 Solution

For a thick good conductor in the normal skin effect regime, the skin-effect surface resistance is determined byIdentical guide geometry then giveswhere the numerical ratio assumes both coatings are nonmagnetic, with $\mu \simeq {\mu }_0$. A magnetic stainless-steel grade would require its magnetic permeability; conductivity alone does not fix that alternative.

Using ${\mu }_0\simeq 4\pi \times 10^{-7}\mathrm{H}{\mathrm{m}}^{-1}$, the gold skin depth at the stated frequency isThe metal coating thickness relative to skin depth sets the useful scale. Thus a layer of order $1\mu \mathrm{m}$ begins to be useful, and a few skin depths, roughly $2$–$3\mu \mathrm{m}$, substantially screen the poorer substrate. This is a thickness scale, not a specified attenuation threshold. It assumes a continuous coating thicker than the relevant microscopic surface scale.^[ref][ref]