Exam1_2009Spr - Physics 8.02 Exam One Exam Please Remove...

Info icon This preview shows pages 1–7. Sign up to view the full content.

View Full Document Right Arrow Icon
Physics 8.02 Exam One Exam Spring 2009 Please Remove this Tear Sheet from Your Exam 2 3 ˆ 4 4 o o q q r r πε πε = = E r G r G ˆ points source q observer r r r = from to G inside-free o closed surface Q κ ε = ∫∫ E dA G G w points from inside to outside dA G q = F E G G = = 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 W U q V = Δ = Δ point charge 4 o q V r πε = = pairs all j i o j i q q U r r G G πε 4 2 1 2 o v U E ε = ∫∫∫ x ol dV 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 C C = + Circumferences, Areas, Volumes: Circle of radius r : Area = π r 2 Circumference = 2 π r Sphere of radius r Surface Area = 4 π r 2 Volume = 3 4 3 r π Cylinder of radius r and height h Side surface area = 2 π r h End cap surface area = 2 π r 2 Volume = π 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 1 N 9 10 4 C e k πε = = × m Breakdown of air E ~ 3 x 10 6 V/m 2 C 1 2 1 2 series C C C C C = + Speed of light c = 3 x 10 8 m/s Electron charge e = 1.6 x 10 -19 C Avogadro’s number N A = 6.02 x 10 23 mol -1
Image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Image of page 2