Final_2006Spring

# Final_2006Spring - Physics 8.02 Final Exam Please Remove...

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Physics 8.02 Final Exam Spring 2006 Please Remove this Tear Sheet from Your Exam Some (possibly useful) Relations: 2 1 ˆ 4 o dq d r πε = Er G ; ˆ . dq obs r r r= from to G free, inside closedsurface o Q d κ ε ⋅= ∫∫ EA G G w points from inside to outside d A G moving from to b ab b a a VV V ∆= = Es G G d WU q V =∆ = ∆ E x = - V x , E y = - V y , E z = - V z sgl loop d d N dt dt Φ = Ed s BdA G GG G v 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 where points source observer rf r o mt o 0 closed surface d BA G G w through 0 contour E o d dI dt µε Φ ⎛⎞ + ⎜⎟ ⎝⎠ 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 is right-handed with respect to d A 2 2 0 1 2 EB o B uE u 2 == () ext q =+ × FE v B GGG G ext d Fs B G G G 2 cent. Fm v = r IA = μn G ± τ μB G z zz dB F dz = VI R 2 2 ohmic heating V PI V I R R =∆ = = Q C V = 2 2 1 2 2 Q UC V C =∆= 1 C R CX C τ ω = = B,self,sgl coil back N dI LL I dt Φ 2 1 2 L UL = I / L L RX L = = Series RLC: 2 22 2 00 tan LC ZRX RXX XR V IR ϕ =+=+− 2 fT k ω =π=π =πλ 1 2 cTf k =λ =ω = µε 0l i g h t 0 ˆˆ ˆ EvB = ×= EB p absorb reflect 0 12 ; SS PP cc = = µ SE B G G G Cross-products of unit vectors: ˆˆ ˆˆˆˆ 0 ×=×= × = ii jjkk ˆ × = ijk ˆ × = j ki ˆ × = ki j Some potentially useful numbers 2 97 2 0 1N m 91 0 4 1 0 4C eo k µπ × = × 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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8.02 Final Exam Spring 2006 FAMILY (last) NAME GIVEN (first) NAME Student ID Number ___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 (40 points) 2 (20 points) 3 (10 points) 4 (20 points) 5 (20 points) 6 (30 points) 7 (60 points) TOTAL
MIT Department Of Physics p. 1 of 20 Problem 1: Eight Short Questions. Circle your choice for the correct answer Each problem is worth 5 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 (5 points out of 40 points): In lab 1 you fixed the potential difference between two plates and measured equipotential lines from which you determined electric field lines and approximate charge distributions. You are given a layout with a conducting plate and conducting circle, as pictured at left, with the circle held at +5 V relative to the plate. Identify the most accurate representation of the equipotential lines and the electric field lines: Equipotential Lines: #__________ Electric Field Lines: #___________ Question B (5 points out of 40 points): In the second lab you worked with a Faraday pail, two nested conducting cylinders as pictured at left (in the lab the shaded regions were thin). You held the outer cylinder at ground (i.e. at the

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Final_2006Spring - Physics 8.02 Final Exam Please Remove...

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