= Poynting flux and local heating in a skin layer
{c}
{title2=$\langle S_z\rangle=\sigma\delta E_0^2e^{-2z/\delta}/4$}
For a good conductor with surface electric-field peak amplitude $E_0$, the <surface impedance of a good conductor> gives the displayed time-averaged <Poynting vector> component into the conductor. The factor one half in $\langle\mathbf S\rangle=\operatorname{Re}(\mathbf E\times\mathbf H^*)/2$ is required for peak phasors. Its loss with depth obeys $-d\langle S_z\rangle/dz=\sigma E_0^2e^{-2z/\delta}/2=\langle\mathbf j\cdot\mathbf E\rangle$. Electromagnetic energy becomes <Joule heating> locally; averaged field-energy storage has zero time derivative.
Back to article page
