What is the statement of Poynting Theorem?

What is the statement of Poynting Theorem?

In words, the theorem is an energy balance: 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.

What is the significance of Poynting Theorem?

Poynting’s theorem is analogous to the work-energy theorem in classical mechanics, and mathematically similar to the continuity equation, because it relates the energy stored in the electromagnetic field to the work done on a charge distribution (i.e. an electrically charged object), through energy flux.

What is the formula of Poynting vector?

The Poynting vector S is defined as to be equal to the cross product (1/μ)E × B, where μ is the permeability of the medium through which the radiation passes (see magnetic permeability), E is the amplitude of the electric field, and B is the amplitude of the magnetic field.

Who discovered the Poynting vector?

Symbol S. A vector that gives a measure of the flow of energy in an electromagnetic field. It is given by the vector product S = E × H, where E is the electric field strength and H is the magnetic field strength. It was discovered by the British physicist John Henry Poynting (1852–1914) in 1884.

What is Poynting theorem derivation?

Poynting Theorem. Statement. This theorem states that the cross product of electric field vector, E and magnetic field vector, H at any point is a measure of the rate of flow of electromagnetic energy per unit area at that point, that is. P = E x H.

What do you mean by work energy theorem?

The work-energy theorem states that the net work done by the forces on an object equals the change in its kinetic energy.

What is Maxwell equation in free space?

Ultimately they demonstrate that electric and magnetic fields are two manifestations of the same phenomenon. In a vacuum with no charge or current, Maxwell’s equations are, in differential form: ∇ · E = 0. ∇ · B = 0. ∇ x E = -(∂B/∂t)

Why are Maxwell’s equations important?

Maxwell’s equations are sort of a big deal in physics. They’re how we can model an electromagnetic wave—also known as light. Oh, it’s also how most electric generators work and even electric motors. Essentially, you are using Maxwell’s equations right now, even if you don’t know it.

What is the Poynting factor?

In physics, the Poynting vector represents the directional energy flux (the energy transfer per unit area per unit time) of an electromagnetic field. It is named after its discoverer John Henry Poynting who first derived it in 1884.

What do you mean by Poynting vector and what does it represent?

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).

How do electromagnetic waves propagate?

Electromagnetic waves differ from mechanical waves in that they do not require a medium to propagate. This means that electromagnetic waves can travel not only through air and solid materials, but also through the vacuum of space.

Which is the formula for the Poynting theorem?

This theorem states that the cross product of electric field vector, E and magnetic field vector, H at any point is a measure of the rate of flow of electromagnetic energy per unit area at that point, that is. P = E x H. Here P → Poynting vector and it is named after its discoverer, J.H. Poynting.

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.

When does the second term of a Poynting vector vanish?

If either k or E0 is proportional to a real vector (i.e., all of the components of the vector have the same phase angle), then it is easily demonstrated that the second term vanishes. In this case, the Poynting vector becomes: (3.27)S = 1 2ωμ * |ψ|2|E 0|2k *.

How is the Poynting vector used in science?

The Poynting vector, named after John Henry Poynting, is used in order to demonstrate the energy flux density of an EM field. Per definition, the Poynting vector is the result of the vector product of the field’s electric and magnetic components [JAC06]: (2.22)→S = →E × →H