Maxwell stress tensor

With electromagnetic momentum density $\mathbf{g}={ϵ}_0\mathbf{E}\times \mathbf{B}$, the momentum-flux conventionsatisfies

For a monochromatic transverse field depending on $x,t$, with vacuum permittivity and permeability and arbitrary induced transverse current, Ampère's law gives $J_y=-{\partial }_x{H}_z-{ϵ}_0{\partial }_t{E}_y$. Multiplying by ${\mu }_0{H}_z$ and averaging Faraday's law gives the displayed gradient. No constitutive assumption $J=\sigma E$ is required. A steady average removes the field-momentum time derivative.

The electromagnetic momentum density in vacuum is $\mathbf{g}={ϵ}_0\mathbf{E}\times \mathbf{B}$. It equals the Poynting vector divided by $c^2$, expressing the relativistic relation between energy flux and momentum density.

With the momentum-flux sign convention used for the Maxwell stress tensor, Maxwell's equations implywhere $\mathbf{g}$ is the electromagnetic momentum density and ${\mathbf{f}}_{\mathrm{L}}$ is the Lorentz force density exerted by the field on matter. Thus total field-plus-matter momentum is locally conserved.

A normally incident vacuum wave of time-averaged intensity $I$ transfers momentum $I/c$ per unit area and time to a perfectly absorbing surface, so its radiation pressure isA perfect reflector reverses the normal momentum and gives $2I/c$.