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.

View More On Wikipedia.org
1. I How to Measure the Energy of an Electromagnetic Wave?

We know a way of measuring energy of a electromagnetic wave is the Poynting vector, which is independent of the frequency. But let's say we want to make two different electromagnetic waves, with different wavelengths and so different frequency, but with the same amplitude (so same Poynting...
2. I Is the Poynting Vector Field the Only Factor in Energy Flow in Circuits?

In a simple circuit consisting of a battery and a resistor, current will flow if the circuit is closed. Resistor uses the energy provided by the battery, creating heat with a power ##P = UI##, where ##U## is a voltage across the resistor and ##I## is a current through the resistor. In my...
3. I Does gravitational energy travel like electrical energy?

Electrons flowing through a resistor are dissipating electrical energy. The electrical energy is transported from the battery to the electrons along the curved field lines of the Poynting vector. It seems like a meaningful idea that electrical energy necessarily travels from the source to the...
4. A uniformly charged rotating sphere does not radiate, why not?

The problem says I have a spherically symmetric spinning constant charge distribution of charge Q and angular momentum w; I saw two possible explanations but none of them has made me realize why it is zero, one mentions thata constant w somehow implies a constant E which would mean there is no B...
5. Doubts on Exercise Wording: Energy Density & Poynting Vector

I have doubts about the wording of the exercise: (1) energy density is ##u=\varepsilon_0 (cB)^2## but since the question asks for mean energy density should I perhaps average over ##cos^2 (\omega t)## (there due to the ##B^2##) and thus use ##<u>=\frac{1}{2}\varepsilon_0 (cB)^2##? (2) it seems...
6. I Help with electromagnetics: the Poynting Vector and Ampere contradiction

According to equation (2.33) divergence of the Poynting vector or the outflow of electromagnetic power is equal to the stored magnetic field, stored electric field and ohmic losses. My contradiction is the following: Inside a steady state DC current carrying wire, there will presumably be a...
7. I EM Power transmitted from one region to another (normal incidence)

High! I have a EM plane wave hitting normally a surface dividing universe in media 1 and 2, both without losses. So we have incident, reflected and transmitted waves. It's a simple exercise in which you are given the basic data about two media and wave incident amplitude H in medium 1. I get...
8. I Energy Flow From Battery to the Light Bulb

When we connect tungsten filament light bulb to the battery, filament becomes hot due to electrons losing kinetic energy in the electric field inside of conductor. Heat is eventually converted to electromagnetic radiation making light bulb shine. Light energy comes from flow of electrons and...
9. Propagation Wave Expressions and Wave Velocity

Hello everyone, I would really appreciate some help on the following problem on plane waves and propagation. Not too sure if my attempt at writing the propagation wave expressions are correct, and how to handle the arbitrary function f(u). For the velocity, the wavelength is not specified, so is...
10. Poynting vector and single electron in free space

I am trying to draw the Poynting vector field for a single electron in free space between two capacitor plates. The electron is moving (and accelerating) to the positive plate at the right. I expected the Poynting vector field lines to converge to the electron, because that is where the work...
11. Average Energy density and the Poynting vector of an EM wave

Hi, In Problem 9.12 of Griffiths Introduction to Electrodynamics, 4th edition (Problem 9.11 3rd edition), in the problem, he says that one can calculate the average energy density and Poynting vector as using the formula I don't really understand how to do...

37. A Poynting Vector in a Medium?

Hello all, When light travels in a medium with negligible absorbance, it looks exactly like light in free space but with a different speed relative to that medium given by the refractive index. In free space, the Poynting vector is given by ##\vec{S} = \frac{1}{\mu _{0} } (\vec{E} \times...
38. Determining the Poynting Vector for Loop Antennas

So I came across the following image (from Wikipedia) where the electric and magnetic field lines are depicted for a dipole antenna. From the field lines, it is possible to determine the direction of the poynting vector, using the right-hand rule. If all possible combinations of poynting...
39. I Poynting energy flow in Eath's atmosphere?

1.There is an electric field between ionosphere and ground, also Earth's magnetic field is perpendicular to this E field, hence by poynting theorem integrating E x H across the entire surface of Earth gives a great deal of energy flowing west to east. 2. |S| = (E X B)/u0 = (150 V/m X...
40. What is the Poynting "vector" mathematically?

Hi. The Poynting vector is a 3-tuple of real or complex numbers (depending on the respective formulation of electrodynamics) times a unit. It may be pictured as an arrow with some length and direction in IR^3 or IC^3. But is it a "vector" in the strict mathematical sense, i.e. an element of a...
41. Understanding Linear Momentum of Waves with No Mass

Hi people, I studying electromagnetic waves (intermediate) and I don't understand how the expression for linear momentum of a wave is obtained, if the wave doesn't carry any mass. In particular, I have to explain why the radiation pressure on a perfect absorber is half that on a perfect...
42. Using Fresnel Formulae and Poynting vector problem

Homework Statement I'm having a problem using the fresnel formulae for these two problems below: 1. Using Fresnel formulae and expression for the Poynting vector show that at the interface between two dielectrics in the absence of absorption R+T=1, where R – is reflectivity and T –...
43. Missing a Factor of 2 in a Poynting Vector Verification

The question reads: A fat wire, radius a, carries a constant current I, uniformly distributed over its cross section. A narrow gap in the wire, of width w << a, forms a parallel-plate capacitor. I have drawn a red box at the bottom of the page where the Poynting theorem is supposedly verified...
44. Poynting Vector Problem

Homework Statement In free space, the electric field of a plane EM wave is given by: E(z,t)= 50î cos[wt-kz] where w= 6 x 10^15 and k=2x10^7 (A) calculate the amplitude of the magnetic field H How much energy does this wave transmit in 30s when it passes through a window of dimensions 2mx3m if...
45. Poynting Vector at an interface with no free current flowing

Homework Statement How do the normal and tangential components of the Poynting vector in matter, S = E x H , behave at an interface between two simple media where no free current flows, but either free charge or polarization charge is present at the interface? Homework Equations E1(para) -...
46. Poynting vector in dielectric

Hi. According to classical electromagnetism (and common sense) the intensity of a beam of light entering a dielectric medium should remain constant. Hence the length of the poynting vector must remain constant. But how do you derive mathematically the last point? Because if you just replace...
47. Issue with radiated field, conservation of energy and Poynting vector

Hello, I have found an issue in a simple classical electrodynamics problem that I have not been able to explain, so I’m writing this post hopping to find some answer to it. The problem is this: we have two charged particles with the same charge but different sign, one is massive and I will...
48. Poynting Vector and Sources

Suppose we have a charge, ##q## and a magnetic dipole moment, ##\vec m##. They don't move, nothing changes with time, in short, a static situation. Now, we have at least some regions of space where both the electric field, ##\vec E## and the magnetic field, ##\vec B## are non-zero. That means...
49. Work Done on a System of Charges

Something I have read in Griffith's Electrodynamics is confusing me. In deriving the Poynting vector, he says to suppose that we have some charge and a current configuration which at some time t produces fields E and B. In the next instant, dt, the charges move around. He then asks the question...
50. What is the poynting vector?

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