Problem 1. A conducting slab
A plane polarized electromagnetic wave E = Eteikz-wt is incident normally on a flat uniform sheet of an excellent conductor (o > w) having thickness D. Assume that in space and in the conducting sheet = e = 1, discuss the reflection an transmission of the incident wave.
(a) Show that the amplitudes of the reflected and transmitted waves, corrrect to first order in (w/o)1/2, are:
ER (1 - e2X) (v-2+1)+(v-3-I)=1 ET 2^ye-X
(1)
(2)
where
(3)
2.
x=(1-i)D/8
(4)
(b) andifythat/fotozehfidkineslenth infinite skin depth you obtain the proper limiting results.
(c) Optional: Show that, except for sheets of very small thickness, the transmission coefficient is 8(Re)2e-2D/8 (5)
Sketch log T as a function of D/, assuming Re = 10-2. Define "very small thickness" .
Problem 1.A conducting slab
AplanepolarizedelectromagneticwaveE = E,eikz-ot isincidentnormallyonaflatuniform sheetof anexcellent conductor(!) having thickness D. Assumethatinspace andin theconductingsheetu = = 1, discuss the ref lection an transmission of the incident wave
(a) Showthattheamplitudesofthereflectedandtransmittedwaves,corrrecttofirstorder in(!/ )1/2,are:
ER (1 e-2^) E. 1e-2+(1+e-2) ET. 2 e-^ E1 (1 e-2+(1+e-2)
(1)
(2)
where
(3)
=(1 i)D/
(4)
and. P2l!u istheskindepth.,
results.
(c) Optional: Show that, except for sheets of very small thickness, the transmission coefficientis 8(Re )2e-2D/8 T= (5) 12e-2D/8 cos(2D/)+ e-4D/8 Sketch logT asafunctionofD/ , assumingRe = 10 -2. Define"verysmallthickness".
i.
=
-
1i