Electromagnétisme 1 - Université Paris-Sud

er
α ω z =e−αx+i(ky−ωt)
−→
E(−→ r , t) = A(k+ik0)e−αx+i(kz ωt)−→ uy
−→
E(−→ r , t) = Acos(kx−ωt)−→ uy+Asin(kx−ωt)−→ uz
−→
A=
A0cos(kx ωt)
A0sin(kx ωt)
0
et −→
B=
B0sin(kx ωt)
−B0cos(kx ωt)
B0sin(kx ωt)
f(t) = Acos(t)
f(t, x) = Acos(kx −ωt)
f(t, x) = Acos2(x)sin(ωt)
f(t, x) = Ae−αx cos2(kx −ωt)
f0+αf = 0 α6= 0
f00 +αf = 0 α6= 0 α
V(−→ r , t) = Ae−αx cos(ky −ωt)
−→
E(−→ r , t) = A(k+ik0)e−αx+i(kz ωt)−→ uy
−→
E(x, y, z) = E0sin(πx
α)−→
uz−→ E
z=z00< x < a 0< y < b
ρ
V=(ρ
6ε0(a2−r2) + Q 4πε0apour r ≤a
Q
4πε0rpour r ≥a

−→
E
div−→ E‚S−→ E−→ .dS
R > a R < a
−→
ur−→ uθ−→ uz
−→
uz−→
j
−→
B(−→ r)
B(r)r=a
B r = 1cm I = 1A a = 1mm

er
~
E
~u = (α, β, γ)~ k= (a, b, c)
E0
λ ν ω
~
∇.~ E~ ∇ ∧ ~ E4~ E∂~
E
∂t
~
∇ ≡ i~ k∂
∂t ≡ −iω ~
∇≡−i~ k∂
∂t ≡iω
~
E~ k, ~ E, ~ B
~
E~ B k/ω
E0/B0
λ= 488 nm
~
k, ~ E, ~ B~ R
D~
RE
e
heiD~ REhei

1mm2
~
k, ~ E, ~ B
~
E ExEy
~
E=
Exei(kz−ωt)
Eyei(kz−ωt+ϕ)
0