Schmucker-Weidelt Lecture Notes, Aarhus, 1975 - MTNet

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Let C = g - 5-11. Then a first approximation u (z ) of u(z) is ob-
tained by setting
(2.G8)
This cannot be proved rigorous1.y but the' following arguments are
in favour of it:
1) zX = g can be considered as the depth of the "centre of gravity"
.of the in-phase induced current system.
2) It w ill be shorvn below that z" continuously increases when the
frequency decreases. According to a) its maximum value is 3.
3) For a uniform half-space and K=O we have h = T. I-rence,
X
ax is correct in this case. For perfect conductions u +m since
h+O.
This approximate method performs prrticularly well when there is a
monotone increase in con6uctivi.ty. The following .two figures (P- 24)
illustrate capabilities and limitations of the method.
dl Properties of C in the comul'ex frequency plane
For the following considerations it is useEull to coilsider the fre-
quency w as a comples quan-tity. Then in the coniplex frequency
plane outside the -- positive - imasinar~ .> axis C is an analytical func- --
tion of frequency. - For s proof multiply (2.59) by fX and inteqrate
over z. Then the integration by parts yields
Hence, for w not on the positive imaginary axis f' (0,w) cannot
vanish. There are neither isolated poles nor a dense spectrun of
poles (branch cut).
Division of (2.63) by 1 f ' ( 0,~) 1 yields
We can easily deduce Eroni (2.70) that