# Question #edf8b

Aug 30, 2017

In electromagnetic theory, the Poynting vector describes the flow of energy per unit area in unit time in an electromagnetic field.

It may be defined as (in free space),

$\vec{S} = \frac{1}{\mu} _ 0 \left(\vec{E} X \vec{B}\right)$ where $\vec{E}$ and $\vec{B}$ are respectively the electric and magnetic fields.

It points in the direction of flow of energy.

It arises in the Poynting's theorem which expresses energy conservation in electromagnetic theory,

$\frac{\partial \left({u}_{m} + {u}_{e}\right)}{\partial t} + \nabla \cdot \vec{S} = 0$

Where, ${u}_{m}$ and ${u}_{e}$ are respectively the mechanical and electromagnetic energy densities.

This is the analog of continuity equation in electromagnetic theory.