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Exam2_2006Spring

# Exam2_2006Spring - Physics 8.02 Exam Two Spring 2006 Please...

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Physics 8.02 Exam Two Spring 2006 Please Remove this Tear Sheet from Your Exam Some (possibly useful) Relations: inside, free closedsurface o Q d κ ε = ∫∫ E A G G w points from inside to outside d A G moving from to b a b b a a V V V = = − E s G d G 0 d = E s G G v many point charges 1 4 N i i o i q V πε = = r r G G V Q C = C Q V = parallelplate o A C d ε = U = 1 2 C V 2 = Q 2 2C series 1 2 1 1 1 C C C = + parallel 1 2 C C = + C where is the resistivity ρ ρ = E J G G V = i R L R A ρ = 1 R parallel = 1 R 1 + 1 R 2 R series = R 1 + R 2 2 2 ohmic heating V P i V i R R = ∆ = = 2 ˆ 4 o q c r µ π × = << v r B v G G G 2 ˆ r 4 o I d d µ π × = B s r G G ˆ points source observer r from to through contour o d I µ = 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 right-handed with respect to d A sgl loop d d N dt dt ε Φ = − = − ∫∫ E ds B dA G G v ext q = × F v B G G G ext d I d = × F s B G G G 2 cent. F mv = r = perpendicular to loop, right-handed with respect to I A I μ n n G ± ± = × τ μ B G G G z z z dB F dz µ = 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 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 p. 1 of 11 8.02 Exam Two Spring 2006 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 #2 Spring 2006