Exam1_2009Spr_Solutions

# Exam1_2009Spr_Solutions - Physics 8.02 Exam One Exam Please...

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Physics 8.02 Exam One Exam Spring 2009 Please Remove this Tear Sheet from Your Exam 23 ˆ 44 oo qq rr πε == Er G r G ˆ points source q observer r r r= from to G inside-free o closed surface Q κ ε ⋅= ∫∫ EdA G G w points from inside to outside dA G q = FE GG = = Δ b a a b b to a from moving V V V s d E G G 0 = path closed s d E G G WU q V =Δ = Δ point charge 4 o q V r = = pairs all j i o j i q q U r r G G 4 2 1 2 ov UE ⎡⎤ = ⎢⎥ ⎣⎦ ∫∫∫ x o l d V E x = - V x , E y = - V y , E z = - V z r V E r =− for spherical symmetry Q C V = Δ U = 1 2 C Δ V 2 = Q 2 2C 1 parallel CC =+ Circumferences, Areas, Volumes: Circle of radius r : Area = π r 2 Circumference = 2 π r Sphere of radius r Surface Area = 4 r 2 Volume = 3 3 r 4 Cylinder of radius r and height h Side surface area = 2 r h End cap surface area = 2 r 2 Volume = r 2 h Definition of trig functions sin is opposite/hypotenuse; cos is adjacent/hypotenuse; tangent is opposite over adjacent; Properties of 30, 45, and 60 degrees ( π /6, π /4, and π /3 radians) : sin( π /6) = cos( π /3) = 1/2, sin( π /3) = cos( π /6) = 2 / 3; sin( π /4) = cos( π /4) = 2 / a b dr b a = 1 ; Integrals that may be useful 2 C 12 series C = + ) / ln( 1 a b dr r b a = = b a dr r b a 1 1 1 2 Some potentially useful numbers 2 9 2 0 1N m 91 0 4C e k × Breakdown of air E ~ 3 x 10 6 V/m Speed of light c = 3 x 10 8 m/s 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 page 2 of 16 Problem 1: Five Short Questions. Circle your choice for the correct answer. Question A (3 points out of 15 points): A positive charge is brought near a neutral, spherical, conducting shell, causing the shell to generate an electric field with the grass seed representation at right. The combination of this induced electric field and the field of the charge itself combine together to make a potential landscape best represented in which of the figures below (with streaks parallel to equipotentials)? (1) (2) (4) The positive charge is to the right of the shell (field is stronger there and diverges from there). So equipotentials surround it, as pictured. 8.02 Exam #1 Solutions Spring 2009
MIT PHYSICS DEPARTMENT page 3 of 16 Question B (3 points out of 15 points): Two pairs of hollow, spherical conducting shells are connected with wires and switches. The system AB (where A and B are far apart) is extremely far from CD. In both systems the large shells have four times the radius of the small shells. Before the switches are closed each pair has a charge of +20 nC on the small shell (A,C) and +60 nC on the large shell (B,D) B C (+60 nC) A (+20 nC) (+20 nC) D (+60 nC) When the switches are closed, charge is free to flow along the conducting wires connecting the spherical shells. What is the rank of the magnitude of the charge on each of the shells after the switches have been closed?

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## This note was uploaded on 02/27/2011 for the course PHYSICS 8 taught by Professor Dourmashkin during the Fall '10 term at MIT.

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Exam1_2009Spr_Solutions - Physics 8.02 Exam One Exam Please...

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