Past exam of the physics B course of the University of Cambridge / 2014 / Paper 1 / Section B / B8

The macroscopic Maxwell equations, with free charge and current, areInside this body $\mathbf{D}={ϵ}_0\mathbf{E}$ and $\mathbf{B}={\mu }_0\mathbf{H}$. The wave magnetic field lies along $z$; its sign follows the local wave component. Faraday's and Ampère's laws giveStatic background fields are excluded from this wave solution. The magnetic force density is along $x$, with $f_x={\mu }_0{J}_y{H}_z$. For a steady periodic state, $\overline{H_z{\partial }_t{E}_y}=-\overline{E_y{\partial }_t{H}_z}$. ThereforeThe result gives radiation-force density without Ohm's law. Integrating through the body gives its pressure as the boundary value of the averaged electromagnetic energy density minus its value deep inside. In both limiting cases below the latter is zero. Take $A$ as the incident electric field's peak amplitude and write $Z_v=\sqrt{{\mu }_0/{ϵ}_0}$.

With no reflected field, $\overline{E_y^2}=A^2/2$ and $\overline{H_z^2}=A^2/(2Z_v^2)$ at the entrance. ThusComplete absorption transfers the incident normal momentum flux to the body.

At a perfect conductor, the reflected electric field cancels the incident tangential field, while their magnetic fields add. Thus $E_y(0)=0$ and $H_z(0)$ has peak amplitude $2A/Z_v$. Taking the zero-penetration limit, including its surface force, givesReversal of the normal momentum doubles the pressure compared with absorption at the same incident Poynting flux.