Electromagnetic waves propagate much differently in conductors than they do in dielectrics or in vacuum. If the resistivity of the conductor is sufficiently low $($that is$,$ if it is a sufficiently good conductor$),$ the oscillating electric field of the wave gives rise to an oscillating conduction current that is much larger than the displacement current. In this case, the wave equation for an electric field E$($x$,$t$)=$Ey$($x$,$t$)$j$^$E$($x$,$t$)=$Ey$($x$,$t$)$j$^$ propagating in the $+$x$+$x$-$direction within a conductor is $2$Ey$($x$,$t$)$x$2=$$$Ey$($x$,$t$)$t$2$Ey$($x$,$t$)$x$2=$$$Ey$($x$,$t$)$t where is the permeability of the conductor and is its resistivity. A solution to this wave equation is Ey$($x$,$t$)=$Emaxe$$kcxsin$($kCx$$t$)$Ey$($x$,$t$)=$Emaxe$$kcxsin$($kCx$$t$)$ where kC$=$$/2$$$kC$=$$/2$$.$

Part A

The electric$-$field amplitude decreases by a factor of $1/$e in a distance $1/$kC$=2$$/$$1/$kC$=2$$/$$.$ Calculate this distance for a radio wave with frequency f$=1\mathrm{.}0$MHzf$=1\mathrm{.}0$MHz in copper $($resistivity $1\mathrm{.}72108$m$1\mathrm{.}72108$m$,$ permeability $=$$0$$=$$0).$ Since this distance is so short, electromagnetic waves of this frequency can hardly propagate at all into copper. Instead, they are reflected at the surface of the metal. This is why radio waves cannot penetrate through copper or other metals, and why radio reception is poor inside a metal structure.