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Final_2002Fall

Final_2002Fall - Physics 8.02 Some(possibly useful...

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1 Physics 8.02 Final Exam Fall 2002 Some (possibly useful) Relations: closed surface d 0 = ∫∫ E A G G w closed open path surface d d d dt = − E s B A G G G G v 0 closed surface d = ∫∫ B A G G w 2 1 closed open loop surface d d d c dt ∫∫ B s = E A G G G G v 0 2 ˆ 4 µ π × = = s r B B source source Id d r G G G q q q = + × F E v B G G G G 0 ˆ 1 4 2 dq r πε = r dE G 2 0 1 ˆ 4 V dq r πε = E r G b a V V(b ) V( a ) d = − E s G G i N e i i 1 i,P k q V r = = = vol e source dV V k r ρ = Q C V = 2 2 1 2 2 C Q U C V C = = 0 vol all space U dV 2 ε = E E G G 2 0 1 2 elec u E = ε 9 2 2 0 1 9.0 10 / 4 e k N m C πε = = × A m T / 10 4 7 0 × = π µ 2 0 1 2 mag u B = µ mag mag vol U u dV = 0 0 1 c = µ ε cT λ = 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 B G G G 0 1 ( , ) ( , ) T x t x t dt T = S S G G 2 0 1 2 1 sin ( ) 2 T x ct dt T π = 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 = ± ± ± single slit: sin , 1, 2, 3, ... a m m π θ = π = ± ± ± λ rad P c = S G 2 rad P c = S G oneturn N d LI = B A G G closed path dI d L dt = − E s G G v ( ) (1 ) R L t tot I t e R ε = L R τ = RC = τ 0 1 LC = ω single slit 2 max sin sin sin a I I a π θ λ = π θ λ double slit 2 max cos 2 I I φ = with 2 sin d π φ = θ λ
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PHYSICS DEPARTMENT 8.02 Final Exam Fall 2002 FAMILY (last) NAME GIVEN (first) NAME Student ID Number Your Section (check one): ___MWF 10 am ____MWF 12 pm Your Group (for example, 10A): ____________ Instructions: 1. Show all work. 2. This is a closed book test. 3. Crib Sheets are not allowed (Key equations are provided.) Problem Score Grader 1 (10 points) 2 (35 points) 3 (35 points) 4 (35 points) 5 (35 points) TOTAL
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Problem 1:(10 points) Question 1: Which of the following statement(s) correctly identifies possible sources of magnetic fields. A. Time changing electric fields B. Point-like stationary magnetic charges C. Moving point-like electric charges D. Time changing magnetic fields E. Point-like stationary electric charges F. Moving point-like magnetic charges Answer:
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