Correction 1 Courant de déplacement et courant de conduction

−→ =γ−→
E
−→d=ε0
∂−→ E
∂t
−→
E=−→ E0cos(ωt)−→ E0
−→ =γ−→
E0cos(ωt)
−→d=−ε0ω−→
E0sin(ωt)
γ||−→ E0||
ω ε0||−→ E0||
α=γ
ω ε0
ε0=1
36π.109F.m−1ω= 2π.106rad.s−1
α= 1,1.1012 ≫1
α= 1,8≃1
α= 1,8.10−2≪1

M
M−→
E
M M (M, −→ uz)
−→
E(M, t) = E(M, t)−→ uz
−→
uzz
−→
E(M, t) = E(z, t)−→ uz
ρ= 0
div(−→ E) = ∂E(z, t)
∂z = 0 =⇒E(z, t)z
E
σ(t)
−→
E(z= 0+, t)−−→ E(z= 0−, t)
=−→ 0
=σ(t)
ε0−→
uz
−→
E
−→
E(t) = σ(t)
ε0−→
uz=Q(t)
πa2ε0−→
uz
−→
j
−→
E(t)−→ jD
−→
uz
M M (Oz)
M
M−→
B(M, t) = B(M, t)−→ uθ
(Oz)
−→
B θ
−→
B(M, t) = B(r, z, t)−→ uθ

Cr(Oz)
−→
uz
C
−→
B·−→ ℓ=µ0Σ(C)−→ ·−−→
2S+µ0ε0Σ(C)
∂−→ E
∂t ·−−→
2S
Σ(C)rC
⃗uz−→
B
C
−→
B·−→ ℓ=2π
0
[B(r, z, t)−→ uθ]·(r θ −→ uθ) = 2πr B(r, z, t)
r < a r > a r < a
µ0ε0Σ(C)
∂−→ E
∂t ·−−→
2S=µ0ε0Σ(C)
˙
Q
Sε0
⃗uz·(S ⃗uz) = µ0
˙
Q
Sπr2=µ0˙
Qr2
a2
2πr B(r, z, t) = µ0˙ Qr2
a2B(r, z, t) = µ0˙
Q r
2π a2
Q(t) = Q0cos(ωt)
E(t) = Q0
πa2ε0
cos(ωt)−→ uzB(r, z, t) = −µ0Q0rω
2π a2sin(ωt)−→
uθ
E0=Q0
πa2ε0
c=1
√µ0ε0
E(t) = E0cos(ωt)−→ uzB(r, z, t) = −E0
2c2rω sin(ωt)−→
uθ
ue=1
2ε0E2=1 2ε0E02cos2(ωt)
V
Ee=V ue3V=πa2e
2ε0E02cos2(ωt)
⟨Ee⟩=πa2e
4ε0E02=Q02e 4πa2ε0

um=1
2µ0
B2=1
2µ0
E02
4c4r2ω2sin2(ωt)
umue
V
Em=V um3V=ω2
8µ0c4E02a
r=02π θ=0 e z=0
r2sin2(ωt)r r θ z
Em=πa4eω2
16µ0c4E02sin2(ωt)
⟨Em⟩=πa4e ω2
32µ0c4E02=Q02eω2 32πε0c2
α=⟨Em⟩
⟨Ee⟩=a2ω2 8c2
aω
8c=π 4
τ
T
τ=a
c
T=ω
2π
τ≪T aω/c ≪1
⟨Em⟩
⟨Ee⟩≪1
−→
Π = −→
E∧−→ B
µ0
=
E0cos(ωt)−→ uz∧E0
2c2rω sin(ωt)−→
uθ
µ0
−→
Π = rω
2µ0c2E02cos(ωt) sin(ωt)−→
ur=Q02rω
2πa2cos(ωt) sin(ωt)−→
ur
Pray =Slat
−→
Π (r=a, t)·−−→
2S
=2π
θ=0 e z=0
aω
2µ0c2E02cos(ωt) sin(ωt)−→
ur·(a θ z −→ ur)
=π a2e ω
µ0c2E02cos(ωt) sin(ωt)

Pray =π a2e ω
µ0c2E02cos(ωt) sin(ωt) = Q02ω e πa2ε0
cos(ωt) sin(ωt)
dEem
dt+Pray =−PL
PL=−→ j·−→ E= 0
dEem
dt=−Pray =−Q02ω e πa2ε0
cos(ωt) sin(ωt)
t= 0 t
Eem(t)− Eem(0) = Q2
0e
2πa2ε0cos2(ωt)−1
Eem(0) = Q02e
2πa2ε0Eem(t) = Q02e 2πa2ε0
cos2(ωt)
−→
rot(−→ E) = −→ 0̸=−∂−→
B
∂t
∂−→ B
∂t ≈−→
0