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Exam3_2009Spr_Solutions

# Exam3_2009Spr_Solutions - Physics 8.02 Exam Three Solutions...

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Physics 8.02 Exam Three Solutions Spring 2009 Please Remove this Tear Sheet from Your Exam Some (possibly useful) Relations: 2 ˆ 4 o d r πε = E r 1 dq G inside closedsurface o d Q ε = ∫∫ E A w G G points from inside to outside d A G total dt dt ε = − = − ∫∫ E ds B dA v d d Φ G G G G b d G G moving from to a b b a a V V V Δ = = − E s 2 4 o c r ˆ q μ π = < × v r B v G G < G 2 4 o d r ˆ I d μ π × = B s r G G ˆ where points source observer r from to d = B A 0 closed surface ∫∫ w G G through 0 contour E o d I dt μ ε d Φ + v = B s G G 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 1 2 2 0 2 E B o B u E u ε μ = = ( ) G G G G G G G ext q = + × F E v B ext d I d = × F s B 2 cent. F mv r = IA = μ n G ± = × τ μ B G G G U = − μ B G G V IR Δ = L R A ρ = 2 2 ohmic heating V P I V I R R Δ = Δ = = Q C V = 2 2 1 2 2 Q U C V C = Δ = Δ B,self,sgl coil back N dI L L Φ I dt ε = = − 2 1 2 L U LI = 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 2 slit interference: sin Constructive 1 slit diffraction: sin Destructive d m a m Interference θ λ θ λ = = Far field: sin y L θ ˆ ˆ ˆ ˆ ˆ ˆ 0 Cross-products of unit vectors: × = × = × = i i j j k k ˆ ˆ ˆ k ˆ ˆ ˆ × = i j × = k i ˆ ˆ ˆ j × = k i j Some potentially useful numbers 2 9 7 2 0 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 (violet 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 Calories 1 cal = 10 -3 Cal = 4.184 J

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