Exam1_2005Fall_Solutions

# Exam1_2005Fall_Solutions - Physics 8.02 Exam One Solutions...

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Physics 8.02 Exam One Solutions Fall 2005 23 ˆ 44 oo qq rr πε == Er G r G ˆ points source q observer r r r= from to G inside o closed surface Q κ ε ⋅= ∫∫ EdA G G w points from inside to outside dA G q = FE GG = = 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 =∆ = ∆ 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 = U = 1 2 C V 2 = Q 2 2C 1 parallel CC =+ 2 C 12 series C = + 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 4 3 r 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 / 1 ; Integrals that may be useful a b dr b a = ) / 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 91 0 4C e k × m 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 Avagadro’s number N A = 6.02 x 10 23 mol -1

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MIT PHYSICS DEPARTMENT page 2 Problem 1: Seven Short Questions. Circle your choice for the correct answer. Question A (3 points out of 21 points): An electric dipole, consisting of two equal and opposite point charges at the ends of a insulating rod, sits in the electric field of a stationary positive point charge, as shown. The dipole is free to move. The dipole will 1. rotate clockwise and move to the right 2. rotate clockwise and move to the left 3. rotate clockwise but otherwise not move 4. rotate counterclockwise and move to the right 5. 6. rotate counterclockwise but otherwise not move Question B (3 points out of 21 points): A parallel plate capacitor is filled with a slab of material with dielectric constant κ . The capacitor is connected to a battery and charged to a charge Q = Q 0 . The battery is first removed from the circuit and then the slab of dielectric material is removed from between the plates of the capacitor. Which one of the following statements is true about the charge Q on the capacitor plates and the voltage difference V between the plates? 1. Q increases; V increases 2. Q increases; V stays the same 3. stays the same; V 4. Q stays the same; V stays the same 5. Q decreases; V decreases 6. Q decreases; V stays the same 8.02 Exam #1 Solutions Fall 2005
MIT PHYSICS DEPARTMENT page 3 Question C (3 points out of 21 points): Two charges lie on the x-axis.

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Exam1_2005Fall_Solutions - Physics 8.02 Exam One Solutions...

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