Formulaire-2

2020–2021
LPHY1103 – Compl´ements de physique
Formulaire
Constantes
g= 9,81 m s−2G= 6,67 .10−11 N m2kg−2
NA= 6,02 .1023 vson = 340 m s−1
I0= 10−12 W m−2e= 1,6.10−19 C
k=1
4πε0
= 9 .109N m2C−2µ0= 4π . 10−7T m A−1
c= 3 .108m s−1σ= 5,67 .10−8W m−2K−4
h= 6,63 .10−34 J s = 4,14 .10−15 eV s mp= 938 MeV c−2
mn= 940 MeV c−2me= 0,511 MeV c−2
u= 931 MeV c−2kB= 1,38 .10−23 J K−1
1

Vibrations et ondes
x=Acos(ωt +ε)v=dx
dta=d2x dt2=−ω2x
ω= 2πν =rk
mE=1
2mv2+1 2kx2
θ=θmcos(ωt +ε)˙ θ=dθ
dtα=d2θ dt2=−ω2θ
ω= 2πν =rg
`E=1
2mv2+1 2mg`θ2
Z=sb2+m2ω21−ω2
0
ω22
ξ=Acos(ωt ±ky +ε)v=λν =λω
2π=ω kv=sT µ=r`T m
A=qA2
1+A2 2+ 2A1A2cos(ε1−ε2)
d2−d1=dsin θ=nλ d2−d1=dsin θ=nλ +λ
2
y=λ
4+nλ 2y=nλ 2νn=nv 2Lνn=(2n−1)v 4L
sin θ=1,22λ
d
Z=ρv P =IS L = 10 log I
I0
ν0=v±uo
v±us
ν
r=Z1−Z2
Z1+Z22
t=4Z1Z2
(Z1+Z2)2I=I0e−αy
2

´
Electromagn´etisme
F=k|q1q2|
r2φE=~
E•~ S=qint
ε0
E=k|Q|
r2E=|σ| 2ε0
E=k|λ|
2r
UAB =VB−VA=−ZB
A
~
E•d~r Ep=qV V =V∞+kQ
r
C=Q
U=Q Ed =εrε0S dC=X
i
CiC−1=X
i
C−1
iEp=1
2CU2
R=U
I=ρ` SR=X
i
RiR−1=X
i
R−1
iP=UI
~
F=I~ `×~ B B =µ0I
2πa B=µ0NI 2rB=µ0nI
φB=~ B•~ S r =mv
|q|B
~
F=q~ E+q~v ×~ B
E=−NdφB
dtL=µrµ0N2S `Ep=1
2LI2
I=E
R(1 −e−t/τ )I=E Re−t/τ τ=L R
Q=CE(1 −e−t/τ )Q=CEe−t/τ τ=RC
E=Emsin(ωt +ε) = BN Sω sin(ωt +ε)Eeff =Em
√2Ieff =Im √2
Z=R Z =Lω Z =1
Cω hPi=RI2
eff
Eeff,2
Eeff,1
=Ieff,1
Ieff,2
=N2
N1
3

Optique
FT = It
Ii
FA = Ia
Ii
R=Ir
Ii
θi=θr
n=c
vn1sin θ1=n2sin θ2θc= arcsin n2 n1
1
f=n2 n1−1 1 R1−1 R2=1 u+1 vV=n1 fG=hi ho
=−v
u
θR= arcsin 1,22λ
dABmin =0,61λ nsin αGm
θ=Gc θ+ 1 = PP
f+ 1
Gc
θ=Gob . Gc θ,oc =L
fob
.PP
foc
AA = VPP −VPR =1
PP −1 PR
It=Iicos2θ It=1
2Ii
Physique moderne
λmT= 2,898 .10−3m K Pe=εσST 4∆P=Pe−Pa
E=hν =hc
λEn=−13,6 eV .Z2 n2hν = 10,2 eV .(Z−1)2
hν =W0+Ec=hν0+eU0E=mc2+Ec
N=N0e−µx =N0e−µ
ρ. ρx =N01
2x/CDA CDA = ln 2
µ
EL=1
AZ . mpc2+N . mnc2−Mc2
N=N0e−λt =N01
2t/T T=ln 2
λA=A0e−λt =λN
4