= Radiation-force density without Ohm's law
{title2=$\overline f_x=-\partial_x[\mu_0\overline{H_z^2}/2+\epsilon_0\overline{E_y^2}/2]$}
For a monochromatic transverse field depending on $x,t$, with vacuum permittivity and permeability and arbitrary induced transverse current, Ampère's law gives $J_y=-\partial_xH_z-\epsilon_0\partial_tE_y$. Multiplying by $\mu_0H_z$ 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.
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