Final_2006Fall

Final_2006Fall - Physics 8.02 Final Exam Equation Sheet Fall 2006 Some(possibly useful Relations Force Laws Current F = q(Eext v Bext J = v dF = I

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Physics 8.02 Final Exam: Equation Sheet Fall 2006 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 closedsurface o Q d κ ε ⋅= ∫∫ Ea G G w 0 closed surface d = Ba G G w B d dt Φ =− through 0 contour oo open surface d d dt µµε Br G G G G v Electromotive Force: ( ) d = +× ⋅ EvB r G G G G v Magnetic and Electric Flux: B open surface d Φ≡ G G E open surface d Φ ≡⋅ G G Electric Potential Difference: moving from to b ab b a a VV V d =−= −⋅ G G many point charges 1 4 N i i oi q V = = rr G G Capacitance: V Q C = 2 2 11 22 Q UC C V = =∆ Resistance: VI R ∆= 2 2 ohmic heating V Pi V i R R =∆ = =
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Inductance: B,self,sgl coil N L I Φ = back dI L dt ε =− 2 1 2 L UL = I Energy Stored in Fields: 2 2 0 1 22 EB o B uE u µ == Energy Flow: 0 1 µ SE G GG B power Pd = ∫∫ Sa G G AC circuits: 0 1 LC ω = L X L = 1/ C X C = R X R = Series : RLC () 2 2 Lc ZRX RXX =+=+− tan / X R φ = 00 VI Z = Magnetic Dipoles: = perpendicular to loop, right-handed with respect to IA I μn n G ± ± τ μB G z zz dB F dz = Waves: 1 c = µε 1 f T = 2 f ω 2 k = πλ cTf k = λ= ω Interference and Diffraction: Double Slit: Constructive : sin , 0, 1, 2, 3, . .. dm m θ= λ = ± ± ± Destructive: 1 sin , 0, 2, 3, . .. 2 dm m ⎛⎞ + λ = ± ± ± ⎜⎟ ⎝⎠ Single Slit: Destructive: sin , 2, 3, . .. an n λ ± ± Some potentially useful numbers 7- 41 0T 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
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8.02 Final Exam Fall 2006 FAMILY (last) NAME GIVEN (first) NAME Student ID Number Your Section: ___L01 MW 10 am ____L02 MW 12 pm Your Group (e.g. 10A): ______________ Problem Score Grader Part 1 (30 points) Problem 1 (15 points) Problem 2 (20 points) Problem 3 (20 points) Problem 4 (15 points) TOTAL
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Part 1: Concept Questions. Circle the correct answer. Question 1. As shown in the diagram, a particle of mass and charge is traveling through a region containing both a constant electric field of magnitude m q E (in the negative -direction) and a constant magnetic field of magnitude y B (in the negative - direction). If the particle moves with constant velocity in the -direction, what is the magnitude of this velocity in terms of z x v E and B ? 1. v = qE / mB 2. v = E / mB 3. v = E / B 4. v = qB / mE 5. v = B / mE 6. v = B / E 7. v = mqEB 8. v = qEB 9. v = EB
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Question 2. A parallel-plate capacitor with circular plates of radius R and separated by a distance d is charged through a straight wire carrying current I , as shown in the figure below: During the time interval that the plates are charging, the Poynting vector associated with the electric and magnetic fields 1.
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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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Final_2006Fall - Physics 8.02 Final Exam Equation Sheet Fall 2006 Some(possibly useful Relations Force Laws Current F = q(Eext v Bext J = v dF = I

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