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### Final_2006Fall_Solutions

Course: 8 8.02, Fall 2006
School: MIT
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Word Count: 323

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8.02 Final Physics Exam: Equation Sheet Fall 2006 Some (possibly useful) Relations: Force Laws: Current: F = q(Eext + v Bext ) J = v dF = I d s Bext I= open surface J da 1 dq ^ Source equations: dE = 4 r 2 r o dB = B= ^ o q v r 2 4 r v &lt;&lt; c ^ o I d s r 2 4 r ^ r points from source to observer Qinside Maxwell's Equations: closed surface E da = o closed surface B da =...

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8.02 Final Physics Exam: Equation Sheet Fall 2006 Some (possibly useful) Relations: Force Laws: Current: F = q(Eext + v Bext ) J = v dF = I d s Bext I= open surface J da 1 dq ^ Source equations: dE = 4 r 2 r o dB = B= ^ o q v r 2 4 r v << c ^ o I d s r 2 4 r ^ r points from source to observer Qinside Maxwell's Equations: closed surface E da = o closed surface B da = 0 = - dB dt contour B dr =o I through + o 0 d E da dt open surface Electromotive Force: = ( E + v B ) dr open surface Magnetic and Electric Flux: B B da E open surface E da Electric Potential Difference: Vmoving from a to b = Vb - Va = - E dr a b Vmany point charges = i =1 N qi 4 o r - ri 1 Q2 1 = C V 2 2 C 2 V 2 = i V = i R = R 2 Capacitance: C= Q V U= Resistance: V = IR Pohmic heating Inductance: L= N B,self,sgl coil I back = -L dI dt U L = 1 LI 2 2 1 2 Energy Stored in Fields: uE = 2 0 E 1 S = EB Energy Flow: = 0 Ppower S da uB = B2 2 o AC circuits: 0 = LC 1 X L = L X C = 1/ C 2 XR = R tan = X / R Series RLC : Z = R 2 + X 2 = R 2 + ( X L - X c ) Magnetic Dipoles: =I A n V0 = I 0 Z n perpendicular to loop, right-handed with respect to I = B Fz = z dBz dz Waves: c= 1 00 f =1 T = 2f k = 2 c = T = f = k Interference and Diffraction: Double Slit: Constructive: d sin = m, m = 0, 1, 2, 3, ... 1 Destructive: d sin = m + , m = 0, 1, 2, 3, ... 2 Single Slit: Destructive: a sin = n , n = 1, 2, 3, ... Some potentially useful numbers o = 4 10-7 T m A -1 c = 3 108 m s -1 ke = 1 4 0 = 9 109 N m 2 C-2 e = 1.6 10-19 C 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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