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Exam3_2006Spr_Solutions

# Exam3_2006Spr_Solutions - Physics 8.02 Exam Three Solutions...

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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 G free, inside closedsurface o Q d κ ε = ∫∫ E A G G w points from inside to outside d A G total d d dt dt ε Φ = − = − ∫∫ E ds B dA G G G G v moving from to b a b b a a V V V = = − E s G G d 2 ˆ 4 o q c r µ π × = << v r B v G G G 2 ˆ 4 o I d d r µ π × = s r B G G ˆ where points source observer r from to 0 closed surface d = ∫∫ B A G G w through 0 contour E o d d I dt µ ε Φ = + B s G G v where I through is the current flowing through any open surface bounded by the contour: through open surface I d = J A G G d s is right-handed with respect to d A 2 2 0 1 2 2 E B o B u E u ε µ = = ( ) ext q = + × F E v B G G G G ext d I d = × F s B G G G 2 cent. F mv = r IA = μ n G ± = × τ μ B G G G 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 ω = = B,self,total back dI L L I dt ε Φ = = − 2 1 2 L U L = I / L L R X L τ ω = = Series RLC: ( ) 2 2 2 2 tan L C Z R X R X X X R ϕ = + = + = 2 2 2 f T k ω = π = π = π λ ( ) 1 2 0 0 c T f k = λ = λ = ω = µ ε 0 light 0 ˆ ˆ ˆ E v B = × = E B p absorb reflect 0 1 2 ; S S P P c c = × = = µ S E B G G G If the function ( ) D t satisfies the equation ( ) ( ) d D D t dt t τ = − , then / ( ) t o D t D e τ = Cross-products of unit vectors: ˆ ˆ ˆ ˆ ˆ ˆ 0 × = × = × = i i j j k k ˆ ˆ ˆ × = i j k ˆ ˆ ˆ × = j k i ˆ ˆ ˆ × = k i j Some potentially useful numbers 2 9 7 2 0 1 N m 9 10 4 10 4 C e o k µ π πε = = × = × T m A 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

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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): ______________ Problem Score Grader 1 (20 points) 2 (5 points) 3 (25 points) 4 (25 points) 5 (25 points) TOTAL 8.02 Exam #3 Solutions Spring 2006

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