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 d0 ⋅= ∫∫ EA G G w closed open path surface d dd dt Es BA G GG G v 0 closed surface d G G w 2 1 closed open loop surface d cd t ⋅⋅ Bs = G G v 0 2 ˆ 4 µ π × == sr BB source source Id d r G q qq =+ × FE v B G G 0 ˆ 1 4 2 dq r πε = r dE G 2 0 1 ˆ 4 V dq r = Er G b a VV ( b )V ( a ) d ∆≡ = − ⋅ G G iN ei i1 i,P kq V r = = ∆= vol e source dV Vk r ρ = QCV =∆ 2 2 1 22 C Q UC V C = 0 vol all space Ud V 2 ε =⋅ EE 2 0 1 2 elec uE 92 2 0 1 9.0 10 / 4 e kN m C × A m T / 10 4 7 0 × = 2 0 1 2 mag uB = µ mag mag vol Uu d V = 00 1 c = µ ε cT λ= 1 f T = f T ω= π = π 2 k = πλ cT f k = λ = ω 0 1 = × µ SE B G G G 0 1 (,) T x tx t d t T = SS G G 2 0 12 1 sin ( ) 2 T xc t d t T π  =  λ  double slit: constructive: sin , 0, 1, 2, 3, . .. dm m θ = ±± ± destructive: 1 sin , 0, 1, 2, 3, . .. 2 m θ= + λ = ± ± ± single slit: sin , 1, 2, 3, . .. am m π θ= π =± ± ± λ rad Pc = S G 2 rad = S G oneturn Nd L I G G closed path dI dL dt G G v () (1 ) R L t tot It e R =− LR τ = RC = 0 1 LC = ω single slit 2 max sin sin sin a II a π θ λ = π θ λ double slit 2 max cos 2 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: Question 2: When a current flows in a wire of length L and cross sectional area A, the resistance of the wire is a) proportional to the area A and inversely proportional to the length L b) proportional to the length L and inversely proportional to the area A c) inversely proportional to the product of the length L with the area A d) proportional to the product of the length L with the area A Question 3: Suppose that at the moment shown in the figure the magnetic flux through the loop is decreasing (in the direction indicated by the normal ˆ n ). Is the y-component of the electric field ( ) y Ex a) greater than b) equal to c) less than the electric field ( ) y Ex x + .
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## This note was uploaded on 04/07/2008 for the course 8 8.02 taught by Professor Hudson during the Fall '07 term at MIT.

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Final_2002Fall - Physics 8.02 Some(possibly useful...

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