Electromagnetic field ($\mathbf{E},\mathbf{B}$)

The combined electric field and magnetic field that determine the Lorentz force on a charged particle.

An electromagnetic field carries momentum as well as energy. In vacuum, its SI momentum density iswhere $\mathbf{S}=\mathbf{E}\times \mathbf{B}/{\mu }_0$ is the Poynting vector. Thus the field momentum in a region is ${\mathbf{P}}_{\mathrm{field}}=\int \mathbf{g}dV$. ^[ref]

For a directed vacuum plane wave, $\mathbf{S}=cu\hat{\mathbf{n}}$, so a pulse with total energy $U$ carries momentum $U\hat{\mathbf{n}}/c$. 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. ^[ref]