) = nct n 1 Ct n dt = 1

Transcription

1 Constnts: g 9.8 m/s G N m / kg c m / s M E kg E m v sound n r 343 m/s t 0 C k B J/K N A k 4π Nm C C N m q e C m e kg T m m p kg ev J 4π 0 7 A h J s h π Spheres: A 4πr V 4 3 πr 3 Cylnders: A πr + πrh V πr h c m/s Crcles: A πr C πr Qudrtc Formul: z + bz + c 0 solutons re Bnoml Approxmton: for ε the followng pproxmton holds ( + ε n + nε Clculus: d ( Ct n nct n Ct n n + Ct n+ + D Knemtcs: Δx x f x Δv v f v Δ f Δt t f t v Δx Δt Δ ( t lm Δx v( t lm Δt d t Δt dx t d v t Δv Δt d 3 x( t 3 Δx v t Δv ( t lm t Δt dv t d x( t Δ Δt t t t Δv t Δ t x f x + v t + t v f v + t v f v + ( x f x x f x ( v + v f t crculr moton: c v r Forces & Newton s Second Lw: t lm Δv F net Δt dv F m t unform crculr moton: work, constnt force: W F Δr FΔr cosθ work, vrble force: W F dr work-energy theorem: W net ΔKE KE f KE Potentl Energy: ΔPE PE f PE F conservtve dr t v πr T πrf Knetc Energy: KE trnslton mv KE rotton Iω Power: P F v Δr lm F Δt dw Energy Conservton, conservtve forces: PE + KE PE f + KE f Energy Conservton, nonconservtve forces: Lner Momentum: p m v P net momentum conservton: f F net externl d P net m v MV CM PE + KE + W nonconservtve PE f + KE f F F net externl d P net z b ± b 4c 0 then P net ntl P net fnl or m v ntl m v fnl

2 ottonl Knemtcs: θ f θ + ω t + αt ω f ω + αt ω f ω + α ( θ f θ rottonl-to-lner connectons: v rω c rω t rα ottonl Dynmcs: τ net τ Iα d L net momentum conservton: f τ net externl d L net where τ r F rf snβ ˆn nd I m r r dm 0 then L net ntl L net fnl or L ntl L fnl energy: KE rot Iω nd for generl moton KE net KE trns + KE rot MV CM Electrc Force nd Electrc Feld: Coulomb s Lw F kq q r pont chrge E kq r ˆr pont chrges E ˆr E F q o kq ˆr contnuous chrge r + I CMω k E r dqˆr chrge denstes λ q l or dq λdl σ q A or dq σda ρ q or dq ρdτ (τ s volume τ Guss s Lw: Φ E Electrc Dpole Moment: E d A q enclosed p q L nd nfnte lne E τ p E λ π r ˆr nfnte sheet E σ ˆn Electrc Potentl Energy nd Electrc Potentl: ΔPE PE B PE A q o E dl r A ΔV V B V A ΔPE r B E dl q o pont chrge V kq r pont chrges V kq contnuous chrge V k r dq Cpctors nd esstors: r A ΔV I prllel C eq C + C r B r A d + eq + C eq C C C Q ΔV C κc o where ε κ prllel plte C κ eq + seres energy stored U Q C QΔV C( ΔV power dsspted P IΔV I ΔV energy densty u E E Electrc Current: I dq conductors I nqv d A where v d qe m τ current densty J I A nqv d resstvty ρ ρ o + α ( T T o nd ρ m nq τ nd ρ L A

3 C Crcuts: chrgng q(t Cε e t C nd I(t ε e t C dschrgng q(t Qe t C nd I(t Q C e t C Mgnetc Force: Mgnetc Dpole Moment: F q v B F I l B d F Id s B prllel wres µ I A nd τ µ B Mgnetc Flux: Φ B B da Ampere s Lw: Frdy s Lw: ε E dl dφ B Mgnetc Felds: solenod B NI l motonl emf ε Blv B d l I enclosed F l I I π Bot-Svrt db Ids ˆr wre B µ I o 4π r πr torod B µ NI o πr ni loop on symmetry xs perpendculr to plne B x I! x + fnte wre s shown t rght B µ I o ( 4πr snθ + snθ energy densty u B B Inductors: self-nduced emf ε L L di nductnce L NΦ B I L Crcuts: chrgng I(t ε ( e t / L LC Crcuts: Q( t Q o cos( ωt + δ I ( t ωq o sn( ωt + δ LC Crcuts: Q Q o e t L cos( ω d t where ω d dschrgng I(t ε t / L e LC L AC Crcuts: rms vlues x rms x mx rectnces X C ωc I energy U LI nd X L ω L 3 gven genertor v V mx snωt then V mx snωt V mx C sn ωt + π X C L V mx sn ωt π X L generl mpednce Z + ( X L X C phse ngle tnφ X X L C Ohm s Lw equvlent V mx I mx Z or V rms I rms Z AC LC Crcut I rms V rms Z V rms + X L X C resonnce ω o LC P ve I rms qulty fctor Q ω o Δω FWHM!! r V rms + X L X C power P ve I rms V rms cosφ V rms ω + L ω ω o

4 Mxwell s Eqns: B d A 0 where Φ E E A or Φ E wve equtons E x Electromgnetc dton: E d A q enc B d l I enc + dφ E E da nd Φ B B A or Φ B B da µ E B o t x E E mx cos kx ωt B t where v c nd c f λ ω πf k π λ ĵ nd B B mx cos( kx ωt ˆk B mx E mx c E d l dφ B energy densty u E u B ε E o B so u u E + u B E B ndu v ( E µ v o ε E o mx ntensty I S A E B where power Iv S v E mx c cb mx cu v momentum p U c (complete bsorpton pressure P F A A Δp Δt ΔU ca Δt ca S c emf B mx Optcs: lw of reflecton θ θ I Snell s Lw n snθ n snθ where n c v n crtcl ngle θ c sn lens/mrror eqn f p + q mgnfer NP f M NP f n + telescope M f o f e norml eye NP 5 cm nd FP nfnty mgnfcton M q p mcroscope M NP l f e f o ylegh crteron for slt θ mn λ for crcle θ mn. λ D polrzton I I o cos θ Two Slt: constructve δ d snθ m mλ or δ d y m L mλ where m 0,±,±... destructve δ d snθ m m + λ or δ d y m L m + λ where m 0,±,±... Sngle Slt: destructve snθ m m λ or y m m λl where m ±,±,±3... Dffrcton Grtng: constructve d snθ m mλ where m 0,,... Trgonometrc Identtes: sn A cos A ( cos ( A + tn A sec A cos( A cos A sn A ( + cos ( A + cot A csc A sn( A ± B sn Acos B ± cos Asn B sn A + cos A sn( A sn Acos A cos( A ± B cos Asn B sn Acos B

5 sn Asn B cos( A B cos( A + B cos Acos B cos( A B + cos( A + B eltvty: L L p v c Δt Δt p v c p mu u c Lorentz Trnsformtons: S to S S to S ΔE (Δmc coordntes: x γ (x vt x γ (x+ vt where γ v y y nd z z y y nd z z t γ t v c x t γ t + v c x u veloctes: u x x v u x v c u u x + v x + u x v c c u y u z u y u u y y γ ( + u x v c γ u x v c u z γ u x v c u u z z γ ( + u x v c Photon: E hf p h λ DeBrogle: λ h p h mv Hesenberg: ΔxΔp ΔEΔt Photoelectrc Effect: KE mx eδv s hf φ Schrödnger Eqn: d ψ + Vψ Eψ m dx λ c c f c hc φ Compton: Δλ λ λ h cosθ m e c normlzton ψ dx probblty P b ψ dx expectton x x ψ dx Prtcle n Infnte Well: ψ n nπx sn L L E n h 8mL n where n,, 3... Blmer-ydberg: λ f c H n f n where.097 H 07 m Bohr: E n π m( ke h n ke o n n 3.6eV r h n n 4π mke n o Blckbody: Stefn-Boltzmnn P AeσT 4 Plnck ( λ πhc λ 5 e hc λkt b Wen λ mx T mk ylegh-jens λ πk B Tc λ 4 o m