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# Formulaire-2

publicité
```2020–2021
LPHY1103 – Compléments de physique
Formulaire
Constantes
G = 6,67 . 10−11 N m2 kg−2
g = 9,81 m s−2
vson = 340 m s−1
NA = 6,02 . 1023
I0 = 10−12 W m−2
k=
e = 1,6 . 10−19 C
1
= 9 . 109 N m2 C−2
4πε0
&micro;0 = 4π . 10−7 T m A−1
c = 3 . 108 m s−1
σ = 5,67 . 10−8 W m−2 K−4
h = 6,63 . 10−34 J s = 4,14 . 10−15 eV s
mp = 938 MeV c−2
mn = 940 MeV c−2
me = 0,511 MeV c−2
u = 931 MeV c−2
kB = 1,38 . 10−23 J K−1
1
Vibrations et ondes
x = A cos(ωt + ε)
r
ω = 2πν =
v=
k
m
ω = 2πν =
b2
Z=
+
θ̇ =
g
`
s
m2 ω 2
a=
d2 x
= −ω 2 x
dt2
E = 12 mv 2 + 12 kx2
θ = θm cos(ωt + ε)
r
dx
dt
dθ
dt
α=
d2 θ
= −ω 2 θ
dt2
E = 12 mv 2 + 12 mg`θ2
2
ω02
1− 2
ω
s
λω
ω
v = λν =
=
2π
k
ξ = A cos(ωt &plusmn; ky + ε)
v=
T
=
&micro;
r
q
A = A21 + A22 + 2A1 A2 cos(ε1 − ε2 )
d2 − d1 = d sin θ = nλ
y=
λ nλ
+
4
2
sin θ =
y=
r=
nλ
2
νn =
λ
2
nv
2L
νn =
(2n − 1)v
4L
I
I0
ν0 =
v &plusmn; uo
ν
v &plusmn; us
1,22λ
d
Z = ρv
d2 − d1 = d sin θ = nλ +
Z1 − Z2
Z1 + Z2
P = IS
L = 10 log
2
t=
4Z1 Z2
(Z1 + Z2 )2
2
I = I0 e−αy
`T
m
Électromagnétisme
F =
k|q1 q2 |
r2
E=
k|Q|
r2
~ •S
~ = qint
φE = E
ε0
|σ|
2ε0
E=
Z
E=
k|λ|
2r
B
~ • d~r
E
UAB = VB − VA = −
Ep = qV
V = V∞ +
A
C=
R=
Q
Q
εr ε0 S
=
=
U
Ed
d
U
ρ`
=
I
S
C −1 =
Ci
X
B=
r=
dφB
dt
R−1 =
Ri
E
(1 − e−t/τ )
R
Q = CE(1 − e−t/τ )
B=
mv
|q|B
X
Z = Lω
Ri−1
P = UI
&micro;0 N I
2r
B = &micro;0 nI
Ep = 21 LI 2
E −t/τ
e
R
τ=
Q = CEe−t/τ
Z=
L
R
τ = RC
Em
Eeff = √
2
E = Em sin(ωt + ε) = BN Sω sin(ωt + ε)
Z=R
Ep = 12 CU 2
~ + q~v &times; B
~
F~ = q E
&micro;r &micro;0 N 2 S
`
I=
Ci−1
i
&micro;0 I
2πa
L=
X
i
i
~ •S
~
φB = B
I=
X
i
R=
~
F~ = I ~` &times; B
E = −N
C=
kQ
r
1
Cω
2
hP i = RIeff
Eeff,2
Ieff,1
N2
=
=
Eeff,1
Ieff,2
N1
3
Im
Ieff = √
2
Optique
FT =
n=
1
=
f
It
Ii
FA =
c
v
Ia
Ii
R=
Ir
Ii
n1 sin θ1 = n2 sin θ2
θi = θr
θc = arcsin
n2
1
1
1 1
−1
−
= +
n1
R1 R2
u v
θR = arcsin
1,22λ
d
Gcθ = Gob . Gcθ,oc =
ABmin =
L PP
.
fob foc
It = Ii cos2 θ
V =
n2
n1
n1
f
0,61λ
n sin α
G=
c
Gm
θ = Gθ + 1 =
AA = VPP − VPR =
hi
v
=−
ho
u
PP
+1
f
1
1
−
PP PR
It = 12 Ii
Physique moderne
λm T = 2,898 . 10−3 m K
E = hν =
hc
λ
Pe = εσST 4
En = −13,6 eV .
&micro;
EL =
hν = 10,2 eV . (Z − 1)2
E = mc2 + Ec
hν = W0 + Ec = hν0 + eU0
N = N0 e−&micro;x = N0 e− ρ . ρx = N0
Z2
n2
∆P = Pe − Pa
1 x/CDA
2
CDA =
ln 2
&micro;
1
Z . mp c2 + N . mn c2 − M c2
A
N = N0 e−λt = N0
1 t/T
2
T =
4
ln 2
λ
A = A0 e−λt = λN
```