# Poynting vector

measure of directional energy flux

In physics, the Poynting vector represents the directional energy flux of an electromagnetic field. The Poynting vector is obtained in the direction of a right-handed screw from the cross product of the electric field vector rotated into the magnetic field vector of an electromagnetic wave.

## Quotes

• ... Suppose we take the example of a point charge sitting near the center of a bar magnet, as shown in Fig. 27–6. Everything is at rest, so the energy is not changing with time. Also, E and B are quite static. But the Poynting vector says that there is a flow of energy, because there is an E×B that is not zero. If you look at the energy flow, you find that it just circulates around and around. There isn’t any change in the energy anywhere—everything which flows into one volume flows out again. It is like incompressible water flowing around. So there is a circulation of energy in this so-called static condition. ... Perhaps it isn’t so terribly puzzling, though, when you remember that what we called a “static” magnet is really a circulating permanent current. In a permanent magnet the electrons are spinning permanently inside.
• Richard Feynman: "Chapter 27. Field Energy and Field Momentum". The Feynman Lectures on Physics, Volume II. 1964.
• To a considerable extent, one can understand light's momentum properties without reference to photons. A careful analytic treatment of the electromagnetic field gives the total angular momentum of any light field in terms of a sum of spin and orbital contributions. ... In free space, the Poynting vector, which gives the direction and magnitude of the momentum flow, is simply the vector product of the electric and magnetic field intensities. For helical phase fronts, the Poynting vector has an azimuthal component, as shown in figure 1. That component produces an orbital angular momentum parallel to the beam axis. Because the momentum circulates about the beam axis, such beams are said to contain an optical vortex.
• I have in my "Recent Researches on Electricity and Magnetism" calculated the amount of momentum at any point in the electric field, and have shown that if N is the number of Faraday tubes passing through a unit area drawn at right angles to the direction, B the magnetic induction, θ the angle between the induction and the Faraday tubes, then the momentum per unit volume is equal to N B sin θ, the direction of the momentum being at right angles to the magnetic induction and also to the Faraday tubes. Many of you will notice that the momentum is parallel to what is known as Poynting's vector—the vector whose direction gives the direction in which energy is flowing through the field.