Exam3_2007Spring_Solutions

# Exam3_2007Spring_Solutions - Physics 8.02 Exam Three...

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Unformatted text preview: Physics 8.02 Exam Three Solutions Spring 2006 Please Remove this Tear Sheet from Your Exam Some (possibly useful) Relations: 2 1 ˆ 4 o dq d r πε = E r r free, inside closedsurface o Q d κ ε = E A r r ) points from inside to outside d A r total d d dt dt ε Φ = - = - E ds B dA r r r r ) moving from to b a b b a a V V V d ∆ =- = - R E s r r 2 ˆ 4 o q c r μ π = << v r B v r r r 2 ˆ 4 o I d d r μ π = s r B r r ˆ where points source observer r from to closed surface d = B A r r ) through contour E o d d I dt μ ε Φ = + 1 B s r r ) where I through is the current flowing through any open surface bounded by the contour: through open surface I d = J A r r d s is right-handed with respect to d A 2 2 1 2 2 E B o B u E u ε μ = = ( 29 ext q = + F E v B r r r r ext d I d = F s B r r r 2 cent. F mv r = IA = μ n r ) = τ μ B r r r z z z dB F dz μ = V IR ∆ = L R A ρ = 2 2 ohmic heating V P I V I R R ∆ = ∆ = = Q C V = ∆ parallelplate o A C d ε = 2 2 1 2 2 Q U C V C = ∆ = 1 C RC X C τ ϖ = = B,self,total back dI L L I dt ε Φ = = - 2 1 2 L U LI = / L L R X L τ ϖ = = Series RLC: ( 29 2 2 2 2 tan L C Z R X R X X X R ϕ = + = +- = 2 2 2 f T k ϖ = π = π = π λ ( 29 1 2 0 0 c T f k- = λ = λ = ϖ = μ ε light ˆ ˆ ˆ E v B = = E B p absorb reflect 1 2 ; S S P P c c = = = μ S E B r r r If the function ( ) D t satisfies the equation ( ) ( ) d D t D t dt τ = - , then / ( ) t o D t D e τ- = Cross-products of unit vectors: ˆ ˆ ˆ ˆ ˆ ˆ = = = i i j j k k ˆ ˆ ˆ h = i j k ˆ ˆ ˆ h = j k i ˆ ˆ ˆ h = k i j Some potentially useful numbers 2 9 7 2 1 N m T m 9 10 4 10 4 C A e o k μ π πε- = = = Breakdown of air E ~ 3 x 10 6 V/m Earth’s B Field B ~ 5 x 10-5 T = 0.5 Gauss Speed of light c = 3 x 10 8 m/s Light (blue to red) λ = 400 nm to 700 nm Electron charge e = 1.6 x 10-19 C Avogadro’s number N A = 6.02 x 10 23 mol-1 MIT PHYSICS DEPARTMENT 8.02 Exam Three Spring 2006 Solutions FAMILY (last) NAME GIVEN (first) NAME Student ID Number Your Section: ___L01 MW 9 am ____L02 MW 11 am ____L03 MW 1 pm ____L04 MW 3 pm ___L05 TR 9 am ____L06 TR 11 am ____L07 TR 1 pm ____L08 TR 3 pm Your Group (e.g. 10A): ______________ 8.02 Exam #3 Solutions Spring 2006 Problem Score Grader 1 (20 points) 2 (5 points) 3 (25 points) 4 (25 points) 5 (25 points) TOTAL MIT PHYSICS DEPARTMENT p. 4 of 12 Problem 1: Five Short Questions. Fill in the blanks with the correct answer Each problem is worth 4 points for the correct answer, 2 points for a partially correct answer (at our discretion). If you don’t know the answer you can earn 1 point for admitting that by leaving it unanswered and writing “I don’t know” (make this clear!). Question A (4 points out of 20 points): A circuit consists of a battery with emf V , an inductor with inductance L , a capacitor with capacitance C , and three resistors, each with resistance R , as shown in the sketch. The capacitor is initially uncharged and there is no current flowing anywhere in the circuit....
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Exam3_2007Spring_Solutions - Physics 8.02 Exam Three...

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