Poynting vector Definition and 103 Threads

Here is a chapter from MIT OCW's 8.02 Electromagnetism course. At the end of page 14 is section 13.6 "Poynting Vector". The calculations I am interested in are on page 15. There is a passage that seems to have a typo in it. Let me try to show why despite recognizing a typo I am unsure of what...

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...

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...

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...

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...

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...

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...

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...

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...

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...

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...

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...

Poynting's Theorem (https://en.wikipedia.org/wiki/Poynting's_theorem) says: The rate of energy transfer (per unit volume) from a region of space equals the rate of work done on a charge distribution plus the energy flux leaving that region. $$-\frac{\partial u}{\partial...

The Poynting vector $$\vec S=\frac{1}{\mu_0} \vec E \times \vec B$$ gives the power per unit area. If I need this in terms of electric field only,I should be able to write B=E/c (for EM wave) Assuming they're perpendicular, ##S =\frac{1}{\mu_0 c}E^2##. Now, ##c=\frac{1}{\sqrt{\mu_0 \epsilon_0}}...

I've attached a .txt file of my script for those who want to take a look at it Here's a picture of my vector field at time t = 0 I'm very concerned about this picture because from my understanding the Poynting vector is supposed to point outwards and not loop back around, this looks nothing...

I don't know which part gets wrong

Hello all, Im trying to do a simulation of a poynting vector of an electromagnetic wave and I assume the following: At t=0 the E-field vector is (0,0,e^(-ikx)) and the H-field vector (0,e^(-ikx),0), hence orthogonal to it in vaccum, which is assumed, also the amplitudes are simplified both to...

Hi guys, Consider a circular capacitor with a disk of radius a and plate separation d, as shown in the figure below. Assuming the capacitor is filled with a dielectric constant epsilon and the capacitor is fed by a time harmonic current I0 (a) Find the magnetic field distribution inside the...

Homework Statement A spherical capacitor has internal radius ##a## and external radius ##b##. At time ##t = 0##, the charge of the capacitor is ##Q_0## Then the two shells are connected by a resistor in the radial direction of resistance ##R##. Find the Poynting vector and the energy...

I am trying to understand why an accelerating charge emits radiation/electromagnetic waves but a uniformly moving one does not. I saw one video on Youtube where it seemed that it was explained by the fact that with a uniformly moving charge the Poynting vector was pointing 'in to the volume' -...

If we have a some wire (length L) with a PD of V from one end to the next and a current I moving along it we can work out the Poynting vector. It's pointing radially inwards and so tells you the energy per unit time per unit area flowing into the the surface of the wire. What I don't understand...

Homework Statement I reference problem 9.10 Purcell's Electricity and Magnetism (3rd ed). A very thin straight wire carries current ##I## from infinity radially inward onto a conducting shell with radius R. Show that the total flux of the Poynting vector away from an imaginary tube of radius...

I learned that the Poynting vector was the electromagnetic density of momentum but recently, while reading the Electromagnetic_stress–energy_tensor article at Wikipedia, I thought about the implications of the momentum conservation equation and arrived to an inconsistency, this equation is...

Hello, For calculating the mean power at a specific cross section of a waveguide, one can calculate the mean value of the temporal function of Poynting Vector, P(t), where P(t) is the ExHy-EyHx. Note that I am not talking about phasors or a sinusoidal state. If I integrate over the waveguide...

Homework Statement A long straight wire of radius a and resistance per unit length R carries a constant current I. Find the Poynting vector N = E × H at the surface of the wire and give a sketch showing the directions of the current, the electric field E, the magnetic field H, and N. Integrate...

As we know, work done by an outside agency in creating some current ''I" in an inductor 'L' is 1/2LI2. Now this result is derived by quasistatic approximation if I am not wrong. Now, I am assuming that in non quasistatic (real) scenarios, the work done by outside agency would be different(If you...

Homework Statement An infinitely long cylindrical capacitor with inner radius a and outer radius b carries a free charge per unit length of ##\lambda_{free}##. The region between the plates is filled with a nonmagnetic dielectric of conductivity ##\sigma##. Show that at every point inside the...

A radar antenna transmits 50kW at 10 GHz. Assume transmission is in a narrow beam, 1m^2 in area, and that within the beam, waves are plane waves. The wave is reflected from an aircraft but only 1% of the power propagates i the direction of the antenna. If the airplane is at a distance of 100km...

Homework Statement What are the associated peak amplitudes of the E and H fields if sunlight has a maximum intensity of 1400 W/m2 on the earth’s moon? Homework Equations I = <s> = 1/2 c ε0E2The Attempt at a Solution I = <s> = 1/2 c ε0E02 1400 = (1/2)(3*108)(8.85*10-12)(E02) 1400 /...

The basic idea: I am interested in the possibility of an azimuthally-directed Poynting vector component which drops with the inverse cube of the distance (or as 1/r^3), primarily because it suggests the possibility of emitting field angular momentum, allowing for a uni-directional torque to be...

I found it very interesting to see that surface charge and the Poynting vector are being used to describe how a simple DC circuit actually works. Chabay and Sherwood have made an outstanding contribution to physics and engineering in their texts and papers. Of course others jump on the...

I have some problems in calculating the flux of Poynting's vector through a surface. I have that: S=c/4π⋅H^2⋅n (S: Poynting's vector, n: versor of the direction of the propagation of the em wave) H=1/cR A' but: A=(1/cR) d'; A'=(1/cR) d'' ==> H= (1/cR)^2 d''...

So, the Wiki page on the Poynting vector has this image: I remember hearing/reading somewhere that the energy transmission in a circuit like this is actually not traveling through the wire, but that it actually happens through the electromagnetic field, I.e. essentially the Poynting vectors...

To radiate energy, the Poynting vector must not drop faster than with the inverse square of the distance. Under what circumstances can EM angular momentum be emitted to the vacuum of space (i.e. without being recovered via inductive coupling) and yet not lead to energy losses through radiation...

Hi I have a question about current start signals in a simple circuit such as explained in http://amasci.com/elect/poynt/poynt.html. Turning on a switch somewhere in the circuit, sphere of influences, i.e. motions of electrons in wire and generation of Poynting vector around the wire, start from...

We all know that poynting vector could be used to calculate energy transferred in AC system, but I want to know if that theorem could also be applied to DC current? How to prove this? And how to prove energy transferred in AC system could be calculated via poynting vector?

Hi all, I derived a formula last night for the Poynting vector I have never seen before, and wanted some verification and perhaps insight on. I started with the definition for the Poynting vector in free space: $$\vec{S} = \frac{1}{\mu_{0}} \vec{E} \times \vec{B}$$ and substituted the...

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...

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...

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...

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...

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...

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 –...

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...

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...

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) -...

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...

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...

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...

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...