= Poynting vector
{c}
{title2=$\mathbf S=\mathbf E\times\mathbf B/\mu_0$}
{wiki}
In vacuum the <Poynting vector>
$$
\mathbf S=\frac1{\mu_0}\mathbf E\times\mathbf B
$$
is the local <energy flux>, measured in watts per square metre. Its <surface integral> $P=\int_A\mathbf S\cdot\mathbf n\,dA$ gives signed <power> crossing a surface with unit <normal vector> $\mathbf n$. Positive flux follows the chosen normal; for a closed surface the usual convention is outward. <Power> depends on the normal component and area, rather than just the field magnitude.
The <Poynting vector> applies to steady fields as well as <electromagnetic waves>. In a driven resistive <electrical circuit>, surrounding fields can carry <energy> into the conductor, where electrical <work> becomes <Joule heating>. This turns a circuit-level power balance into a spatial description of energy delivery. https://ocw.mit.edu/courses/res-6-001-electromagnetic-fields-and-energy-spring-2008/0f814aee1c72517df7d7e7e96b7365e1_11.pdf[Haus and Melcher, Electromagnetic Fields and Energy, chapter 11, §§11.0–11.3]{ref}.
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