Field momentum

The electromagnetic field carries momentum. Its density is g = ε₀ E×B = S/c² (where S is the Poynting vector and c is the speed of light), with units of kilogram-metres per second per cubic metre. Integrated over a volume, ∫ g dV gives the total field momentum inside — a real, mechanical momentum that must be included in any conservation accounting involving the EM field.

The most striking consequence is the hidden momentum in seemingly static configurations. A simple example: a stationary charged capacitor sitting in an external magnetic field carries angular momentum because its electric field crossed with the external B gives a non-zero ∫ g dV circulating around the capacitor axis. If you suddenly discharge the capacitor, the mechanical reaction on the container exactly preserves total angular momentum — but only if you count the field's contribution. Without the g-term, angular momentum appears from nowhere; with it, the books balance. The phenomenon is the *Feynman disc paradox* resolved.

For propagating electromagnetic waves, the field momentum points along the direction of propagation and has magnitude |g| = |S|/c² = (energy density)/c. A photon of energy E carries momentum p = E/c — a classical result that falls directly out of ε₀ E×B for a plane wave, predating and motivating the quantum identification. Radiation pressure on an absorbing surface is I/c (intensity over c), which is exactly the momentum flux of the incoming photons. Laser cooling of atoms, optical tweezers, the Yarkovsky effect drifting asteroids over geological time, and the Poynting–Robertson drag on interplanetary dust all rest on the classical field-momentum accounting first made rigorous in Maxwell's and Poynting's 1870s–1880s work.