Exam3_2005Fall_ Solutions

# Exam3_2005Fall_ Solutions - Physics 8.02 Exam Three Mashup...

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Physics 8.02 Exam Three Mashup Solutions Fall 2005 Please Remove this Tear Sheet from Your Exam Some (possibly useful) Relations: 2 1 ˆ 4 o dq d r πε = Er G free, inside closedsurface o Q d κ ε ⋅= ∫∫ EA G G w points from inside to outside d A G sgl loop d d N dt dt Φ = Ed s BdA v moving from to b ab b a a VV V ∆= = Es G G d 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 22 EB o B uE u == () ext q =+ × FE v B GGG G ext d Fs B GG G 2 cent. Fm v = r IA = μn G ± τ μ B G z zz dB F dz = VI R L R A ρ = 2 2 ohmic heating V PI V I R R =∆ = = Q C V = parallelplate o A C d = 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 LR X L = = Series RLC: 2 2 tan LC ZRX RXX XR ϕ =+=+− = 2 fT k ω =π=π =πλ 1 2 00 cTf k =λ =ω = µε ˆˆ ˆ Ec B = ×= EB p absorb reflect 0 12 ; SS PP cc = = µ SE B G G G If the function satisfies the equation Dt dD dt t =− , then / t o De = Cross-products of unit vectors: ˆˆ ˆˆˆˆ 0 ×=×= × = ii jjkk ˆ × = i j k ˆ × = j ki ˆ × = 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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MIT PHYSICS DEPARTMENT p. 1 of 11 Problem 1: Five Short Questions. Circle your choice for the correct answer Each problem is worth 4 points for the correct answer, 2 points for a mostly correct answer (at our discretion) or 1 point for admitting that you don’t know how to do it. Unanswered or incorrectly answered problems will earn a 0. Question A (4 points out of 20 points): A circuit consists of a battery with emf V , an inductor with inductance L , a capacitor with capacitance C , and three resistors, each with resistance R , as shown in the sketch. The capacitor is initially uncharged and there is no current flowing anywhere in the circuit. At t = 0 we will close the switch S (as pictured below), and after a very long time T we open it again. We wish to compare the current at three different times: t = 0 + , right after the switch is closed; t = T - , a long time after the switch has been closed (just before it is opened again); and t = T + , right after the switch has been opened after waiting a long time. Which of the following is correct? 1) 0 () 11 1 22 0; ; 33 VV ii T i T 0 R R +− == + = 2) 4 ; 0 T i T R R +−+ = 3) 2 () () 2 0; 0 ; T i T R R + = 4) 0 2 00 ; ; Ti T R R + = 5) 0 3 ; ; 2 T i T R R + == = 6) 0 ( ) ( )( ) 33 3 ; 0 ; T i T 0 = 7) 1 I don’t know (this answer is worth 1 point) Question B (4 points out of 20 points): Consider a coil of radius a and N turns. An order of magnitude estimate of its inductance is: 1. 0 2 o Na µ 2. 2 o Na 3. 0 / o Na 4. 0 2 / o 5. 0

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## This note was uploaded on 04/07/2008 for the course 8 8.02 taught by Professor Hudson during the Fall '07 term at MIT.

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Exam3_2005Fall_ Solutions - Physics 8.02 Exam Three Mashup...

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