Exam1_2006Spr

Exam1_2006Spr - Physics 8.02 Exam One Please Remove this...

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Physics 8.02 Exam One Spring 2006 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 = = 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 4C air 6 1N m 91 0 e k × Breakdown of E ~ 3 x 10 V/m 8 Speed of light c = 3 x 10 m/s -19 Electron charge e = 1.6 x 10 C Avagadro’s number N A = 6.02 x 10 23 mol -1
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MIT PHYSICS DEPARTMENT page 2 of 14 8.02 Exam One Spring 2006 FAMILY (last) NAME GIVEN (first) NAME Student ID Number Your Section: ___L01 MW 9 am ____L02 MW 11 am ____L03 MW 1 pm ____L04 MW 3 pm ___L05 TR 9 am ____L06 TR 11 am ____L07 TR 1 pm ____L08 TR 3 pm Your Group (e.g. 10A): ______________ Problem Score Grader 1 (20 points) 2 (5 points) 3 (25 points) 4 (25 points) 5 (25 points) TOTAL 8.02 Exam #1 Spring 2006
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MIT PHYSICS DEPARTMENT page 3 of 14 E Φ= ∫∫ EA G Problem 1: Five Short Questions. Circle your choice for the correct answer. Question A (4 points out of 20 points): A negative charge –q sits at the origin. What is the electric flux generated by this charge through a square area (side length 2 a ) centered on the x-axis at x = - a . That is, for the picture at right, calculate: ˆ SS dd A = En GG 1. 0 6 E q ε 2. 0 4 E q 3. 0 E q 4. 0 4 E q 5. 0 6 E q 6. 0 E 7. 0 6 E q 8. 0 4 E q 9. 0
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This test prep 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_2006Spr - Physics 8.02 Exam One Please Remove this...

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