Exam2_2009Spr

# Exam2_2009Spr - Physics 8.02 Exam Two Spring 2009 Please...

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Physics 8.02 Exam Two Spring 2009 Please Remove this Tear Sheet from Your Exam Some (possibly useful) Relations: inside closedsurface o d κ Q ε ⋅= ∫∫ EA w G G points from inside to outside d A G b d G G moving from to ab b a a VV V Δ= = Es 0 d −⋅ = G G v many point charges 1 4 i i oi V πε = = rr GG N q V C Δ = Q C V = Δ Q parallelplate o C d A = U = 1 2 C Δ V 2 = 2 Q 2 C series 1 2 CC =+ 11 1 C parallel 1 2 where ρρ = EJ C is the resistivity Δ 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 Pi V i R R Δ =Δ = = 2 ˆ 4 o q c r μ π × = << vr Bv G G G 2 ˆ 4 o I d d r × = sr B G G ˆ points source observer rf r o mt o through contour o dI Bs G G v where I through is the current flowing through any open surface bounded by the contour: through open surface I d JA G G = d s right-handed with respect to d A sgl loop d d N dt dt Φ = Ed s BdA v ext q Fv B G G G ext d Fs B G 2 cent. Fm v r = = perpendicular to loop, right-handed with respect to IA I μ G nn ± ± = × τ μ B G G G z zz dB F dz = ˆˆ ˆˆˆˆ 0 Cross-products of unit vectors: ×=×= × = ii jjkk ˆˆ ˆ k ˆ × = i j × = ki ˆ j × = j Some potentially useful numbers 2 97 2 0 1N m T m 91 0 4 1 0 4C A eo k μπ == × = × 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
MIT PHYSICS DEPARTMENT 8.02 Exam Two Spring 2009 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

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MIT PHYSICS DEPARTMENT p. 2 of 13 8.02 Exam #2 Spring 2009
MIT PHYSICS DEPARTMENT p. 3 of 13 Problem 1: Five Short Questions. Circle your choice for the correct answer. Question A (4 points out of 20 points): Consider a charged circular loop of radius R and total charge q glued down to the loop. Suppose the loop is rotating about the axis normal to it and going through its center and that it makes N complete revolutions in a time T. During this time the loop acts as a magnetic dipole with magnetic dipole moment μ given by 1) 2 TqR N = 2) 4 TqR = 3) 2 qR T μπ = 4) 2 Nq R T = 5) 2 2 Nq R T = 6) 2 qR π = Question B (4 points out of 20 points): Consider two identical circular loops of radius a , separated by a distance a , with the second (right hand) coil rotated slightly clockwise relative to the first when looking from above: Top view Side view A large current is suddenly injected into the left hand loop. What does the right hand loop feel due to this?

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## This note was uploaded on 02/27/2011 for the course PHYSICS 8 taught by Professor Dourmashkin during the Fall '10 term at MIT.

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Exam2_2009Spr - Physics 8.02 Exam Two Spring 2009 Please...

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