d \ell = 0. Homework Equations -- The Attempt at a Solution \oint \textbf{S}\cdot d \ell = \frac{1}{\mu_{0}}\oint (\textbf{E} \times \textbf{B})\cdot d \ell Now do I just use...

Hello! I' currently reading EM and am in need of a verification that I understood it correctly before proceeding. Just to see if I got this right: The energy flowing out of a point, p, is described by the Poynting vector of the field at that point. The momentum density of the field is...

In case of a circularly polarized wave, is the poynting vector also circularly polarized? If not what happens in this case?

I have a question: when the poynting vector and energy propagation in electromagnetic waves are in the same direction and when are in different direction?

1. I know that 1/2 of the real part of the complex poynting vector gives the average power flow per unit area. But what is the significance of its imaginary part ? 2. What is the significance of the complex intrinsic impedance ? For lossless medium (i.e. with no ohmic losses) it is real , but...

I'm doing a problem where I have to calculate the electric and magnetic fields. I've found B=0, so S=ExB=0. Has it got any meaning? Then I calculate the energy density e=E^2 + B^2 = E^2. And finally I have to verify the conservation theorem grad(S)+de/dt=0 for points out of the particle's...

To calculate the intensity of the scattered radiation from a crystal after irradiating with X-rays, one can add up all electromagnetic fields of the oscillating electrons (calculated using the Liénard–Wiechert potential). Taking the time-average of the norm of the Poynting vector of the...

I'm having a problem in expressing the time-average norm of the Poynting vector of the scattered electromagnetic field from a crystal, as expressed in several textbooks. Concider a monochromatic plane wave \begin{split}...

3 (a) ii) A time-dependent electric field in vacuum is given by ⃗E= E0(0, 0, sin(ky − ωt)) where E0 is a constant. Derive an expression for the corresponding magnetic field ⃗B. [7] Using curl E=-dB/dt I end up with B=(E0/c)sin(ky-wt) Show that both ⃗E and ⃗B are perpendicular to the wave...

General question: Is the magnitude of the poynting vector equal to the intensity of an electromagnetic wave? I know that I= average S which makes me think that I cannot simply assume that that their magnitudes are equal!?

Have viewed PF, first time post (have searched for this question on forum): The energy of EM radiation can be described by the Poynting vector S = E x B (insert conversion factor for cgs, MKS, etc). For a traveling EM wave, what happens to the instantaneous value of S when E and B are...

Homework Statement Problem 8.1 from the third edition of Introduction to Electrodynamics by Griffiths: Calculate the power (energy per unit time) transported down the cables of Ex. 7.13 and Prob. 7.58, assuming the conductors are held at potential difference V, and carry current I (down one...

Homework Statement long solenoid of n turns per unit length is wound upon a cylindrical core of radius a and relative permeability. The current I through the solenoid is increasing with time t at a constant rate. Obtain expression for the rate of increase of stored energy per unit length...

(On phone typing this, so preset subheadings haven't shown) My first question asks me to use the Poynting vector, N, to calculate the average flux of radiation, knowing that the electric field of sunlight arriving at the surface of the Earth is 500Vm^-1 I use that the average flux of...

Something has always bothered me about finding the energy of an EM wave - What justification is there for taking the time average of the wave? I know we do this to find the energy of an EM wave, but I haven't seen this before in any of my courses. Isn't this a violation of conservation of...

If we find the Poynting vector at a point along all possible directions possible, can the different components of the vectors cancel each other, to give a net Poynting vector along some direction? I was wondering about this because Poynting vector after all represents energy flow. So can...

For an evanescent wave, in what direction does the wavevector k point? In several lectures that I've seen in class, it appears to point in some direction that is not normal or along the interface, which confuses me. Additionally, for all wave vectors, what exactly is the magnitude of k? In...

Homework Statement The Poynting vector is, {\bf{S}} = \frac{{{\mu _0}}}{{16{\pi ^2}c}}\frac{{{{({\bf{\hat r}} \times {\bf{\ddot p}})}^2}}}{{{{\left| {\bf{r}} \right|}^2}}}{\bf{\hat r}} [I.1] Consider two charged particles, one at the origin (charge q1 and mass m1) and the other (charge...

Homework Statement Consider a long resistive rod, exhibiting resistance R, of length l and radius r. Calculate the magnitude and direction of the Poynting vector (neglecting edge effects) and relate the rate of energy transfer between the rod and its exterior to the total power dissipated in...

Homework Statement Consider a long resistive rod exhibiting resistance R of length l and radius r. Calculate the magnitude and direction of the poynting vector (neglecting edge effects) and relate the rate of energy transfoer between the rod and its exterior to the total power dissipated in...

This start out as an example in the book: Find Poynting Vector of a long conducting wire with radius = b and conductivity \sigma with DC current through the wire. Assume wire in z direction and use cylindrical coordinates. Since DC current, current distribute evenly inside the wire...

Why is it that that poynting vector is independent of distance from the source? Is it because EM waves are plane waves? Furthermore I do not fully understand why EM waves have to be plane waves. I understand that changing magnetic fields give rise to electric fields and vice versa, but does...

There is a situation, we have an electric field and a magnetic field, both are static. And we know the density of energy is u=E·D/2+B·H/2, so dU/dt=0, but Poynting vector S=ExH is not zero, which means energy is flowing. This confused me. Static field also has energy flux?

Hello Say I have a source of radiation placed at my origin and I know its power is spread uniformly about 2*pi at a certain frequency, I believe this is also called luminosity. (or a 2D equivalent) This means if I put a shell around the source and collect this power, then as long as the shell...

Hi, For the scenario of wire or capacitor, the poynting vector is found to point inward radially, which suggests the energy is flowing into the wire from the air. Isn't this a bit peculiar because energy seems to be transferred from the battery along the wire. What i am speculating is the...

This is not a homework question. Please do not delete it. I am 57 years old and trust me I am not in school. Doe the magnitude of the Poynting vector depend on the frequency of the wave hitting the surface?

Homework Statement If the amplitude of the electric field of the light propagating through a glass whose refractive index is 1.5 is 100 V/m, what is the amplitude of the magnetic field? What is the magnitude of the Poynting vector associated with this wave?Homework Equations Not sure for the...

Hello. I am reading in my book about the Poynting vector for monochromatic plane waves. It includes a cosine term: cos^2 (kz - omega t + phi). My book states that the time average of this term is 1/2. Can anyone explain this? I don't understand how they work that out. Thank you

Hi All, I have been revising the Poynting theory and I cannot interpret "physically" why do we have the terms of stored electric(We) and magnetic field (Wm) minus each other; doesn't it make more sense to have the total energy stored in the field added together when we talk about the Poynting...

Suppose I have a monochromatic electromagnetic plane wave with the E-field linearly polarized in the x-direction (and the B-field linearly polarized in the y-direction). Then the Poynting vector should be pointing in the z direction with a magnitude equal to the product of the B and E-field...

Homework Statement There's a cylindrical resistor of length L, radius a and resistivity \rho in which a current i flows. 1)Calculate the Poynting vector over the surface of the resistor. 2)In which direction does the energy that is transported by the electromagnetic field point. 3)Show...

This is the article that explains it: http://amasci.com/elect/poynt/poynt.html If the energy in a circuit is really just in the form of electromagnetic fields, what's so important about voltage? If I already know the wattage in the circuit, why should I know the potential energy per charge if...

I was curious about how exactly energy was transferred in electrical circuits because all my texts were inadequate. After pouring through many sources ("electrical energy transfer" or anything similar yields crappy results through every search engine I tried) I finally found something I could...

Homework Statement If B0 = 5*10^-7 [T], relative permittivity = 2 and relative permeability = 1.15 how much energy is delivered to an area of 1m^2 by the wave in one second? Where B0 is a magnetic field measured in teslas. Homework Equations < P > = ((B0^2)*c*(1)) / (2*(vacuum...

If the electromagnetic wave is descirbed as: E=Eocosw((eu)^1/2z-t)i + Eosinw((eu)^1/2z-t)j Find the corresponding magnetic field and the poynting vector.

Given E and H, obviously you can calculate Poynting vector (N=ExH), but then how do you find the time average of N (N')? (I won't write all the question I'm trying to answer here but basically I'm trying the verify an equation, the says N' = 0.5* Re{ F x I* } where F and I are fields such...

I am asked to calculate the pointing vector for the following fields: \vec{B}=k^2 \frac{e^{ikr}}{r} \left( 1+\frac{i}{kr} \right) \hat{r} \times \vec{p_{\omega}} \vec{E}=\frac{i}{k} (\vec{\nabla} e^{ikr}) \times \left( \frac{k^2}{r} \left(1+\frac{i}{kr} \left) \hat{r} \times...

I have been working on this problem and I cannot get the solution as shown in the book. I scan the question and solution of the book and my work. It is too difficult for me to type it in, please open the attach scanned pdf file. THe top part is the copy of the book, the lower part is my work...

Homework Statement Hi, this is a repeat post, I fear I put it in the wrong forum to start with (I put it in advance physics and I think it may be more of an introductory physics question). I'm really sorry if this contravenes any of the rules. A fat wire, radius a, carries a constant...

Homework Statement Greetings all, sorry this is a long post but I'm really stuck on this... A fat wire, radius a, carries a constant current I, uniformly distributed over it's cross section. A narrow gap in the wire, of width w<<a, forms a parllel-plate capacitor (see attachment, this...

Im aware that the complex electromagnetic powerflow from a solid is described by the poynting vector (see 1.1), however I am not sure how the 1/2 term arises in the formula 1/2\oint\vec{E} \times \vec{H}.ds (1.1) where \times = vector cross product and ds denotes a variance in the...

Here's the question: An electromagnetic wave is traveling through vacuum. Its electric field vector is given by E= E_0 sin(kx-wt)y_hat where "y hat" is the unit vector in the y direction. What is the Poynting vector S(x,t), that is, the power per unit area associated with the...

I have a question about the Poynting vector: mit.edu/8.02t/www/materials/StudyGuide/guide13.pdf (page 44/51) What is the physical interpretation of "S points radially inward". That seems kinda weird. Energy flows to the center? cheers

I have the following homework problem: a monochromatic plane wave travels from medium 1 to medium 2 and experiences total internal reflection. Find the normal and parallel components of the Poynting vector, discuss the results with respect to the wave's polarization. Now, I think that the...