Feuille d`exercices : Condensateurs

−−→
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

a
z ω
m
U
m= 9,1 10−31 R= 10
U=
r
σ
σ
1R1 2
R3R2
R1< R2< R3Q1 1 V1
Q2 2 Q3 2
V2 2
Q1Q2
r > R3V2
V1
1Q0S2
V1= 0 V2
S e C
d < e S
C0

S P1P2
U0
P1P2Q0P1P2e
U0= 400 e= 3.10−2S= 15 2
C0Q0
P2xe Q0
q
R1R2R3R1< R2< R3
h
x z =a z =−a
−→
j=j0−→ ux|z|< a −→ j=−→ 0|z|> a
x y
a j0a
z= 0
a
ρ ω

I
R R0R0> R
0≤r≤a−→ B=B0r
a3exp −r a−→
uθ
a≤r−→ B=2B0a
r
−→
uθ
r=a