My name is Alexander Fufa

**eV**and here I will explain the following topic:# Poynting Vector: Energy Flow of an Electromagnetic Field

## Formula

## What do the formula symbols mean?

## Power density

`$$ \boldsymbol{S} $$`

Poynting vector describes the

*energy*passing through a cross-sectional area per unit time. The Poynting vector is thus a power density.The cross-sectional area is spanned by \( \boldsymbol{E} \) and \( \boldsymbol{B} \). The Poynting vector is orthogonal to \( \boldsymbol{E} \) and \( \boldsymbol{B} \).

## Magnetic field

`$$ \class{violet}{B} $$`Unit

`$$ \mathrm{T} = \frac{\mathrm{kg}}{\mathrm{A} \, \mathrm{s}^2} $$`

Magnetic flux density determines the strength of the magnetic field and thus the magnitude of the Poynting vector.

## Electric field

`$$ \class{purple}{\boldsymbol E} $$`Unit

`$$ \frac{\mathrm{V}}{\mathrm{m}} = \frac{\mathrm{N}}{\mathrm{C}} = \frac{\mathrm{kg} \, \mathrm{m}}{\mathrm{A} \, \mathrm{s}^3} $$`

The E-field vector indicates the strength of the electric field. The magnitude of the E-field determines the magnitude of the Poynting vector.

## Vacuum permeability

`$$ \mu_0 $$`Unit

`$$ \frac{\mathrm{Vs}}{\mathrm{Am}} = \frac{ \mathrm{kg} \, \mathrm{m} }{ \mathrm{A}^2 \, \mathrm{s}^2 } $$`

The vacuum permeability is a physical constant and has the following experimentally determined value:

`$$ \mu_0 ~=~ 1.256 \, 637 \, 062 \, 12 ~\cdot~ 10^{-6} \, \frac{\mathrm{Vs}}{\mathrm{Am}} $$`**Explanation**

## Video

Poynting vector \( \boldsymbol S \) describes the energy that passes through a cross-sectional area per unit time. The Poynting vector is therefore a power density. The unit of the Poynting vector is watts per square meter.

Formula anchor
$$ \begin{align} \boldsymbol{S} ~=~ \frac{1}{\mu_0} \, \left( \class{purple}{\boldsymbol E} ~\times~ \class{violet}{\boldsymbol{B}} \right) \end{align} $$