# What is the poynting vector?

## Main Question or Discussion Point

i need an interpretation for the poynting vector, and its derivation for EM waves (sinusoidal)

## Answers and Replies

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ShayanJ
Gold Member
Consider the two "curly" Maxwell's equations!(
,
)
Dot the first one with $\mathbf H$ and the second one with $\mathbf E$ and then subtract the second from the first. Using some vector calculus identities, You'll get the following:
$\frac{\partial}{\partial t} \frac 1 2 (\mathbf E \cdot \mathbf D+\mathbf B \cdot \mathbf H) + \mathbf \nabla \cdot (\mathbf E \times \mathbf H)=-\mathbf E \cdot \mathbf J_f$
which is of the form $\frac{\partial u}{\partial t}+\mathbf \nabla \cdot \mathbf K=G$, i.e. is a continuity equation.
Where u is the density of "something", $\mathbf K$ is the current density of that "something"(amount of "something" passing from a unit cross section in the unit of time) and G is the generation of "something" per volume.
For the present case, that something is energy and so the equation is describing the (non-)conservation of electromagnetic energy(which can appear or disappear since its only one of the energy forms present!).
As you can see, the quantity $\mathbf S=\mathbf E \times \mathbf H$(Poynting vector) is playing the role of $\mathbf K$ and so is the electromagnetic energy current density.

Last edited:
Andy Resnick