= Electromagnetic field momentum
{title2=$\mathbf P_{\mathrm{field}}$}
An <electromagnetic field> carries <momentum> as well as <energy>. In vacuum, its <SI> <momentum density> is
$$
\mathbf g=\epsilon_0\mathbf E\times\mathbf B=\frac{\mathbf S}{c^2},
$$
where $\mathbf S=\mathbf E\times\mathbf B/\mu_0$ is the <Poynting vector>. Thus the field <momentum> in a region is $\mathbf P_{\rm field}=\int\mathbf g\,dV$. <The Feynman Lectures on Physics, Volume II by Richard Feynman and others>[Section 27–6, equations 27.21–27.22, momentum density and energy flux]{ref}
For a directed vacuum <plane wave>, $\mathbf S=cu\,\widehat{\mathbf n}$, so a pulse with total <energy> $U$ carries <momentum> $U\widehat{\mathbf n}/c$. Complete <absorption> transfers that <momentum> to matter. Reversing the pulse at a stationary perfect mirror transfers twice as much normal <momentum>, explaining <radiation pressure>.
Conservation joins field <momentum> to the <mechanical momentum> of matter and <momentum> crossing the chosen boundary. Changing a field can therefore accelerate matter even when no material particle carries the <momentum> across the intervening space. Static configurations can also contain nonzero field <momentum>; the vacuum formula does not require radiation. <The Feynman Lectures on Physics, Volume II by Richard Feynman and others>[Section 27–6, charge-magnet example and return of stored angular momentum]{ref}
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