Devoir surveillé n 3 A : électromagnétisme

◦
−→
rot −→ rot −→ F = −−→ grad div −→ F−∆−→ F−→ F
ε0= 8,84.10−12F.m−1µ0= 4π.10−7H.m−1
∆V = 1
r
∂
∂r (r∂V ∂r )+1 r2
∂2V
∂θ2+∂2V ∂z2
◦
•
•r1
•r2r3
•
r1r2ε0µ0
ℓ≫r3

◦
−→
er
−→
eθ
r1
r2
r3
ame
z
gaine
r1
r2
r3
Cable en perspective Vue de cˆot´e
isolant
ame
gaine
ρ
r∈[r1;r2]
−→
E
−→
EN2 −
−→
EN1 =σ
ε0
−→
n12
−→
ET2 −
−→
ET1 =−→ 0
r1r2
σ1σ2
Γ
WE
WE=Q2
2C =1 2CU2
−→
ez
−→
ez
(r)
r∈[r1;r2]

WB
WB=1
2LI2
Λ =
µ0ln (r2
r1)
2π
Λ
−→
Π
div −→ Π + ∂uem
∂t =−
−→
j .−→ E
uem
−→
j .−→ E
Φ = UI
z=−a
2z=a 2
µ0= 4π.10−7H.m−1ε0= 8,85.10−12F.m−1
γ= 6.107S.m−1
−→
E = E−→ ex
−→
B
−→
B
−→
B
−→
E−→ B
div −→ Π + ∂uem
∂t =−
−→
j .−→ E
∆x∆y

◦
ω
t= 0 ρ0
ρ(t)
ρ= 0
ε0
∂−→ E
∂t ω < 1015
D∆−→ B = ∂−→
B
∂t
µ0γ
z= 0
−→
B = B0cos ωt−→ uxz < 0
−→
E−→ B−→ E (M, t) =
−→
E0(z) exp(iωt)−→ B (M, t) = −→ B0(z) exp(iωt)
−→
B0(z)δ
z
δ
J.K−1m1
t1
◦m2t2 ◦
tf
◦
l
•c= 4,18 kJ.kg−1.K−1
•S(T) =
C ln T + C