Final_2003Spring

Final_2003Spring - Physics 8.02 Some(possibly useful...

Info icon This preview shows pages 1–4. Sign up to view the full content.

View Full Document Right Arrow Icon
Physics 8.02 Final Exam Spring 2003 Some (possibly useful) Relations: enclosed o closed surface Q d ε = ∫∫ E A r r ± closed open path surface d d d dt = − ∫∫ E s B A r r r r ± one turn N d = ∫∫ B A r r LI closed path dI d L dt = − E s r r ± 0 closed surface d = ∫∫ B A r r ± thru o E closed path E open surface d d I dt where d µ µ ε = + Φ Φ = ∫∫ o 0 B s E A r r r r ± 0 2 ˆ 4 µ π × = = s r B B source source Id d r r r r q q q = + × F E v B B r r r r d I d = × F s r r r 0 ˆ 1 4 2 dq r πε = r dE r 2 0 1 ˆ 4 V dq r πε = E r r b a V V(b ) V( a ) d = − E s r r i N i i 1 0 i, q 1 V 4 r πε = = = P / R 2 2 Joule Heating P I R V = = ∆ Q C V = 2 2 1 2 2 C Q U C V C = = 0 1 LC = ω 2 0 1 2 elec u E = ε 2 0 1 2 mag u B = µ 0 0 1 c = µ ε 1 f T = 2 2 f T ω = π = π 2 k = π λ c T f k = λ = λ = ω 0 1 = × µ S E r B r r 0 1 ( , ) ( , ) T x t x T = S S r r t dt 2 0 1 2 sin ( ) 2 T x ct dt T π 1 = λ DOUBLE SLIT: constructive: sin , 0, 1, 2, 3, ... d m m θ = λ = ± ± ± destructive: 1 sin , 0, 1, 2, 3, ... 2 d m m θ = + λ = ± ± ± intensity: 2 max cos sin I I d π = θ λ SINGLE SLIT: destructive: sin , 1, 2, 3, ... a n n θ = λ = ± ± ± intensity: 2 max sin sin sin a I I a π θ λ = π θ λ USEFUL INTEGRALS: b a dx b a = ( ) 2 2 1 2 b a x dx b a = 1 ln b a b dx x a = 2 1 1 b a dx 1 x a b =
Image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon