SESSION DE 2006

(1)

S E S S I O N D E 2 0 0 6

section : sciences physiques

D u r é e : 5 h e u r e s

concours interne

de recrutement de professeurs agrégés

et concours d’accès à l’échelle de rémunération

option : physique et chimie composition sur la physique

et le traitement automatisé de l’information

4B81-90

repère à reporter sur la copie

Calculatrice électronique de poche, y compris programmable, alphanumérique ou à écran graphique, à fonctionnement autonome, non imprimante, autorisée conformément à la circulaire n° 99-186 du 16 novembre 1999.

L’usage de tout document et de tout autre matériel électronique est rigoureusement interdit.

Dans le cas où un candidat repère ce qui lui semble être une erreur d’énoncé, il le signale très lisiblement

dans sa copie, propose la correction et poursuit l’épreuve en conséquence.

(2)

m = 9, 11 × 10

⁻³¹

c = 3, 00 × 10

⁸ ⁻¹

e = 1, 60 × 10

⁻¹⁹

μ

0

= 4π × 10

⁻⁷ ⁻¹

ε

0

μ

0

ε

0

c

²

R + e

− e m

R

0

R

0

α

t − → −−→ = − → r = r − → e +e

r

r R

R − → = k.r − → e

r

k R e ε

0

α

(3)

t = 0

ω

0

ω

²₀

= e

²

4πε

₀

mR

³

.

R ω

0

ν

0

λ

0

= 121, 8

a xy

− z

→ p = −e − → r p

x

(t) p

y

(t) p

0

E

_M

p

0

ω

0

m e

−

→ e

x

, − → e

y

, − → e

z

−

→ =

0

cos(ωt − kx) − → e

y 0

k − →

− k

→

−

→ − → − →

−

→ R =

_μ¹₀

[ − → ∧ − → ]

< − →

R >

0

ε

0

c

T < R(t) >=

_T¹

_T

0

R(t)dt

2

P

0

−

→ =

0

cos(ωt − kx) − → e

y

+

0

sin(ωt − kx) − → e

z

−

→ − →

R k

( )

(4)

r = λ

−

→ p (t) = p

0

cos(ωt) − → e

z

θ

= −ω

²

sin θ

4πε

₀

rc

²

p

0

cos[ω(t − r/c)] ;

_ϕ

=

_θ

/c.

−

→ − →

−

→ R < − →

R >

r − →

R r

P

R

= ω

⁴

p

²₀

12πε

₀

c

³

.

= 2πc/ω

(5)

p

x

= p

0

cos(ωt) p

y

= p

0

sin(ωt).

−

→

r α

−

→ = r

z

P

R

p

0

ω

P

R

= −dE

_M

/dt E

_M

p

0

p

0

T = 2π/ω λ = 434, 1

dE

_M

/dt = −E

_M

/τ

τ E

M

(t)

ω = 4, 34 × 10

¹⁵ ⁻¹

τ

T

xy

.

a

(6)

N

x − →

=

0

cos(ωt − kx) − → e

z

−

→ e

z

z x

¨

z + ω

²

z = (−e/m)

0

cos(ωt − kx).

z(t, x) ω

−

→ p (t) = −e.z − → e

z

p

0

P

R

−

→ p

S P

i

=

¹₂

ε

0

c

²₀

S P

R

P

i

P

i 0

P

i

E

0

S x x + dx

dP

i

(x)

dx = − P

i

(x) .

N ω ω m c e

ω ω

ω

λ = 121, 8 N = 10

²⁵ ³

ω

0

−→

0

t = 0

z −→

0

=

₀

− → e

z

−−→ = r − → e

r

0

x x

) (

0 0

(7)

−→

0

a

θ z t = 0

−−−→

0

= a sin θ − → e

z

− a cos θ − → e

y

− → v

0

= ω

0

a − → e

x

xyz z(t) t > 0

Z = x + iy i

²

= −1 Z (t) Ω = e

0

/2m

Ω ω

0

Z (t) = (ia/2)e

^iΩt

[(1 − cos θ)e

^−iω⁰^t

− (1 + cos θ)e

^iω⁰^t

].

x(t) y(t)

ω

0

z

x y ω

1

= (ω

₀

+ Ω) ω

2

= (ω

₀

− Ω)

−

→ p = −e − → r xyz

z −→

0

ν

0

+Δν ν

0

−Δν Δν

Δν Δν/ν

₀

= 0, 1 ν

0

434, 1

x y

;

(8)

P

1 2

P 1 2

x

y f

= 1, 0

1

=

2

e = 1, 050

x

(9)

434, 1

λ

0

ν

0

− Δν/2 ν

0

+ Δν/2 ν

0

e = (

₂

−

₁

)

E(e) e

V

e ν c V

V = (E

₂

− E

1

)/(E

₂

+ E

1

) E

2

E

1

e V

L

c

= c/Δν

ν

1

= ν

0

+ Δν ν

2

= ν

0

− Δν

I

0

E(e)

e =

2

−

1

E(e)

Δν E(e)

Δν

ν

0

Δν

i(t)

0

= 15

u(t) r = 50 Ω

I t = 0

u(t)

E(e

I(ν) = I

δ

(10)

R

e(t) = vt i(t) v

E( t )

t

R

u(t)

∞

V

sat

V

sat

= 15

v (t) − v (t) u

1

(t) − u

2

(t) = u(t)

1 2 3 4

s

1

(t) u(t)

2

u(0) = 0 t

(11)

∞ ∞

s

3

(t)

s

2

(t) s

3

(t)

8

= 100

₇

9 10

9

= 2

10

s(t)

s

4

(t) s(t)

N = 2 τ = 3 × 10

⁻⁵

e = 0, 2721 ν

0

Δν

(12)

dP

T

= hIdT h

h > 0

L

γ λ

I T

1

(x = 0)

T

2

(x = L) ρ c

T(x, t) x

x x+dx x x + dx

T (x, t) T(x)

T (x) d

²

T (x)

dx

²

= −KI

²

K

λ = 400

⁻¹ ⁻¹

γ = 6 × 10

⁷ ⁻¹

= 2

²

T(x)

T (x) x = 0

x = L

T

2

− T

1

= 100 I

1

I

x = 0 x = L L

I dT

(13)

I T

1

T

2

I < I

1

T

2

> T

1

I

T(x)

I

2

I

dT (x)

dx = T

2

− T

1

L

h = 2, 2 ×10

⁻⁶ ⁻¹

I

2

λ = c/ν

θ = λ/a

=

(14)

ANNEXE : EXTRAIT DU PROGRAMME DE PHYSIQUE-CHIMIE EN CLASSE TERMINALE SÉRIE S. B.O. N°4 HORS-SÉRIE DU 30 AOÛT 2001

(;(03/(6'¶$&7,9,7e6 &217(186 &211$,66$1&(6

(76$92,5)$,5((;,*,%/(6 2QGHVSURJUHVVLYHVPpFDQLTXHV 5HFRQQDvWUHXQHRQGHSURJUHVVLYHSpULRGLTXH

SpULRGLTXHV HWVDSpULRGH

([HPSOHVGDQVODYLHFRXUDQWHG¶RQGHV 1RWLRQG¶RQGHSURJUHVVLYHSpULRGLTXH 'pILQLUSRXUXQHRQGHSURJUHVVLYHVLQXVRwGDOH PpFDQLTXHVSURJUHVVLYHVSpULRGLTXHV 3pULRGLFLWpWHPSRUHOOHSpULRGHSpULRGLFLWp ODSpULRGHODIUpTXHQFHODORQJXHXUG¶RQGH

VSDWLDOH &RQQDvWUHHWXWLOLVHUODUHODWLRQO v7

([HPSOHVSULVGDQVQRWUHHQYLURQQHPHQW 2QGHSURJUHVVLYHVLQXVRwGDOHSpULRGHIUpTXHQFH FRQQDvWUHODVLJQLILFDWLRQHWO¶XQLWpGHFKDTXH GHODGLIIUDFWLRQG¶RQGHVPpFDQLTXHV ORQJXHXUG¶RQGHUHODWLRQO v7 vQ WHUPHVDYRLUMXVWLILHUFHWWHUHODWLRQSDUXQH

/DGLIIUDFWLRQGDQVOHFDVG¶RQGHVSURJUHVVLYHV pTXDWLRQDX[GLPHQVLRQV

VLQXVRwGDOHVPLVHHQpYLGHQFHH[SpULPHQWDOH 6DYRLUSRXUXQHORQJXHXUG¶RQGHGRQQpH ,QIOXHQFHGHODGLPHQVLRQGHO¶RXYHUWXUHRXGH TXHOHSKpQRPqQHGHGLIIUDFWLRQHVWG¶DXWDQW O¶REVWDFOHVXUOHSKpQRPqQHREVHUYp SOXV PDUTXpTXHODGLPHQVLRQG¶XQHRXYHUWXUH /DGLVSHUVLRQPLVHHQpYLGHQFHGHO¶LQIOXHQFH RXG¶XQREVWDFOHHVWSOXVSHWLWH

GHODIUpTXHQFHVXUODFpOpULWpGHO¶RQGHjODVXUIDFH 'pILQLUXQPLOLHXGLVSHUVLI

GHO¶HDXQRWLRQGHPLOLHXGLVSHUVLI ([SORLWHUXQGRFXPHQWH[SpULPHQWDOVpULHGH

'DQVOHFDVG¶XQHRQGHXOWUDVRQRUHRXVXUODFXYH SKRWRVRVFLOORJUDPPHDFTXLVLWLRQGHGRQQpHV

jRQGHVREVHUYDWLRQGHVPD[LPXPVHW DYHFXQRUGLQDWHXU«GpWHUPLQDWLRQGHOD

PLQLPXPVG¶DPSOLWXGHSRXUODGLIIUDFWLRQ SpULRGHGHODIUpTXHQFHGHODORQJXHXUG¶RQGH

5HFRQQDvWUHVXUXQGRFXPHQWXQSKpQRPqQH GHGLIIUDFWLRQ

6DYRLUIDLUHH[SpULPHQWDX[

5pDOLVHUXQPRQWDJHSHUPHWWDQWGHPHWWUH HQpYLGHQFHOHSKpQRPqQHGHGLIIUDFWLRQ GDQVOHFDVG¶RQGHVPpFDQLTXHVVRQRUHV

RXXOWUDVRQRUHV

/DOXPLqUHPRGqOHRQGXODWRLUH

)LJXUHVGHGLIIUDFWLRQSDUXQHIHQWHXQWURX 6DYRLUTXHpWDQWGLIIUDFWpHODOXPLqUHSHXWrWUH

XQREVWDFOH 2EVHUYDWLRQH[SpULPHQWDOHGHODGLIIUDFWLRQ GpFULWHFRPPHXQHRQGH

HQOXPLqUHPRQRFKURPDWLTXHHWHQOXPLqUH &RQQDvWUHO¶LPSRUWDQFHGHODGLPHQVLRQ 9pULILFDWLRQSDUGHVPHVXUHVGHODSHUWLQHQFH EODQFKHLULVDWLRQ GHO¶RXYHUWXUHRXGHO¶REVWDFOHVXUOHSKpQRPqQH

GHODUHODWLRQT OD REVHUYp

3URSDJDWLRQGHODOXPLqUHGDQVOHYLGH ([SORLWHUXQHILJXUHGHGLIIUDFWLRQGDQVOHFDV 'LVSHUVLRQGHODOXPLqUHEODQFKHSDUXQSULVPH 0RGqOHRQGXODWRLUHGHODOXPLqUHFpOpULWp GHVRQGHVOXPLQHXVHV

ORQJXHXUG¶RQGHGDQVOHYLGHIUpTXHQFH &RQQDvWUHHWVDYRLUXWLOLVHUODUHODWLRQO FQ 'LVSHUVLRQGHODOXPLqUHGDQVODYLHFRXUDQWH O F7 FQ ODVLJQLILFDWLRQHWO¶XQLWpGHFKDTXHWHUPH

,QIOXHQFHGHODGLPHQVLRQGHO¶RXYHUWXUH &RQQDvWUHHWXWLOLVHUODUHODWLRQT OD RXGHO¶REVWDFOHVXUOHSKpQRPqQHREVHUYp ODVLJQLILFDWLRQHWO¶XQLWpGHFKDTXHWHUPH pFDUWDQJXODLUHGXIDLVFHDXGLIIUDFWpSDUXQHIHQWH 'pILQLUXQHOXPLqUHPRQRFKURPDWLTXH RXXQILOUHFWLOLJQHVGHODUJHXUDT OD HWXQHOXPLqUHSRO\FKURPDWLTXH /XPLqUHPRQRFKURPDWLTXHOXPLqUH &RQQDvWUHOHVOLPLWHVGHVORQJXHXUVG¶RQGH SRO\FKURPDWLTXHIUpTXHQFHHWFRXOHXU GDQVOHYLGHGXVSHFWUHYLVLEOHHWOHVFRXOHXUV 3URSDJDWLRQGHODOXPLqUHGDQVOHVPLOLHX[ FRUUHVSRQGDQWHV

WUDQVSDUHQWVLQGLFHGXPLOLHX 6LWXHUOHVUD\RQQHPHQWVXOWUDYLROHWV 0LVHHQpYLGHQFHGXSKpQRPqQHGHGLVSHUVLRQ HWLQIUDURXJHVSDUUDSSRUWDXVSHFWUHYLVLEOH GHODOXPLqUHEODQFKHSDUXQSULVPHO¶LQGLFH 6DYRLUTXHODOXPLqUHVHSURSDJHGDQVOHYLGH G¶XQPLOLHXWUDQVSDUHQWGpSHQGGHODIUpTXHQFH HWGDQVOHVPLOLHX[WUDQVSDUHQWV

GHODOXPLqUH 6DYRLUTXHODIUpTXHQFHG¶XQHUDGLDWLRQ

PRQRFKURPDWLTXHQHFKDQJHSDVORUVTX¶HOOH SDVVHG¶XQPLOLHXWUDQVSDUHQWjXQDXWUH 6DYRLUTXHOHVPLOLHX[WUDQVSDUHQWVVRQWSOXV RXPRLQVGLVSHUVLIV

'pILQLUO¶LQGLFHG¶XQPLOLHXWUDQVSDUHQW SRXUXQHIUpTXHQFHGRQQpH

6DYRLUIDLUHH[SpULPHQWDX[

9pULILFDWLRQSDUGHVPHVXUHVGHODSHUWLQHQFH 5pDOLVHUXQPRQWDJHSHUPHWWDQWGHPHWWUH

GHODUHODWLRQT OD HQpYLGHQFHOHSKpQRPqQHGHGLIIUDFWLRQ

GDQVOHFDVG¶RQGHVOXPLQHXVHV 5pDOLVHUGHVPHVXUHVSHUPHWWDQWGHYpULILHU ODSHUWLQHQFHGHODUHODWLRQT OD

IMPRIMERIENATIONALE–6 000143–D’après documents fournis.