Feuille d`exercices : Énergie et ondes électromagnétiques

−−→
gradf=∂f
∂r ~ur+1 r
∂f
∂θ ~uθ+∂f ∂z ~uz
div ~ A=1
r
∂
∂r (rAr) + 1 r
∂Aθ
∂θ +∂Az ∂z
−→
rot( ~ A) = 1
r
∂Az
∂θ −∂Aθ ∂z ~ur+∂Ar ∂z −∂Az ∂r ~uθ+1 r∂ ∂r (rAθ)−∂Ar ∂θ ~uz
∆f=1
r
∂
∂r r∂f ∂r +1 r2
∂2f
∂θ2+∂2f ∂z2
−−→
gradf=∂f
∂r ~ur+1 r
∂f
∂θ ~uθ+1 rsin θ
∂f
∂ϕ ~uϕ
div ~ A=1
r2
∂
∂r (r2Ar) + 1 rsin θ
∂
∂θ (sin θAθ) + 1 rsin θ
∂Aϕ
∂ϕ
−→
rot( ~ A) = 1
rsin θ∂ ∂θ (sin θAϕ)−∂Aθ ∂ϕ ~ur+1 rsin θ
∂Ar
∂ϕ −1 r
∂
∂r (rAϕ)~uθ+1 r∂ ∂r (rAθ)−∂Ar ∂θ ~uϕ
∆f=1
r2
∂
∂r r2∂f ∂r +1 r2sin θ
∂
∂θ sin θ∂f ∂θ +1
r2sin2θ
∂2f
∂ϕ2

z
a b
I z
U
σ
σ U σ σ
U r a < r < b
z a b
t < 0γ
t > 0t < 0R1
Q0R2> R1
t < 0
t < 0
ε0
t > 0
Q0
r R1< r < R2
t= 0

z xy x0 ◦
x
λ= 488 2
x0x0S
S t
ω
−→
k1
−→
k1=k[cos α−→ ex+ sin α−→ ey]−→ ez
−→
E1
−→
B1
−→
k2
−→
k1x
−→
k2
−→
E2
−→
B2
~
E=E0cos (ωt −kx)~ux

∂~ j
∂t ~
E
~
j~ E
~
E
ω−→ k
−→
ex−→ ey
l γ
x= 0 x=l
δ km=1−j
δ
x > l Etexp j(ωt −k(x−l))
x < 0Erexp j(ωt +kx)
E0exp j(ωt −kx)
δl
x
r=Er
E0k
km
γ= 107Ω−1−1
kmk=ω
cλ= 0,5µ
r
0≤x≤a0≤y≤b0≤z≤c

ω
−→
E=E0−→ ezsin πx
asin πy bexp (−jωt)
lim
P1→P
P2→P
n~
E(P2, t)−~ E(P1, t)o=σ(P, t)
ε0
~n1→2
lim
P1→P
P2→P
n~
B(P2, t)−~ B(P1, t)o=µ0js(P, t)∧~n1→2