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Final_2004Fall

# Final_2004Fall - Physics 8.02 Final Exam o V = IR Fall 2004...

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Physics 8.02 Final Exam Fall 2004 enclosed o closed surface Q d ε ⋅= ∫∫ EA G G w closed open path surface d dd dt Es BA G GG G v 0 closed surface d G G w E thru o E open surface d dI dt where d µε Φ ⎛⎞ + ⎜⎟ ⎝⎠ Φ= o Bs G G G G v 2 0 1 2 elec uE 2 0 1 2 mag uB = µ 0 2 ˆ 4 wire Id r µ π × = sr B G G q qq =+× FEv G B G B d Fs G 0 1 ˆ 4 2 dq r πε = dE r G 2 0 1 ˆ 4 V dq r = Er G 2 1 P 21 P V(P ) V(P ) d −= G G 0 1 4 dq dV r = 0 1 4 dq V r = E x = - V x , E y = - V y , E z = - V z VI R ∆= 22 Joule Heating PI R V == / R QCV = 2 2 capacitor 1 Q UC V C =∆= self field self one turn Nd L I G G 2 inductor 1 2 UL = I 0 1 LC = ω 8 00 1 31 0 / cm × s 1 f T = f T ω= π = π 2 k = πλ cTf k = λ= ω 0 1 = × µ SE G B G G DOUBLE SLIT: constructive: sin , 0, 1, 2, 3, . .. dm m θ = ±± ± destructive: 1 sin , 0, 2, 3, . .. 2 dm m θ= + λ = ± ± ± SINGLE SLIT: destructive: sin , 2, 3, . .. an n θ = ±± ± Areas, Volumes, etc.: 1) The area of a circle of radius r is π r 2 Its circumference is 2 r 2) The surface area of a sphere of radius r is 4 r 2 . Its volume is 3 3 r 4 3) The lateral area of a cylinder of radius r and height h is 2 r h. Its volume is r 2 h USEFUL INTEGRALS: d c dx d c =− () 1 2 d c rdr d c 1 ln d c d dr rc ⎡⎤ = ⎢⎥ ⎣⎦ 2 11 d c dr 1 d ⎤⎛ ⎦⎝ USEFUL APPROXIMATIONS: ln(1 ) for <<1 +ε≈ε ε 1 (1 ) for <<1 ) =+ ε ε −ε

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MIT PHYSICS DEPARTMENT ` page 1 8.02 Final Exam Fall 2004 FAMILY (last) NAME GIVEN (first) NAME Student ID Number Your Section (check one): ___TTh 10 am ____TTh 12 noon Your Group (e.g. 10A): _________ Problem Score Grader 1 (35 points) 2 (30 points) 3 (30 points) 4 (30 points) 5 (30 points) 6 (35 points) TOTAL
MIT PHYSICS DEPARTMENT ` page 2 Problem 1: Seven Conceptual Questions. Circle your choice for the correct answer. Question A (5 points out of 190 total points): Two charged particles travel along the negative x axis in the positive x direction, each with speed v , and enter the magnetic field at the origin O . The magnetic field for x > 0 is constant, uniform and points out of the page. The two particles have the same charge q , but have different masses, and . In the magnetic field, their trajectories both curve in the same direction, but describe semi-circles with different radii. The radius of the semi-circle traced out by particle 2 is bigger than the radius of the semi-circle traced out by particle 1. Which of the following is correct? 1 m 2 m a) and m 0 q > 1 > m 2 b) and m 0 q > 1 < m 2 c) and m 0 q < 1 > m 2 d) and m 0 q < 1 < m 2 Question B (5 points out of 190 total points): A series RLC circuit is connected to a battery with (constant) emf V o . The capacitor is initially uncharged and the switch connecting the battery to the circuit is closed at t = 0 . What is the value of the current immediately after the switch is closed and a very long time after the switch is closed?

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Final_2004Fall - Physics 8.02 Final Exam o V = IR Fall 2004...

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