What is Poynting vector: Definition and 102 Discussions

In physics, the Poynting vector represents the directional energy flux (the energy transfer per unit area per unit time) of an electromagnetic field. The SI unit of the Poynting vector is the watt per square metre (W/m2). It is named after its discoverer John Henry Poynting who first derived it in 1884. Oliver Heaviside also discovered it independently in the more general form that recognises the freedom of adding the curl of an arbitrary vector field to the definition. The Poynting vector is used throughout electromagnetics in conjunction with Poynting's theorem, the continuity equation expressing conservation of electromagnetic energy, to calculate the power flow in electric and magnetic fields.

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  1. schrodingerscat11

    Solving an Electromagnetic Wave Problem

    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...
  2. A

    Poynting vector and intensity in scalar diffraction theory

    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...
  3. T

    Poynting Vector and Mobile phones in ovens

    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...
  4. S

    From Poynting vector to EM wave

    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...
  5. teroenza

    Poynting Vector Direction Confusion

    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...
  6. stripes

    Show the loop integral of Poynting vector is zero for plane waves

    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...
  7. K

    Electromagnetism - Poynting vector

    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...
  8. X

    Circularly Polarized Wave: Poynting Vector Analysis

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

    Direction of Poynting vector

    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?
  10. E

    Electromagnetism - intrinsic impedance and poynting vector

    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...
  11. L

    Poynting vector. Conservation theorem.

    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...
  12. W

    Time-average Poynting vector of crystal scattering

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  13. W

    Time-average Poynting vector

    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}...
  14. S

    Electromagnetism, Poynting vector

    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...
  15. A

    The Magnitude of the Poynting Vector

    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!?
  16. W

    Instantaneous poynting vector for EM radiation

    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...
  17. R

    Poynting Vector (Griffiths 8.1)

    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...
  18. P

    Poynting Vector - Finding stored energy per unit length of a solenoid

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  19. S

    Flux at Earth's surface and Poynting vector

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  20. E

    Poynting vector / time averaged energy?

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  21. K

    Cancellation of Poynting vector components

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  22. W

    Evanescent waves, wavevector, and Poynting vector

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  23. B

    Zero (e.g., unexpectedly trivial) poynting vector

    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...
  24. B

    Calculating Poynting Vector in Long Resistive Rod

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  25. B

    Calculating Poynting Vector in Resistive Rod

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  26. Y

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  27. N

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  28. Z

    Poynting vector in static electromagnetic field

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  29. M

    Poynting vector and luminosity

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  30. P

    Poynting vector in wire and capacitor

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  31. e2m2a

    Is the Poynting Vector Frequency Dependent?

    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?
  32. fluidistic

    Calculating the Magnetic Field & Poynting Vector of Light

    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...
  33. R

    Why Is the Time Average of the Cosine Squared Term in the Poynting Vector 1/2?

    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
  34. M

    Why does the Poynting vector subtract stored electric and magnetic fields?

    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...
  35. F

    Question about the Poynting vector

    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...
  36. fluidistic

    Poynting vector over a cylinder

    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...
  37. U

    What is the difference between voltage and the poynting vector?

    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...
  38. C

    Understanding the Poynting Vector Dilemma in Electrical Circuits

    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...
  39. S

    Poynting Vector Energy Delivered

    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...
  40. J

    Solving for the Magnetic Field & Poynting Vector of an Electromagnetic Wave

    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.
  41. K

    Finding time average 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...
  42. L

    Calculate Poynting Vector for Given Fields

    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...
  43. Y

    Question of a problem on Poynting vector

    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...
  44. V

    Finding and using the Poynting vector

    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...
  45. V

    Solve Poynting Vector Homework: Part a,b & c

    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...
  46. J

    Poynting vector power flow question

    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...
  47. W

    What Determines the Poynting Vector in an Electromagnetic Wave?

    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...
  48. Y

    Poynting Vector: "S Points Radially Inward" Explained

    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
  49. N

    Poynting Vector in Total Internal Reflection Wave (TIR)

    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...
  50. U

    Why is the Poynting Vector defined as E x B?

    Poynting Vector is by definition: S = 1/u(E x B), where S points in the direction of the EM wave's motion. In other words, for an EM wave moving from left to right, the electric field component always points up as the magnetic field component hits us in the face, and conversely, the...
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