electromagnetic field momentum
Fields carry not only energy but momentum: a beam of light striking a surface pushes on it, and switching on crossed electric and magnetic fields can set a system rocking even with nothing moving. Electromagnetic field momentum is the mechanical momentum stored in the fields themselves, without which momentum conservation would fail.
The momentum stored per unit volume is g = epsilon_0 (E x B), which is exactly the Poynting vector divided by c^2, g = S/c^2. Integrating g over all space gives the total momentum carried by the field. This is why light exerts radiation pressure: a wave of intensity I delivers momentum at a rate I/c per unit area if absorbed (twice that if reflected). The field momentum is the missing piece in Newton's third law for electromagnetism — when two charges interact through their fields, the fields themselves hold momentum so that the total (matter plus field) is conserved.
Field momentum resolves genuine paradoxes. In static crossed E and B fields the momentum density g = epsilon_0 E x B is nonzero even though nothing moves — hidden field momentum that balances the books when the fields are switched off (the Feynman disk paradox). Together with the energy density and the Maxwell stress tensor, it forms the stress-energy tensor of the electromagnetic field, the source of gravity in general relativity and the guarantee that energy and momentum are locally conserved.
Sunlight of intensity I hitting a black (absorbing) surface exerts a radiation pressure I/c; a perfectly reflecting mirror feels 2I/c because it also reverses the light's momentum. At Earth's 1360 W/m^2 this is only about 4.5 micropascals — tiny, but enough to drive a solar sail.
g = epsilon_0 (E x B) = S/c^2: momentum stored in the field, the source of radiation pressure.
Field momentum is real mechanical momentum — omit it and Newton's third law appears to fail for interacting charges. Even fully STATIC crossed fields carry momentum density epsilon_0 E x B, the origin of 'hidden momentum' paradoxes; nothing needs to be moving for the field to hold momentum.