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H ≡ 0 , E = E0 ey . (144)
The stationary Maxwell equations, in region 2,
with
0=c ∇×(E + E D ) , (145)
0=j D el − c ∇×(H + H D ), (146)
H D = −αc∇×E, E D = βc∇×H, j D el = σ E (147)
are satisfied by the general solution
where
Ey = Ec + A e −x/λ , (148)
Hz = − σ
c Ec x + Hc − λ
βc A e−x/λ ,
αβc
λ =
2
; (149)
1+βσ
The constant amplitudes Ec, Hc and A are to be determined from the connecting
conditions at x = 0. These are (91), (93) and (97) (no surface current)
Ht + H D t =0, Et + E D t = E0 ey , (150)
c H D t = ζ1 n × E D , (151)
where the last equation is a result of E D ≡ 0 and H D ≡ 0 in vacuum, leading
to
R sf = ...c H D t · (n × E D ). (152)
So the special solution is
1
Ey =
1+βσ E0 + A e −x/λ , (153)
σ
Hz = −
c (1 + βσ) E0 x − λ
βc A e−x/λ − σλ
A,
c
(154)
E D y = βσ
1+βσ E0 − A e −x/λ , (155)
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