Exam1_2007Spr

Exam1_2007Spr - Physics 8.02 Equation Sheet Exam One Please...

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Physics 8.02 Equation Sheet Exam One Please Remove this Tear Sheet from Your Exam 23 ˆ 44 oo qq rr πε == Er G G r ˆ points source q observer r r r= from to G many point charges 3 1 () 4 N i i i oi q = =− r G G K G K 2 0 1 ˆ 4 source dq = r G G GG qs o u q = FE r c e enc o closed surface Q ε ⋅= ∫∫ EdA G G w points from inside to outside dA G 0 closed path Ed s G G v b moving from a to b b a a VV V ∆= = s G G UqV ∆=∆ point charge ;()0 4 o q r =∞ = many point charges 1 4 N i i q V = = G K V = 0 1 ; ( ) 0 4 source dq r G = 4 ij all pairs j UU = 2 1 2 ov all space UE = ∫∫∫ o l d V E r V r for spherical symmetry, V = −∇ E G G y V E y z V E z x V E x C = Q V U = 1 2 C V 2 = Q 2 2 C Circumferences, Areas, Volumes: 1) The area of a circle of radius r is Its circumference is π r 2 2 r 2) The surface area of a sphere of radius r is . Its volume is 4 r 2 3 (4 / 3) r 3) The area of the sides of a cylinder of radius r and height is h 2 rh . Its volume is r 2 h Integrals that may be useful dr a b = b a ln( / ) b a dr ba r = 1 r 2 dr a b = 1 a 1 b Some potentially useful numbers k e = 1 4 0 = 9 × 10 9 N m 2 C 2 1
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8.02 Exam One Spring 2007 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 TTh 9 am ____L06 TTh 11 am ____L07 TTh 1 pm ____L08 TTh 3 pm Your Group (e.g. 10A): ______________ Score Grader Section I (25 points) Problem 1 (25 points) Problem 2 (25 points) Problem 3 (25 points) TOTAL 3
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SECTION I In this section you are asked to answer 5 questions, each worth 5 points. You do not have to show your work; in most cases you may simply circle the chosen answer.
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Exam1_2007Spr - Physics 8.02 Equation Sheet Exam One Please...

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