The vector of Poynting , noted $\backslash \; vec\; \{S\}$, $\backslash \; vec\; \{\backslash \; pi\}$, or $\backslash \; vec\; \{R\}$ is a Vecteur whose direction indicates, in an isotropic medium, the direction of propagation of a electromagnetic Onde and whose intensity is worth the density of power conveyed by this wave. The Module of this vector is thus a power per unit of Surface.

$\backslash \; vec\; \{S\}\; =\; \backslash \; frac\; \{\backslash \; vec\; \{E\}\; \backslash \; wedge\; \backslash \; vec\; \{B\}\}\; \{\backslash \; mu\_\; \{0\}\}$ with $\backslash \; vec\; E$ the Electric field and $\backslash \; vec\; B$ the Magnetic field, in the vacuum.

General expression of the vector of Poynting

In a magnetic material of permeability $\backslash \; mu$, it is appropriate to replace $\backslash \; mu\_0$ by the magnetic Perméabilité $\backslash \; mu=\; \backslash \; mu\_0\; \backslash \; mu\_r$ of material in question. The more general expression of the vector of Poynting is thus:

Temporal average in complex notation

In the case of a electromagnetic Onde planes progressive harmonic, one has $\backslash \; vec\; E=\; \backslash \; vec\; \{E\_0\}\; \backslash \; cos\; \{(\backslash \; Omega\; T\; \backslash \; phi)\}$ and $\backslash \; vec\; B=\; \backslash \; vec\; B\_0\; \backslash \; cos\; \{(\backslash \; Omega\; T\; \backslash \; psi)\}$; one can thus associate complex sizes with the fields $\backslash \; vec\; E$ and $\backslash \; vec\; B$ by posing $\backslash \; underline\; \{\backslash \; vec\; E\}\; =\; \backslash \; underline\; \{\backslash \; vec\; E\_0\}\; e^\; \{I\; \backslash \; Omega\; T\}\; =\; \backslash \; vec\; \{E\_0\}\; e^\; \{-\; I\; \backslash \; phi\}\; e^\; \{I\; \backslash \; Omega\; T\}$ and $\backslash \; underline\; \{\backslash \; vec\; B\}\; =\; \backslash \; underline\; \{\backslash \; vec\; B\_0\}\; e^\; \{I\; \backslash \; Omega\; T\}\; =\; \backslash \; vec\; \{B\_0\}\; e^\; \{-\; I\; \backslash \; psi\}\; e^\; \{I\; \backslash \; Omega\; T\}$, where $i$ is the Complex number such as $i^2=-1$.

The temporal average of the vector of Poynting is worth then

where $\backslash \; underline\; \{\backslash \; vec\; B\}\; ^\; \backslash \; star$ indicates the Conjugué of $\backslash \; underline\; \{\backslash \; vec\; B\}$.

Electromagnetic power crossing a surface $S$

A consequence of the Théorème of Poynting is that the electromagnetic power crossing a surface $S$ is given by the flow vector of Poynting through this surface.

See too

Internal bonds

• Theorem of Poynting

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