Exam3_2007Spr

# Exam3_2007Spr - Physics 8.02 Exam Three: Equation Sheet...

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Physics 8.02 Exam Three: Equation Sheet Some (possibly useful) Relations: Force Laws: () ext ext q =+ × FEv B GG G G ext dI d Fs B G G G Current: ρ = Jv G G open surface I d = Ja G G Source equations: 2 1 ˆ 4 o dq d r πε = Er G 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 Maxwell’s Equations: inside o closed surface Q d ε ⋅= ∫∫ Ea G G w 0 closed surface d = Ba G G w contour open surface d dd dt v through 0 contour oo open surface d d dt μμ Br G G G G v Electromotive Force: ( ) d = +× ⋅ EvB r G G G G v Electric Potential Difference: moving from to b ab b a a VV V d Δ =−= −⋅ G G many point charges 1 4 N i i oi q V = = rr G G Capacitance: V Q C Δ = 2 2 11 22 Q UC C == Δ V Resistance: VI R Δ= 2 2 ohmic heating V PI V I R R Δ =Δ = = Inductance: B,self,sgl coil N L I Φ = back dI L dt =− 2 1 2 L UL = I 1

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Energy Stored in Fields: 2 0 1 2 E uE ε = ; 2 0 2 B B u μ = Energy Flow: 0 1 SE G GG B ; power surface Pd = ∫∫ Sa G G AC Circuits: 0 1 LC ω = ; L X L = ; 1 C X C = ; R X R = Series RLC : () 2 22 2 Lc ZR X RX X =+ ; tan ( )/ LC X XR φ = ; 00 VI Z = Magnetic Dipoles: = perpendicular to loop, right-handed with respect to IA I μ nn G ± ± τ μ B G z zz dB F dz = Waves: 1 c = με 1 f T = 2 f ω 2 k = πλ cT f k = λ= λ = ω Some potentially useful numbers: 7- 41 0 T m A o μπ 1 92 0 1 91 0Nm C 4 e k πε - 2 = ⋅ ⋅ 8- 31 0ms c 1 19 1.6 10 C e 2
8.02 Exam Three Spring 2007 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 TTh 9 am ____L06 TTh 11 am ____L07 TTh 1 pm ____L08 TTh 3 pm Your Group (e.g. 10A): ______________ Score Grader Part I (25 points) Problem 1 (25 points) Problem 2 (25 points) Problem 3 (25 points) TOTAL 3

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PART I (25 points) Question A (5 points). A parallel-plate capacitor with circular plates of radius R and separated by a distance
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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_2007Spr - Physics 8.02 Exam Three: Equation Sheet...

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