Exam1_2007Fall_Solutions

# Exam1_2007Fall_Solut - Physics 8.02 Exam One Solutions Please Remove this Tear Sheet from Your Exam Fall 2007 r 4 o r 4 o r 3 r ^ r = points from

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Physics 8.02 Exam One Solutions Fall 2007 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 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 2 C 12 series C = + 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 of 12 Problem 1: Five Short Questions. Circle your choice for the correct answer. Question A (4 points out of 20 points): Two charges -4Q and -Q lie on the y-axis, with the -4Q charge above the -Q charge. Below are four possible “grass seed” representations of the electric field of the two charges. Which of these representations is most nearly right for the two charges in this problem? (1) (2) (3) (4) Since charges are the same sign the field lines must “fight” (can’t go from one into other) and the top one is stronger so should “win.” 8.02 Exam #1 Solutions Fall 2007
MIT PHYSICS DEPARTMENT page 3 of 12 Question B (4 points out of 20 points): Two charges lie on the y-axis. A representation of the equipotentials of the electric potential of these two charges is shown at left. The “streaks” in this representation are parallel to the equipotential curves. Which one of the following statements about the sign and magnitude of the charges is true? Compared to the bottom charge, the top charge… 1. has the opposite sign and is smaller in magnitude 2. has the opposite sign and is larger in magnitude 3. has the same sign and is smaller in magnitude 4. has the same sign and is larger in magnitude Equipotentials circle around the two charges individually, showing they are of opposite sign. The bottom one exerts its effects over a larger area and is hence stronger.

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## This homework help 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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Exam1_2007Fall_Solut - Physics 8.02 Exam One Solutions Please Remove this Tear Sheet from Your Exam Fall 2007 r 4 o r 4 o r 3 r ^ r = points from

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