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 µ0 = 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 ± ky + ε) v= T = µ 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 ± uo ν v ± 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 µ0 N I 2r B = µ0 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 × B ~ F~ = q E µr µ0 N 2 S ` I= Ci−1 i µ0 I 2πa L= X i i ~ •S ~ φB = B I= X i R= ~ F~ = I ~` × 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 . µ EL = hν = 10,2 eV . (Z − 1)2 E = mc2 + Ec hν = W0 + Ec = hν0 + eU0 N = N0 e−µx = N0 e− ρ . ρx = N0 Z2 n2 ∆P = Pe − Pa 1 x/CDA 2 CDA = ln 2 µ 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