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Physic 102 formula sheet (SP2015)
Kinematics and mechanics x = x 0 + v 0 t +
at^2 v = v 0 + at v^2 = v^20 + 2a∆x
F = ma ac = v
2 r Etot = K + U K =
mv^2 = p^2 2 m p = mv WF = F d cos θ
Electrostatics F 12 = k q 1 q 2 r^2
E =
F
q 0 U 12 = k q 1 q 2 r
V ≡
U
q 0 WE = −∆U = −Wyou
Point charge E = k q r^2 V^ =^ k
q r Electric dipole p = qd τdip = pE sin θ Udip = −pE cos θ
Resistance R =
V
I
I =
∆q ∆t Physical resistance: R = ρ
L
A
P = IV = I^2 R =
V 2
R
RS = R 1 + R 2 + · · ·
RP
R 1
R 2
Capacitance
C =
Q
V Parallel plate capacitor:^ C^ =^
κ 0 A d E^ =^
Q
0 A V^ =^ Ed UC =
QV =
CV 2 =
Q^2
C
CP = C 1 + C 2 + · · ·
CS
C 1
C 2
Circuits ∑ ∆V = 0
Iin =
Iout q(t) = q∞(1 − e−t/τ^ ) q(t) = q 0 e−t/τ^ I(t) = I 0 e−t/τ^ τ = RC
Magnetism F = qvB sin θ r = mv qB Fwire = ILB sin θ τloop = N IAB sin ϕ Magentic dipole: μ = N IA τdip = μB sin ϕ Udip = −μB cos ϕ Bwire = μ^0 I 2 πr Bsol = μ 0 nI
Electromagnetic induction
E = −N
∆t Φ = BA cos ϕ |Ebar| = BLv Egen = Emax sin ωt = ωN AB sin ωt ω = 2πf Vrms = Vmax √ 2
Irms = Imax √ 2
Vp Vs
Is Ip
Np Ns Electromagnetic waves λ = c f E = cB
uE =
0 E^2 uB =
2 μ 0 B^2 u =
0 E^2 rms +
2 μ 0 B rms^2 = 0 E^2 rms = B rms^2 μ 0 S = I = uc =
P
A
f 0 = fe
1 + vrel/c 1 − vrel/c ≈ fe
1 + vrel c
I = I 0 cos^2 θ
Reflection and refraction
θr = θi
do
di
f f = ±
R
m = hi ho
di do
n 1 sin θ 1 = n 2 sin θ 2 v = c n sin θc = n 2 n 1
M =
θ′ θ
dnear f
Compound microscope: mobj = Ltube fobj Meye = dnear feye Mtot = Meyemobj
Interference and diffraction
Double-slit interference: d sin θ = mλ d sin θ =
m +
λ m = 0, ± 1 , ± 2 , · · ·
Single-slit diffraction: a sin θ = mλ m = 0, ± 1 , ± 2 , · · · Circular aperture: D sin θ ≈ 1. 22 λ
Quantum mechanics
E = hf = hc λ λ = h p ∆px∆x ≥
h 2 π Bohr atom: 2 πrn = nλ n = 1, 2 , 3 , · · · Ln = mevnrn = nℏ
rn =
ℏ^2
meke^2
n^2 Z ≈ (5. 29 × 10 −^11 m) n^2 Z En = −
mek^2 e^4 2 ℏ^2
Z^2
n^2 ≈ −(13.6 eV)
Z^2
n^2 1 λ ≈ (1. 097 × 107 m−^1 )Z^2
n^2 f
n^2 i
Quantum atom: L =
( + 1)ℏ LZ = m`ℏ Sz = msℏ
Atomic magnetism: μe,z = − e 2 me Lz μs,z = − ge 2 me Sz , g ≈ 2 μB ≡ eℏ 2 me ≈ 5. 8 × 10 −^5 eV/T
Nuclear physics and radioactive decay
A = Z + N r ≈ (1. 2 × 10 −^15 m)A^1 /^3 E 0 = mc^2
mnucleus = Zmproton + N mneutron − |Ebind| c^2 ∆N ∆t = λN N (t) = N 0 e−λt^ = N 02 −t/T^1 /^2 T 1 / 2 = ln 2 λ
λ
Constants and unit conversion
g = 9.8 m/s^2 e = 1. 60 × 10 −^19 C
0 = 8. 85 × 10 −^12 C^2 /Nm^2 k ≡
4 π 0 = 8. 99 × 109 Nm^2 /C^2 μ 0 = 4π × 10 −^7 T · m/A
c =
0 μ 0 = 3 × 108 m/s h = 6. 626 × 10 −^34 J · s hc = 1240 eV · nm
1 eV = 1. 60 × 10 −^19 J melectron = 9. 11 × 10 −^31 kg = 511 keV/c^2
mproton = 1. 673 × 10 −^27 kg = 938 MeV/c^2 mneutron = 1. 675 × 10 −^27 kg = 939.5 MeV/c^2
SI Prefixes Power Prefix Symbol 109 giga G 106 mega M 103 kilo k 100 — — 10 −^3 milli m 10 −^6 micro μ 10 −^9 nano n 10 −^12 pico p
