What is a complex Poynting vector?

What is a complex Poynting vector?

The complex Poynting vector for a plane wave, giving the complex power flow, is (assuming peak notation for phasors): (3.24) Using equation 3.19, the Poynting vector for a plane wave can be written as: (3.25) Using the triple product rule A ×(B × C) = (A ⋅ C) B − (A ⋅ B) C, this can be rewritten as: (3.26)

What is meant by Poynting Theorem?

: a statement in electromagnetic theory: the transfer of energy by an electromagnetic wave is at right angles to both electric and magnetic components of the wave vibration and its rate is proportional to the vector product of their amplitudes.

What does the Poynting vector represent?

Due to the fact that the Poynting vector represents the field’s energy flux density, its physical unit is watts per square metre (W m−2). Consequently, the Poynting vector provides information about the direction of propagation of the EM field and information about the direction of energy transport in the EM field.

What is the use of Poynting Theorem?

[31] Application of Poynting’s Theorem to electromagnetic energy transfer between the magnetosphere and ionosphere, based on observations of the perturbation Poynting vector Sp above the ionosphere, gives an accurate quantitative measure of this transfer in a spatially integrated sense.

Does the Poynting vector oscillate?

2w. The poynting vector is proportional to the cross product of electric and magnetic field vectors. Because both fields oscillate sinusoidally with frequency w, trigonometric identities show that their product is a sinusoidal function of frequency of 2w.

What is the direction of Poynting vector?

The direction of Poynting vector is perpendicular to the direction of propagation of wave. Explanation: The Poynting vector is proportional to the cross product of Electric and magnetic field, E X B. Therefore, its direction is perpendicular to Electric and Magnetic waves, i.e., in the direction of propagation of wave.

What is Maxwell’s fourth equation?

The four Maxwell equations, corresponding to the four statements above, are: (1) div D = ρ, (2) div B = 0, (3) curl E = -dB/dt, and (4) curl H = dD/dt + J. In the early 1860s, Maxwell completed a study of electric and magnetic phenomena.

What do you mean by displacement current?

displacement current, in electromagnetism, a phenomenon analogous to an ordinary electric current, posited to explain magnetic fields that are produced by changing electric fields.

How does Poynting vector relate to intensity?

The Poynting vector represents the direction of propagation of an electromagnetic wave as well as the energy flux density, or intensity. The constant in front serves to provide the correct magnitude for the intensity: S ⃗ = 1 μ 0 E ⃗ × B ⃗ .

What is the dimension of Poynting vector?

Therefore, Poynting vector is a dimensional vector quantity and it is expressed as VA/m2 or W/m2, because electric and magnetic fields are both vectors. Computer-aided 2D mapping is a common plot method to characterise the Poynting vector in a certain electromagnetic field.

What is the importance of Poynting vector?

A Poynting vector represents the directional energy flux density of an electromagnetic field, which meeans that it represent the rate of energy transfer per unit area. SI unit of the Poynting vector is the watt per square metre.

Which information can be extracted from the Poynting theorem?

It is the rate of change of the energy stored in the fields that is endogenous. The Poynting theorem should read rate of change of energy in the fields = negative of work done by the fields on the charged particles minus the Poynting vector term.

Which is the correct definition of the Poynting vector?

In Poynting’s original paper and in many textbooks, the Poynting vector is defined as S = E × H , {\\displaystyle \\mathbf {S} =\\mathbf {E} \imes \\mathbf {H} ,} where bold letters represent vectors and

How is the curl of a vector field related to the Poynting theorem?

Adding the curl of a vector field. The Poynting vector occurs in Poynting’s theorem only through its divergence ∇ ⋅ S, that is, it is only required that the surface integral of the Poynting vector around a closed surface describe the net flow of electromagnetic energy into or out of the enclosed volume.

How is the Poynting vector bent in a conductor?

Once the Poynting vector enters the conductor, it is bent to a direction that is almost perpendicular to the surface. This is a consequence of Snell’s law and the very slow speed of light inside a conductor. The definition and computation of the speed of light in a conductor can be given.

How to find the time averaged Poynting vector?

the time-averaged Poynting vector is given by (2.31) P ¯(r ¯) = (1 / 2)Re{E ¯(r ¯) × H ¯ ∗ (r ¯)}. The asterisk denotes the complex conjugate. From the expressions obtained in Section 2.2.5, the time-averaged Poynting vector of a simple SPP wave turns out be as follows: