Exam1_2005Spr

Exam1_2005Spr - Physics 8.02 F= Exam One C= Q V Spring 2005...

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Physics 8.02 Exam One Spring 2005 F = 1 4 πε o q 1 q 2 r 2 23 ˆ 44 oo qq rr == Er G r G ˆ points source q observer r r r= from to G 2 0 1 ˆ 4 V dq r = G inside o closed surface Q κ ε ⋅= ∫∫ EdA G G w outside to inside from points A d G = = 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 point charge 4 o q V r = many point charges 1 4 N i i oi q V = = G K = 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: 1) The area of a circle of radius r is π r 2 Its circumference is 2 π r 2) The surface area of a sphere of radius r is 4 r 2 Its volume is 3 4 3 r 3) The area of the sides of a cylinder of radius r and height h is 2 r h Its volume is 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
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MIT PHYSICS DEPARTMENT ` page 2 8.02 Exam One Spring 2005 FAMILY (last) NAME GIVEN (first) NAME Student ID Number Your Section: ___L01 MW 10 am ____L02 MW 12 noon ____L03 MW 2 pm ___L04 TTh 10 am ____L05 TTh 12 noon ____L06 TTh 2 pm Your Group (e.g. 10A): ______________ Problem Score Grader 1 (25 points) 2 (25 points) 3 (25 points) 4 (25 points) TOTAL
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MIT PHYSICS DEPARTMENT ` page 3 Problem 1: Five Short Questions. Circle your choice for the correct answer. Question A (5 points out of 25 points): The field line to the right is a field line of the vector field a) ˆˆ ( , ) sin( ) x yx =+ Fi G j b) (, ) c o s () x =− G j c) s i n x G j d) c o s x G j 2 egative b) ace charge at O2 is negative ositive 2 2 e) None of these I1 I2 O1 O2 Question B (5 points out of 25 points): Two hollow conducting shells are concentric.
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Exam1_2005Spr - Physics 8.02 F= Exam One C= Q V Spring 2005...

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