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Interpretation Let us examine the relation between complex S and the real N. Since the real electric
field is given in terms of the corresponding complex phasor by
E(x, y, z, t) =
E(x, y, z)ejωt + E∗(x, y, z)e−jωt
2
(7.16)
and the real magnetic field is given in terms of the corresponding complex phaser by
H(x, y, z, t) =
H(x, y, z)ejωt +H∗(x, y, z)e−jωt
2
(7.17)
we find that the real Poynting vector can be written in the form
E ×H =
E × H∗ + E∗ × H
4
+
E × H e2jωt + E∗ ×H∗ e−2jωt
4
If we take the time average of each side, the second term on the right hand side
contributes zero and hence
=
E × H∗ + E∗ × H
4
=
S + S∗
2
(7.18)
The right hand side is just the real part of S, so we have shown that
=
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