Phys 218 formula sheet, Cheat Sheet of Physics

Download Phys 218 formula sheet and more Cheat Sheet Physics in PDF only on Docsity! Formula Sheet CCNY PHYS 208 HEDBERG | 2018 General Waves y(x , t) = ym sin(kx −ωt +φ0) k = 2π λ ω 2π = f = 1 T v = ω k = λ T = λ f v = √ √τ µ y(x , t) = 2ym sin kx cosωt f = n v 2L Sound Waves v = √ √ B ρ I = P A I = PS 4πr2 β = (10dB) log I I0 fbeat = f1 − f2 f = f v ± vD v ± vS Geo. Optics 1 p + 1 i = 1 f 1 f = (n− 1)  1 r1 − 1 r2 ‹ m= − i p |m|= h′ h mθ = 25cm f Interference λn = λ n d sinθ = mλ d sinθ =  m+ 1 2 ‹ λ 2L =  m+ 1 2 ‹ λ n2 2L = m λ n2 Diffraction a sinθ = mλ sinθ = 1.22 λ d θR = 1.22 λ d d sinθ = mλ ∆θhw = λ Nd cosθ Electrostatics F = 1 4πε0 q1q2 r2 E= F q E= 1 4πε0 q r2 r̂ τ = p× E p= qd ΦE = ∮ E · dA= qenc ε0 E = σ ε0 E = λ 2πε0r Eins. ∞ plane = σ 2ε0 E = 1 4πε0 q r2 ∆U = U f − Ui = −W ∆V = Vf − Vi = − W q V = U q Vf − Vi = − ∫ f i E · ds V = 1 4πε0 q r V = 1 4πε0 ∫ dq r E = −∇V = − ∂ V ∂ s Capacitance Q = V C C = ε0A d Ceq = ∑ n Cn 1 Ceq = ∑ n 1 Cn U = q2 2C = 1 2 CV 2 Current I = dq d t I = ∫ J · dA J= (ne)vd V = IR ρ = 1 σ = E J R= ρ L A P = IV = I2R= V 2 R Circuits E = dW dq Req = ∑ n Rn 1 Req = ∑ n 1 Rn Q = CE 1− e−t/RC
Q =Q0e−t/RC Magnets F = q(E+ v×B) qvB = mv2 r FB = IL×B τ = µ×B µ= N IA dB= µ0 4π Ids× r̂ r2 Bwire = µ0 I 2πR Magnets Barc = µ0 Iφ 4πR F = µ0 LIa Ib 2πd ∮ B · ds= µ0 Ienc Bsol = µ0 In Btoroid = µ0 IN 2π 1 r B(z) = µ0 2π µ z3 Magnets ΦB = ∫ B · dA E = − dΦB d t E = −N dΦB d t ∮ E · ds= − dΦB d t L = NΦB I Inductance L l = µ0n2A EL = −L d I d t I = E R 1− e−tR/L
I = I0e−tR/L UB = 1 2 LI2 LC(R) circuits q =Q cos (ωt +φ) ω= 1 p LC qdamped =Qe−Rt/2L cos ω′ t +φ
ω′ = Æ ω2 − (R/2L)2 EM waves S= 1 µ0 E×B S = 1 cµ0 E2 c = 1 p µ0ε0 Mechanics x(t) = x0 + vx0 t + 1 2 ax t2 v(t) = vx0 + ax t v2 x − v2 x0 = 2ax(x − x0) F= ma K .E.= 1 2 mv2 ac = v2 r FG = G m1m2 r2 = mg Constants ε0 = 8.85× 10−12 F/m µ0 = 4π× 10−7 V · s/(A ·m) c = 3.00× 108 m/s I0 = 1× 10−12 W/m2 qelectron = −1.602× 10−19 C melectron = 9.11× 10−31 kg qproton = +1.602× 10−19 C mproton = 1.623× 10−27 kg