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SESSION 2019
PCPH003
ÉPREUVE SPÉCIFIQUE - FILIÈRE PC ____________________ PHYSIQUE
Mardi 30 avril : 8 h - 12 h ____________________ N.B. : le candidat attachera la plus grande importance à la clarté, à la précision et à la concision de
la rédaction. Si un candidat est amené à repérer ce qui peut lui sembler être une erreur d’énoncé, il le
signalera sur sa copie et devra poursuivre sa composition en expliquant les raisons des initiatives
qu’il a été amené à prendre. ___________________________________________________________________________________ 



(
)

∂

= ∂
∂

∂ −∂
∂ −∂
=
−
⋅
=
−
⋅
=
−
⋅
ε =

⋅
−
⋅
=
=
∂ 

∂ 
∂ 
∂ −∂
⋅
⋅
−
⋅
⋅
−
⋅
−
⋅
−
(
  
α

α
=

(
=
)=
⋅

()
(
  
θ

( ) = ( )⋅

)


∞



θ
ϕ




θ


ε

→+∞
=
( )=
ε
⋅
⋅π ⋅ ε

)
α

(
  
α
) 
=
⋅

+ ⋅



•
θ=
θ
(
α
  
)
•
θ


α
ϕ
ϕ

α
θ
•
θ θ
α
→∞
→+∞
ϕ 
 =
⋅
 
ϕ
ϕ− =− ⋅
ϕ 
 
 
α
ϕ 
 ⋅
 
ϕ= ⋅
θ ( ) ≈ϕ
⋅
ϕ 
 
 
ϕ
ϕ
=
α
ϕ
⋅
ϕ
α


⋅ +






ϕ 
 
 

ϕ
ϕ


−

θ



θ


θ

θ

= ⋅

θ=

( )
(
 
ε
( )=
( )
⋅
ε
)
( )=
ω ⋅ ⋅
⋅π ⋅ ε ⋅
ω
( )=
⋅
⋅
=


= ⋅ = ⋅
⋅π
∈
=
=−
⋅π ⋅ε
=
⋅
⋅
ε
λ

⋅π ⋅ ε ⋅
⋅
=−
ε
λ

⋅

=
−



>
λ
λ
λ



( )

   
= ⋅
(
(
)
)
Ω




γ
=γ ⋅

γ

θ





( )

( )= (


 
Γ( ) = ∧ (

)⋅



ω =ω⋅

=ω∧

)
θ
=
=

∆


∆

∆

⋅
⋅
Ω =
(
(
∂ 


 ∂ 
)
=
=
∂ 


 ∂ 
=
=
 
⋅
)
∆

(
=
)=
∂ 
⋅

 ∂ (
⋅
=

+
)
∂ 
⋅

 ∂ (
⋅
=

)


(
=
∂ 
⋅

 ∂ (
)=
⋅
=
(

)

λ

+µ ⋅
µ =
⋅
⋅π ⋅
∆λ
−µ ⋅
=
)
∆ =µ ⋅
∆

=


=
⋅
≈
λ
θ
θ
θ
θ
θ

δ
θ
δ= ⋅ ⋅
ϕ
θ
δ
θ
θ
θ
ϕ
(ϕ ) =
⋅
+
=
⋅
ϕ 
 
 
⋅
(ϕ )
∆ϕ
∆ϕ
=
⋅( −
)
(ϕ )
(ϕ )

(ϕ )
∆ϕ
ρ
∆ρ
∆ρ
= ∆ϕ
⋅
λ⋅
⋅π ⋅ ⋅ ρ
∆ρ
ρ
ρ
∆λ
∆λ ≥
λ
⋅ ⋅ ⋅
=
θ
π⋅
−
∆λ


( )=−
⋅π ⋅ε

⋅
−

⋅
⋅ ∆ϕ
ϕ



( ) + ( ) ⋅ϕ ( ) =
⋅ϕ

()
∆
ϕ
ϕ


()
()
=
π⋅
⋅
−
ϕ
( )
=
π ⋅(
)
⋅
−
⋅
ϕ
π ⋅(
)
( )

()
ε
∆
( )=



⋅
( )=
⋅
( )
( )


⋅
⋅
−
⋅
=
0
1
2
3
4
5
6

⋅
I M P R I M E R I E N A T I O N A L E – 19 1151 – D’après documents fournis
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